UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT
INVESTMENT COMPANIES

Investment Company Act file number 811-4103

Seligman High Income Fund Series
(Exact name of Registrant as specified in charter)

100 Park Avenue
New York, New York 10017
(Address of principal executive offices) (Zip code)

Lawrence P. Vogel
100 Park Avenue
New York, New York 10017
(Name and address of agent for service)

Registrant's telephone number, including area code:    (212) 850-1864

Date of fiscal year end:      12/31

Date of reporting period:      06/30/04

FORM N-CSR

ITEM 1. REPORTS TO STOCKHOLDERS.

SELIGMAN HIGH INCOME FUND SERIES:
Semi-Annual Report June 30, 2004

Seligman

140 Years of Investment Experience

J. & W. Seligman & Co. Incorporated is a firm with a long tradition of investment expertise, offering a broad array of investment choices to help today’s investors seek their long-term financial goals.

Established in 1864, Seligman has a history of providing financial services marked not by fanfare, but rather by a quiet and firm adherence to financial prudence. While the world has changed dramatically in the 140 years since Seligman first opened its doors, the firm has continued to offer its clients high-quality investment solutions through changing times.

In the late 19th century, as the country grew, Seligman helped finance the westward expansion of the railroads, the construction of the Panama Canal, and the launching of urban transit systems. In the early 20th century, the firm helped fund the growing capital needs of new industries, including the nascent automobile and steel industries.

With the formation of Tri-Continental Corporation in 1929 — today, one of the nation’s largest diversified publicly-traded closed-end equity investment companies — Seligman began shifting its emphasis to investment management. In 1930, Seligman established what would be the first in an impressive lineup of mutual funds.

Seligman is proud of its distinctive past and of the traditional values that continue to shape the firm’s business decisions and investment judgment. While much has changed over the years, the firm’s commitment to providing prudent investment management that seeks to build wealth for clients over time is an enduring value that will continue to guide Seligman.

Table of Contents
To The Shareholders	1
Performance Overview	2
Portfolio of Investments	4
Statement of Assets and Liabilities	6
Statement of Operations	7
Statements of Changes in Net Assets	8
Notes to Financial Statements	9
Financial Highlights	15
Trustees and Executive Officers	20
For More Information	back cover

To The Shareholders

Your mid-year shareholder report for Seligman U.S. Government Securities Series follows this letter. This report contains the Fund’s investment results and financial statements, including a portfolio of investments.

For the six months ended June 30, 2004, the Fund posted a total return of –0.82% based on the net asset value of Class A shares. During the same time period, the Fund’s peers, as measured by the Lipper General US Government Bond Funds Average, returned –0.32%, and the Lehman Brothers Government Bond Index returned –0.13%.

We thank you for your continued support of Seligman U.S. Government Securities Series and look forward to serving your investment needs for many years to come.

By Order of the Trustees,

William C. Morris

Chairman

Brian T. Zino

President

August 13, 2004

1

Performance Overview  (unaudited)

Investment Results

Total Returns
For the Six Months Ended June 30, 2004
				Average Annual
	Six Months*			One Year			Five Years			Ten Years			Class B Since Inception 4/22/96			Class C Since Inception 5/27/99			Class R Since Inception 4/30/03
Class A**
With Sales Charge		(5.52	)%		(7.02	)%		4.49	%		5.23	%		n/a			n/a			n/a
Without Sales Charge		(0.82	)		(2.39	)		5.50			5.73			n/a			n/a			n/a
Class B**
With CDSC††		(6.07	)		(7.76	)		4.41			n/a			n/a			n/a			n/a
Without CDSC		(1.18	)		(3.00			4.74			n/a			4.62	%		n/a			n/a
Class C**
With Sales Charge and CDSC†††		(3.23	)		(5.10	)		4.49			n/a			n/a			4.24	%		n/a
Without Sales Charge and CDSC		(1.32	)		(3.13	)		4.71			n/a			n/a			4.46			n/a
Class D**
With 1% CDSC		(2.17	)		(4.08	)		n/a			n/a			n/a			n/a			n/a
Without CDSC		(1.19	)		(3.13	)		4.71			4.90			n/a			n/a			n/a
Class R**
With 1% CDSC		(1.74	)		(3.31	)		n/a			n/a			n/a			n/a			n/a
Without CDSC		(0.76	)		(2.35	)		n/a			n/a			n/a			n/a			(0.70	)%
Lehman Brothers Government Bond Index†		(0.13	)		(1.36	)		6.72			7.16			6.72			6.55	‡		0.58
Lipper General US Government Bond Funds Average†		(0.32	)		(1.42	)		5.71			6.17			5.70			5.45			(0.17	)

Net Asset Value Per share										Dividend Per Share and Yield Information
	6/30/04			12/31/03			6/30/03			For the Six Months Ended June 30, 2004
										Dividends Paidø			SEC Yieldsøø
Class A		$	7.07		$	7.23		$	7.44		$	0.102		6.68	%
Class B			7.09			7.25			7.45			0.075		6.27
Class C			7.08			7.25			7.45			0.075		6.20
Class D			7.08			7.24			7.45			0.075		6.27
Class R			7.08			7.23			7.44			0.096		7.54

Weighted Average Maturity          20 years

(Continued on page 3.)

2

Performance Overview  (unaudited)

(Continued from page 2.)

The rates of return will vary and the principal value of an investment will fluctuate so that shares, if redeemed, may be worth more or less than their original cost. Performance data quoted does not reflect the deduction of taxes that an investor may pay on Fund distributions or the redemption of Fund shares. Performance data quoted represents past performance. Past performance is not indicative of future investment results. Current performance may be higher or lower than the performance shown above. With respect to Class I shares, the Manager voluntarily reimbursed certain expenses in 2002 and 2001. Absent reimbursement, returns that include these periods would be lower.

*	Returns for periods of less than one year are not annualized.
**	Return figures reflect any change in price per share and assume the reinvestment of all distributions. Returns for Class A shares are calculated with and without the effect of the initial 4.75% maximum sales charge. Returns for Class B shares are calculated with and without the effect of the maximum 5% contingent deferred sales charge (“CDSC”), charged on redemptions made within one year of purchase, declining to 1% in the sixth year and 0% thereafter. Returns for Class C shares are calculated with and without the effect of the initial 1% maximum sales charge and the 1% CDSC that is charged on redemptions made within 18 months of purchase. Returns for Class D and R shares are calculated with and without the effect of the 1% CDSC, charged on certain redemptions made within one year of purchase.
†	The Lehman Brothers Government Bond Index and the Lipper General US Government Bond Funds Average are unmanaged benchmarks that assume reinvestment of dividends and exclude the effect of taxes and sales charges. The Lehman Brothers Government Bond Index also excludes the effect of fees. Investors cannot invest directly in an average or an index.
††	The CDSC is 5% for periods of one year or less, and 2% for the five-year period.
†††	The CDSC is 1% for periods up to 18 months.
‡	From May 28, 1999.
ø	Represents per share amount paid or declared for the six months ended June 30, 2004.
øø	Current yield, representing the annualized yield for the 30-day period ended June 30, 2004, has been computed in accordance with SEC regulations and will vary.

An investment in the Fund is not insured by the Federal Deposit Insurance Corporation or any other government agency.

3

Portfolio of Investments (unaudited)
June 30, 2004

	Principal Amount		Value
US Government and Government Agency Obligations 87.0% US Full Faith and Credit Obligations 86.7%
US Treasury Notes:
4.375%, due 5/15/2007	$	1,400,000	$	1,447,470
3.125%, due 4/15/2009		5,000,000		4,859,575
Government National Mortgage Association (“Ginnie Mae”)      Obligations, Mortgage Pass-through Certificates:*
5%, due 4/16/2018		4,680,805		4,732,648
4.5%, due 10/20/2024		5,223,291		5,102,506
4.25%, due 7/20/2027		6,000,709		5,907,589
4.5%, due 8/20/2028		2,822,199		2,841,484
4%, due 12/16/2028		4,519,268		4,485,619
6%, due 5/20/2029		234,827		237,520
5%, due 5/20/2029		17,535,588		17,636,197
4.75%, due 1/16/2032		4,661,626		4,619,390
5.5%, due 2/20/2033		4,270,013		4,306,486
3.625%, due 4/16/2033		5,447,122		5,096,252
4.25%, due 6/20/2033		7,428,192		7,067,746
4.5%, due 5/20/2034		13,994,677		14,136,807
Guaranteed Trade Trust      7.02%, due 9/1/2004*		133,333		134,681
Small Business Administration      5.199%, due 8/1/2012		1,870,603		1,882,978
US Government Gtd. Title XI (Vessel Management)      6.75% due 7/15/2025		1,720,000		1,890,067
US Trade Funding      4.26% due 11/15/2014		1,909,749		1,883,912
Veteran Affairs Vendee Mortgage Trust*      7.5% due 12/15/2006		880,200		904,444
Total US Full Faith and Credit Obligations (Cost $90,541,363)				89,173,371
Agency Obligations 0.3%
Federal Home Loan Mortgage (“Freddie Mac”):*      6%, due 11/1/2010 (Cost $292,719)		297,520		313,260
Total US Government and Government Agency Obligations      (Cost $90,834,082)				89,486,631

(Continued on page 5.)

4

Portfolio of Investments  (unaudited)
June 30, 2004

	Principal Amount		Value
Short-Term Investments 13.3%
Repurchase agreement, State Street Bank & Trust 1.18%, dated      6/30/2003 maturing 7/1/2004 in the amount of $2,505,082,      collateralized by $2,095,000 US Treasury Notes 10.375%, due      11/15/2012, with a fair market value of $2,582,087	$	2,505,000	$	2,505,000
US Treasury Bill due 7/8/2004		11,132,857		11,132,857
Total Short-Term Investments (Cost $13,637,857)				13,637,857
Total Investments (Cost $104,471,939) 100.3%				103,124,488
Other Asset Less Liabilities (0.3)%				(321,645	)
Net Assets 100.0%			$	102,802,843

*	Investments in mortgage-backed securities are subject to principal paydowns. As a result of prepayments from refinanc ing or satisfaction of the underlying mortgage instruments, the average life may be less than the original maturity. This in turn may impact the ultimate yield realized from these securities.
See Notes to Financial Statements.
5

Statement of Assets and Liabilities (unaudited)
June 30, 2004

Assets:
Investments, at value:
US Government and Government agency obligations (cost $90,834,082)	$	89,486,631
Short-term investments (cost $13,637,857)		13,637,857
Total investments (cost $104,471,939)		103,124,488
Cash		304,598
Receivable for interest		404,945
Expenses prepaid to shareholder service agent		34,960
Receivable for shares of Beneficial Interest sold		24,570
Total Assets		103,893,561
Liabilities:
Payable for shares of Beneficial Interest repurchased		811,249
Dividends payable		96,506
Distribution and service fees payable		55,188
Management fee payable		42,850
Accrued expenses and other		84,925
Total Liabilities		1,090,718
Net Assets	$	102,802,843
Composition of Net Assets:
Shares of Beneficial Interest, at par ($0.001 par value; unlimited shares authorized; 14,523,842 shares outstanding):
Class A	$	7,001
Class B		4,052
Class C		1,668
Class D		1,748
Class R		55
Additional paid-in capital		109,787,242
Dividends in excess of net investment income		(40,581	)
Accumulated net realized loss		(5,610,891	)
Net unrealized depreciation of investments		(1,347,451	)
Net Assets	$	102,802,843
Net Asset Value Per Share:
Class A ($49,504,565 ÷ 7,001,245 shares)	$	7.07
Class B ($28,712,961 ÷ 4,051,958 shares)	$	7.09
Class C ($11,817,149 ÷ 1,668,150 shares)	$	7.08
Class D ($12,378,332 ÷ 1,747,394 shares)	$	7.08
Class R ($389,836 ÷ 55,095 shares)	$	7.08

See Notes to Financial Statements.

6

Statement of Operations (unaudited)
For the Six Months Ended June 30, 2004

Investment Income:
Interest	$	2,304,835
Expenses:
Distribution and service fees		385,967
Management fees		295,154
Shareholder account services		228,878
Registration		52,807
Custody and related services		21,918
Shareholder reports and communications		14,890
Auditing and legal fees		13,313
Directors’ fees and expenses		4,533
Miscellaneous		7,153
Total Expenses		1,024,613
Net Investment Income		1,280,222
Net Realized and Unrealized Loss on Investments:
Net realized loss on investments		(1,525,374	)
Net change in unrealized depreciation of investments		(784,227	)
Net Loss on Investments		(2,309,601	)
Decrease in Net Assets from Operations	$	(1,029,379	)

See Notes to Financial Statements.

7

Statements of Changes in Net Assets
 (unaudited)

	Six Months Ended June 30, 2004				Year Ended December 31, 2003
Operations:
Net investment income		$	1,280,222			$	3,367,059
Net realized gain (loss) on investments			(1,525,374	)			1,190,290
Net change in unrealized appreciation/depreciation of investments			(784,227	)			(4,425,134	)
Increase (Decrease) in Net Assets from Operations			(1,029,379	)			132,215
Distributions to Shareholders:
Net investment income:
Class A			(681,592	)			(1,683,740	)
Class B			(329,249	)			(948,534	)
Class C			(140,259	)			(397,431	)
Class D			(126,268	)			(337,333	)
Class R			(2,854	)			(21	)
Total			(1,280,222	)			(3,367,059	)
Dividends in excess of net investment income:
Class A			(89,729	)			(365,851	)
Class B			(43,344	)			(206,102	)
Class C			(18,464	)			(86,356	)
Class D			(16,623	)			(73,297	)
Class R			(376	)			(4	)
Total			(168,536	)			(731,610	)
Decrease in Net Assets from Distributions			(1,448,758	)			(4,098,669	)
Capital Share Transactions:
Net proceeds from sales of shares			4,396,494				35,976,490
Investment of dividends			1,136,936				3,112,959
Exchanged from associated funds			6,849,939				71,077,284
Total			12,383,369				110,166,733
Cost of shares repurchased			(27,456,807	)			(73,839,727	)
Exchanged into associated funds			(13,494,125	)			(94,886,553	)
Total			(40,950,932	)			(168,726,280	)
Decrease in Net Assets from Capital Share Transactions			(28,567,563	)			(58,559,547	)
Decrease in Net Assets			(31,045,700	)			(62,526,001	)
Net Assets:
Beginning of period			133,848,543				196,374,544
End of Period (net of dividends in excess of net investment income of $40,581 and $203,725, respectively)		$	102,802,843			$	133,848,543

See Notes to Financial Statements.

8

Notes to Financial Statements  (unaudited)

1.	Multiple Classes of Shares — Seligman U.S. Government Securities Series (the “Fund”) is a series of Seligman High Income Fund Series (the “Series”). The Fund offers the following five classes of shares:
	Class A shares are sold with an initial sales charge of up to 4.75% and a continuing service fee of up to 0.25% on an annual basis. Class A shares purchased in an amount of $1,000,000 or more are sold without an initial sales charge but are subject to a contingent deferred sales charge (“CDSC”) of 1% on redemptions within 18 months of purchase.
	Class B shares are sold without an initial sales charge but are subject to a distribution fee of 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 5% on redemptions in the first year of purchase, declining to 1% in the sixth year and 0% thereafter. Class B shares will automatically convert to Class A shares approximately eight years after their date of purchase.
	Class C shares are sold primarily with an initial sales charge of up to 1%, and a CDSC, if applicable, of 1% imposed on redemptions made within 18 months of purchase. Shares purchased through certain financial intermediaries may be bought without an initial sales charge and with a 1% CDSC on redemptions made within 12 months of purchase. All Class C shares are subject to a distribution fee of up to 0.75% and a service fee of up to 0.25% on an annual basis.
	Class D shares are sold without an initial sales charge but are subject to a distribution fee of up to 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 1% imposed on redemptions made within one year of purchase.
	Class R shares are offered to certain employee benefit plans and are not available to all investors. They are sold without an initial sales charge, but are subject to a distribution fee of up to 0.25% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 1% on redemptions made within one year of a plan’s initial purchase of Class R shares.
	All classes of shares represent interests in the same portfolio of investments, have the same rights and are generally identical in all respects except that each class bears its separate distribution and certain other class-specific expenses, and has exclusive voting rights with respect to any matter on which a separate vote of any class is required.
2.	Significant Accounting Policies — The financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America, which require management to make certain estimates and assumptions at the date of the financial statements. Actual results may differ from these estimates. These unaudited interim financial statements reflect all adjustments which are, in the opinion of management, necessary to a fair statement of the results for the interim period presented. All such adjustments are of a normal recurring nature. The following summarizes the significant accounting policies of the Fund:
	a.	Security Valuation — Investments in US Government and Government agency obligations are valued at current market values or, in their absence, at fair values determined in accordance with procedures approved by the trustees. Securities traded on an exchange are valued at last sales prices or, in their absence and in the case of over-the-counter securities, at the mean of bid and asked prices. Short-term holdings maturing in 60 days or less are valued at amortized cost.
	b.	Federal Taxes — There is no provision for federal income tax. The Fund has elected to be taxed as a regulated investment company and intends to distribute substantially all taxable net income and net realized gain.

9

Notes to Financial Statements (unaudited)

	c.	Security Transactions and Related Investment Income — Investment transactions are recorded on trade dates. Identified cost of investments sold is used for both financial reporting and federal income tax purposes. Dividends payable are recorded on ex-dividend dates. Interest income is recorded on an accrual basis. The Fund amortizes premiums and discounts on purchases of portfolio securities for financial reporting purposes.
	d.	Repurchase Agreements — The Fund may enter into repurchase agreements with commercial banks and with broker/dealers deemed to be creditworthy by J. & W. Seligman & Co. Incorporated (the “Manager”). Securities received as collateral subject to repurchase agreements are deposited with the Fund’s custodian and, pursuant to the terms of the repurchase agreements, must have an aggregate market value greater than or equal to the repurchase price plus accrued interest at all times. Procedures have been established to monitor, on a daily basis, the market value of repurchase agreements’ underlying securities to ensure the existence of the proper level of collateral.
	e.	Multiple Class Allocations — All income, expenses (other than class-specific expenses), and realized and unrealized gains or losses are allocated daily to each class of shares based upon the relative value of shares of each class. Class-specific expenses, which include distribution and service fees and any other items that are specifically attributable to a particular class, are charged directly to such class. For the six months ended June 30, 2004, distribution and service fees were the only class-specific expenses.
	f.	Distributions to Shareholders — Dividends are declared daily and paid monthly. Other distributions paid by the Fund are recorded on the ex-dividend date. The treatment for financial reporting purposes of distributions made to shareholders during the year from net investment income or net realized gains may differ from their ultimate treatment for federal income tax purposes. These differences are caused primarily by differences in the timing of the recognition of certain components of income, expense, or realized capital gain for federal income tax purposes. Where such differences are permanent in nature, they are reclassified in the components of net assets based on their ultimate characterization for federal income tax purposes. Any such reclassification will have no effect on net assets, results of operations, or net asset values per share of the Fund.
3.	Purchases and Sales of Securities — Purchases and sales of portfolio securities, excluding short-term investments, for the six months ended June 30, 2004, amounted to $76,718,258 and $112,039,171, respectively.
	At June 30, 2004, the cost of investments for federal income tax purposes was $104,512,520. The tax basis cost was greater than the cost for financial reporting purposes due to the amortization of premium for financial reporting purposes of $40,581. The tax basis gross unrealized appreciation and depreciation of portfolio securities amounted to $231,544 and $1,619,576, respectively.
4.	Management Fee, Distribution Services, and Other Transactions — The Manager manages the affairs of the Fund and provides the necessary personnel and facilities. Compensation of all officers of the Fund, all directors of the Fund who are employees of the Manager, and all personnel of the Fund and the Manager is paid by the Manager. The Manager receives a fee, calculated daily and payable monthly, equal to 0.50% per annum of the Fund’s average daily net assets.
	Seligman Advisors, Inc. (the “Distributor”), agent for the distribution of the Fund’s shares and an affiliate of the Manager, received concessions of $1,061 from sales of Class A shares. Commissions of $8,532 and $2,717 were paid to dealers for sales of Class A and Class C shares, respectively.
	The Fund has an Administration, Shareholder Services and Distribution Plan (the “Plan”) with respect to distribution of its shares. Under the Plan, with respect to Class A shares, service organizations can enter into agreements with the Distributor and receive a continuing fee of up to 0.25% on an annual basis, payable quarterly, of the average daily net assets of the Class A shares attributable to the particular service organizations for

10

Notes to Financial Statements (unaudited)

providing personal services and/or the maintenance of shareholder accounts. The Distributor charges such fees to the Fund pursuant to the Plan. For the six months ended June 30, 2004, fees incurred under the Plan aggregated $66,544, or 0.25% per annum of the average daily net assets of Class A shares.

Under the Plan, with respect to Class B shares, Class C shares, Class D shares, and Class R shares, service organizations can enter into agreements with the Distributor and receive a continuing fee for providing personal services and/or the maintenance of shareholder accounts of up to 0.25% on an annual basis of the average daily net assets of the Class B, Class C, Class D, and Class R shares for which the organizations are responsible; and, for Class C and Class D shares, fees for providing other distribution assistance of up to 0.75% (0.25%, in the case of Class R shares) on an annual basis of such average daily net assets. Such fees are paid monthly by the Fund to the Distributor pursuant to the Plan.

With respect to Class B shares, a distribution fee of 0.75% on an annual basis of average daily net assets is payable monthly by the Fund to the Distributor; however, the Distributor has sold its rights to this fee with respect to a substantial portion of Class B shares to third parties (the “Purchasers”), which provide funding to the Distributor to enable it to pay commissions to dealers at the time of the sale of the related Class B shares. For the six months ended June 30, 2004, fees incurred under the Plan, equivalent to 1% per annum of the average daily net assets of Class B, Class C, and Class D shares, and 0.50% per annum of average daily net assets of Class R shares amounted to $176,231, $74,594, $67,967, and $631, respectively. The Distributor is entitled to retain any CDSC imposed on certain redemptions of Class A, Class C, Class D and Class R shares. For the six months ended June 30, 2004, such charges amounted to $24,176.

The Distributor has sold its rights to collect any CDSC imposed on redemptions of Class B shares to the Purchasers. In connection with the sale of its rights to collect any CDSC and the distribution fees with respect to Class B shares described above, the Distributor receives payments from the Purchasers based on the value of Class B shares sold. The aggregate of such payments and distribution fees retained by the Distributor, for the six months ended June 30, 2004, amounted to $1,886.

Seligman Services, Inc., an affiliate of the Manager, is eligible to receive commissions from certain sales of shares of the Fund, as well as distribution and service fees pursuant to the Plan. For the six months ended June 30, 2004, Seligman Services, Inc. received commissions of $966 from the sales of shares of the Fund. Seligman Services, Inc. also received distribution and service fees of $6,810 pursuant to the Plan.

Seligman Data Corp., which is owned by certain associated investment companies, charged the Fund at cost $228,878 for shareholder account services in accordance with a methodology approved by the Fund’s trustees. Costs of Seligman Data Corp. directly attributable to the Fund were charged to the Fund. The remaining charges were allocated to the Fund by Seligman Data Corp. pursuant to a formula based on the Fund’s net assets, shareholder transaction volume and number of shareholder accounts.

The Series and certain other associated investment companies (together, the “Guarantors”) have severally but not jointly guaranteed the performance and observance of all the terms and conditions of two leases entered into by Seligman Data Corp., including the payment of rent by Seligman Data Corp. (the “Guaranties”). The leases and the Guaranties expire in September 2008 and January 2009. The obligation of the Series to pay any amount due under either Guaranty is limited to a specified percentage of the full amount, which generally is based on the Series’ percentage of the expenses billed by Seligman Data Corp. to all Guarantors in the preceding calendar quarter. As of June 30, 2004, the Series’ potential obligation under the Guaranties is $541,800. As of June 30, 2004, no event has occurred which would result in the Series becoming liable to make any payment under a Guaranty. The Fund would bear a portion of any payments made by the Series under the

11

Notes to Financial Statements (unaudited)

	Guaranties. A portion of rent paid by Seligman Data Corp. is charged to the Fund as part of Seligman Data Corp.’s shareholder account services cost.
	Certain officers and directors of the Fund are officers or directors of the Manager, the Distributor, Seligman Services, Inc., and/or Seligman Data Corp.
	The Fund has a compensation arrangement under which trustees who receive fees may elect to defer receiving such fees. Trustees may elect to have their deferred fees accrue interest or earn a return based on the performance of the Fund or other funds in the Seligman Group of Investment Companies. The cost of such fees and earnings/loss accrued thereon is included in trustees’ fees and expenses and the accumulated balance thereof at June 30, 2004, of $14,942 is included in accrued expenses and other liabilities. Deferred fees and related accrued earnings are not deductible by the Fund for federal income tax purposes until such amounts are paid.
5.	Committed Line of Credit — The Fund is a participant in a joint $425,000,000 committed line of credit that is shared by substantially all open-end funds in the Seligman Group of Investment Companies. The trustees have currently limited the Fund’s borrowings to 10% of its net assets. Borrowings pursuant to the credit facility are subject to interest at a rate equal to the overnight federal funds rate plus 0.50%. The Fund incurs a commitment fee of 0.10% per annum on its share of the unused portion of the credit facility. The credit facility may be drawn upon only for temporary purposes and is subject to certain other customary restrictions. The credit facility commitment expires in June 2005, but is renewable annually with the consent of the participating banks. For the six months ended June 30, 2004, the Fund did not borrow from the credit facility.
6.	Capital Loss Carryforward and Other Tax Adjustments — At December 31, 2003, the Fund had a net capital loss carryforward for federal income tax purposes of $3,320,170, which is available for offset against future taxable net capital gains, with $522,463 expiring in 2005, $1,359,544 expiring in 2007, and $1,438,163 expiring in 2008. Accordingly, no capital gain distributions are expected to be paid to shareholders until net capital gains have been realized in excess of the available capital loss carryforward.
	In addition, the Fund elected to defer until January 1, 2004, the recognition for tax purposes of net losses of $433,667 realized on sales of investments after October 31, 2003. These losses will be available to offset future taxable net gains.
7.	Transactions in Shares of Beneficial Interest — The Fund has authorized unlimited shares of $0.001 par value Shares of Beneficial Interest. Transactions in Shares of Beneficial Interest were as follows:

	Six Months Ended June 30, 2004					Year Ended December 31, 2003
Class A	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	358,484		$	2,587,984		3,535,309		$	26,078,441
Investment of dividends	86,175			621,946		215,577			1,580,283
Exchanged from associated funds	600,539			4,365,966		7,650,469			56,313,073
Converted from Class B**	70,225			500,614		—			—
Total	1,115,423			8,076,510		11,401,355			83,971,797
Cost of shares repurchased	(1,431,479	)		(10,339,579	)	(4,959,470	)		(36,310,173	)
Exchanged into associated funds	(933,081	)		(6,768,419	)	(9,094,844	)		(66,782,844	)
Total	(2,364,560	)		(17,107,998	)	(14,054,314	)		(103,093,017	)
Decrease	(1,249,137	)	$	(9,031,488	)	(2,652,959	)	$	(19,121,220	)

12

Notes to Financial Statements (unaudited)

	Six Months Ended June 30, 2004					Year Ended December 31, 2003
Class B	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	51,359		$	372,550		221,854		$	1,632,736
Investment of dividends	36,937			267,465		112,271			825,400
Exchanged from associated funds	110,918			807,616		1,111,952			8,197,545
Total	199,214			1,447,631		1,446,077			10,655,681
Cost of shares repurchased	(1,137,094	)		(8,170,949	)	(2,686,241	)		(19,685,826	)
Exchanged into associated funds	(550,316	)		(3,977,900	)	(2,138,628	)		(15,682,664	)
Converted to Class A**	(70,053	)		(500,360	)	—			—
Total	(1,757,463	)		(12,649,209	)	(4,824,869	)		(35,368,490	)
Decrease	(1,558,249	)	$	(11,201,578	)	(3,378,792	)	$	(24,712,809	)
Class C	Shares			Amount		Shares			Amount
Net proceeds from sales of shares	52,121		$	379,408		909,164		$	6,729,146
Investment of dividends	16,920			122,539		50,398			370,264
Exchanged from associated funds	69,132			495,536		413,452			3,047,914
Total	138,173			997,483		1,373,014			10,147,324
Cost of shares repurchased	(904,360	)		(6,523,479	)	(1,366,384	)		(10,021,066	)
Exchanged into associated funds	(152,101	)		(1,101,413	)	(863,433	)		(6,324,619	)
Total	(1,056,461	)		(7,624,892	)	(2,229,817	)		(16,345,685	)
Decrease	(918,288	)	$	(6,627,409	)	(856,803	)	$	(6,198,361	)
Class D	Shares			Amount		Shares			Amount
Net proceeds from sales of shares	88,314		$	638,580		209,195		$	1,534,328
Investment of dividends	16,889			122,127		45,864			336,987
Exchanged from associated funds	162,123			1,180,821		476,360			3,518,752
Total	267,326			1,941,528		731,419			5,390,067
Cost of shares repurchased	(333,806	)		(2,403,333	)	(1,068,878	)		(7,822,662	)
Exchanged into associated funds	(227,374	)		(1,646,393	)	(832,113	)		(6,096,426	)
Total	(561,180	)		(4,049,726	)	(1,900,991	)		(13,919,088	)
Decrease	(293,854	)	$	(2,108,198	)	(1,169,572	)	$	(8,529,021	)
						April 30, 2003* December 31, 2003
Class R	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	57,199		$	417,718		251		$	1,839
Investment of dividends	400			2,859		3			25
Total	57,599			420,577		254			1,864
Cost of shares repurchased	(2,758	)		(19,467	)	—			—
Increase	54,841		$	401,110		254		$	1,864

*	Commencement of offering of shares.
**	Automatic conversion of Class B shares to Class A shares approximately eight years after the initial purchase date.

13

Notes to Financial Statements (unaudited)

8.	Other Matters— The Manager has conducted an extensive internal review in response to developments regarding disruptive or illegal trading practices within the mutual fund industry. As of September 2003, the Manager had one arrangement that permitted frequent trading in the Seligman registered investment companies (“Seligman Funds”). This arrangement was in the process of being closed down by the Manager before the first proceedings relating to trading practices within the mutual fund industry were publicly announced. Based on a review of the Manager’s records for 2001 through 2003, the Manager identified three other arrangements that had permitted frequent trading in the Seligman Funds. All three had already been terminated prior to the end of September 2002. The Securities and Exchange Commission (the “SEC”), the NASD and the Attorney General of the State of New York also are reviewing these matters.
	The Manager also has reviewed its practice of placing some of the Seligman Funds’ orders to buy and sell portfolio securities with brokerage firms in recognition of their sales of Seligman Funds. This practice is permissible when done properly; however, the Manager believes that it may have violated applicable requirements for certain of such orders as a result of compensation arrangements the Manager had with certain brokerage firms. The Manager discontinued this practice entirely in October 2003. The Manager is confident that the execution of all such orders was consistent with its best execution obligations and that the Seligman Funds did not pay higher brokerage commissions than they would otherwise have paid for comparable transactions. The Manager has also responded fully to information requests from the SEC and the NASD relating to the Manager’s use of revenue sharing and fund portfolio brokerage commissions and will continue to provide additional information if, and as, requested.
	The results of the Manager’s internal reviews were presented to the Independent Trustees of the Seligman Funds. In order to resolve matters with the Independent Trustees relating to the four arrangements that permitted frequent trading, which did not adversely affect Seligman U.S. Government Securities Series, the Manager has made payments to three funds and has agreed to waive a portion of its management fee with respect to another fund. In order to resolve matters with the Independent Trustees with regard to portfolio brokerage commissions, in May 2004, the Manager made payments to each of twenty-four funds in an amount equal to the commissions paid by each such fund during the period from 1998 through 2003 to certain brokerage firms in recognition of sales of fund shares. Seligman U.S. Government Securities Series does not pay brokerage commissions and thus did not receive any payment from the Manager.
14

Financial Highlights (unaudited)

The tables below are intended to help you understand each Class’s financial performance for the past five and one-half years or from its inception if less than five and one-half years. Certain information reflects financial results for a single share of Beneficial Interest of a Class that was held throughout the periods shown. Per share amounts are calculated using average shares outstanding. “Total return” shows the rate that you would have earned (or lost) on an investment in each Class, assuming you reinvested all your dividends. Total returns do not reflect any taxes or sales charges and are not annualized for periods of less than one year.

Class A
	Six Months Ended 6/30/04				Year Ended December 31,
					2003			2002			2001ø			2000			1999
Per Share Data:
Net Asset Value, Beginning of Period		$	7.23		$	7.39		$	6.97		$	6.91		$	6.50		$	7.09
Income (Loss) from Investment Operations:
Net investment income			0.09			0.18			0.26			0.32			0.36			0.34
Net realized and unrealized gain (loss) on investments			(0.15	)		(0.14	)		0.45			0.08			0.41			(0.59	)
Total from Investment Operations			(0.06	)		0.04			0.71			0.40			0.77			(0.25	)
Less Distributions:
Dividends from net investment income			(0.09	)		(0.18	)		(0.26	)		(0.32	)		(0.36	)		(0.34	)
Dividends in excess of net investment income			(0.01	)		(0.02	)		(0.03	)		(0.02	)		—			—
Total Distributions			(0.10	)		(0.20	)		(0.29	)		(0.34	)		(0.36	)		(0.34	)
Net Asset Value, End of Period		$	7.07		$	7.23		$	7.39		$	6.97		$	6.91		$	6.50
Total Return:			(0.82	)%		0.55	%		10.45	%		5.95	%		12.26	%		(3.63	)%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	49,505		$	59,660		$	80,556		$	81,722		$	62,982		$	64,575
Ratio of expenses to average net assets			1.32	%†		1.27	%		1.24	%		1.16	%		1.21	%		1.25	%
Ratio of net investment income to average net assets			2.57	%†		2.38	%		3.68	%		4.59	%		5.49	%		4.99	%
Portfolio turnover rate			69.67	%		250.49	%		184.24	%		66.84	%		37.42	%		51.59	%

See footnotes on page 19.

15

Financial Highlights (unaudited)

Class B
	Six Months Ended 6/30/04				Year Ended December 31,
						2003			2002			2001ø			2000			1999
Per ShareData:
Net Asset Value, Beginning of Period		$	7.25			$	7.40		$	6.98		$	6.93		$	6.51		$	7.11
Income (Loss) from Investment Operations:
Net investment income			0.07				0.12			0.21			0.27			0.32			0.29
Net realized and unrealized gain (loss) on investments			(0.15	)			(0.13	)		0.45			0.07			0.42			(0.60	)
Total from Investment Operations			(0.08	)			(0.01	)		0.66			0.34			0.74			(0.31	)
Less Distributions:
Dividends from net investment income			(0.07	)			(0.12	)		(0.21	)		(0.27	)		(0.32	)		(0.29	)
Dividends in excess of net investment income			(0.01	)			(0.02	)		(0.03	)		(0.02	)		—			—
Total Distributions			(0.08	)			(0.14	)		(0.24	)		(0.29	)		(0.32	)		(0.29	)
Net Asset Value, End of Period		$	7.09			$	7.25		$	7.40		$	6.98		$	6.93		$	6.51
Total Return:			(1.18	)%			(0.08	)%		9.63	%		5.01	%		11.59	%		(4.47	)%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	28,713			$	40,659		$	66,563		$	44,557		$	30,064		$	25,611
Ratio of expenses to average net assets			2.07	%†			2.03	%		1.99	%		1.91	%		1.96	%		2.00	%
Ratio of net investment income to
average net assets			1.82	%†			1.62	%		2.93	%		3.84	%		4.74	%		4.24	%
Portfolio turnover rate			69.67	%			250.49	%		184.24	%		66.84	%		37.42	%		51.59	%

See footnotes on page 19.

16

Financial Highlights (unaudited)

Class C
	Six Months Ended 6/30/04				Year Ended December 31,
																	5/27/99* to 12/31/99
					2003			2002			2001ø			2000
Per Share Data:
Net Asset Value, Beginning of Period		$	7.25		$	7.40		$	6.98		$	6.92		$	6.51			$	6.78
Income (Loss) from Investment Operations:
Net investment income			0.07			0.12			0.21			0.27			0.32				0.17
Net realized and unrealized gain (loss) on investments			(0.16	)		(0.13	)		0.45			0.08			0.41				(0.27	)
Total from Investment Operations			(0.09	)		(0.01	)		0.66			0.35			0.73				(0.10	)
Less Distributions:
Dividends from net investment income			(0.07	)		(0.12	)		(0.21	)		(0.27	)		(0.32	)			(0.17	)
Dividends in excess of net investment  income			(0.01	)		(0.02	)		(0.03	)		(0.02	)		—				—
Total Distributions			(0.08	)		(0.14	)		(0.24	)		(0.29	)		(0.32	)			(0.17	)
Net Asset Value, End of Period		$	7.08		$	7.25		$	7.40		$	6.98		$	6.92			$	6.51
Total Return:			(1.32	)%		(0.08	)%		9.63	%		5.16	%		11.43	%			(1.59	)%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	11,817		$	18,739		$	25,488		$	15,961		$	4,714			$	2,851
Ratio of expenses to average net assets			2.07	%†		2.03	%		1.99	%		1.91	%		1.96	%			2.03	%†
Ratio of net investment income to  average net assets			1.82	%†		1.62	%		2.93	%		3.84	%		4.74	%			4.37	%†
Portfolio turnover rate			69.67	%		250.49	%		184.24	%		66.84	%		37.42	%			51.59	%††

See footnotes on page 19.

17

Financial Highlights  (unaudited)

Class D
	Six Months				Year Ended December 31,
	Ended
	6/30/04				2003			2002			2001ø			2000			1999
Per Share Data:
Net Asset Value, Beginning of Period		$	7.24		$	7.40		$	6.98		$	6.92		$	6.51		$	7.11
Income (Loss) from Investment Operations:
Net investment income			0.07			0.12			0.21			0.27			0.32			0.29
Net realized and unrealized gain (loss) on investments			(0.15	)		(0.14	)		0.45			0.08			0.41			(0.60	)
Total from Investment Operations			(0.08	)		(0.02	)		0.66			0.35			0.73			(0.31	)
Less Distributions:
Dividends from net investment income			(0.07	)		(0.12	)		(0.21	)		(0.27	)		(0.32	)		(0.29	)
Dividends in excess of net investment income			(0.01	)		(0.02	)		(0.03	)		(0.02	)		—			—
Total Distributions			(0.08	)		(0.14	)		(0.24	)		(0.29	)		(0.32	)		(0.29	)
Net Asset Value, End of Period		$	7.08		$	7.24		$	7.40		$	6.98		$	6.92		$	6.51
Total Return:			(1.19	)%		(0.22	)%		9.63	%		5.16	%		11.43	%		(4.47	)%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	12,378		$	14,789		$	23,768		$	20,106		$	15,138		$	17,797
Ratio of expenses to average net assets			2.07	%†		2.03	%		1.99	%		1.91	%		1.96	%		2.00	%
Ratio of net investment income to average net assets			1.82	%†		1.62	%		2.93	%		3.84	%		4.74	%		4.24	%
Portfolio turnover rate			69.67	%		250.49	%		184.24	%		66.84	%		37.42	%		51.59	%

See footnotes on page 19.

18

Financial Highlights  (unaudited)

Class R
	Six Months Ended 6/30/04				4/30/03* to 12/31/03
Per Share Data:
Net Asset Value, Beginning of Period		$	7.23			$	7.36
Income (Loss) from Investment Operations:
Net investment income			0.09				0.10
Net realized and unrealized gain (loss)
on investments			(0.14	)			(0.10	)
Total from Investment Operations			(0.05	)			—
Less Distributions:
Dividends from net investment income			(0.09	)			(0.10	)
Dividends in excess of net investment income			(0.01	)			(0.03	)
Total Distributions			(0.10	)			(0.13	)
Net Asset Value, End of Period		$	7.08			$	7.23
Total Return:			(0.76	)%			(0.05	) %
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	390			$	2
Ratio of expenses to average net assets			1.57	%†			1.57	%†
Ratio of net investment income to average net assets			2.32	%†			2.01	%†
Portfolio turnover rate			69.67	%			250.49	%†††

*	Commencement of offering of shares.
†	Annualized.
††	For the year ended December 31, 1999.
†††	For the year ended December 31, 2003.
ø	As required, effective January 1, 2001, the Fund adopted the provisions of the AICPA Audit and Accounting Guide for Investment Companies and began amortizing premium on debt securities. The effect of this change for the year ended December 31, 2001, was to decrease net investment income per share by $0.02, increase net realized and unrealized gain (loss) on investments by $0.02 for each class and decrease the ratios of net investment income to average net assets from 4.83% to 4.59% for Class A, and from 4.08% to 3.84% for Classes B, C, and D. The per share data and ratios for periods prior to January 1, 2001, have not been restated.
See Notes to Financial Statements.

19

Trustees

Robert B. Catell  2, 3
•	Chairman, Chief Executive Officer and Director, KeySpan Corporation
John R. Galvin  1, 3
•	Dean Emeritus, Fletcher School of Law and Diplomacy at Tufts University
Alice S. Ilchman  2, 3
•	President Emerita, Sarah Lawrence College
•	Director, Jeannette K. Watson Summer Fellowship
•	Trustee, Committee for Economic Development
Frank A. McPherson  2, 3
•	Retired Chairman of the Board and Chief Executive Officer, Kerr-McGee Corporation
•	Director, ConocoPhillips
•	Director, Integris Health
John E. Merow  1, 3
•	Retired Chairman and Senior Partner, Sullivan & Cromwell LLP
•	Director, Commonwealth Industries, Inc.
•	Trustee, New York-Presbyterian Hospital
Betsy S. Michel  1, 3
•	Trustee, The Geraldine R. Dodge Foundation
William C. Morris
•	Chairman, J. & W. Seligman & Co. Incorporated
•	Chairman, Carbo Ceramics Inc.
Leroy C. Richie  1, 3
•	Chairman and Chief Executive Officer, Q Standards Worldwide, Inc.
•	Director, Kerr-McGee Corporation
Robert L. Shafer  2, 3
•	Retired Vice President, Pfizer Inc.
James N. Whitson  1, 3
•	Retired Executive Vice President and Chief Operating Officer, Sammons Enterprises, Inc.
•	Director, CommScope, Inc.
Brian T. Zino
•	Director and President, J. & W. Seligman & Co. Incorporated
•	Chairman, Seligman Data Corp.
•	Director, ICI Mutual Insurance Company
•	Member of the Board of Governors, Investment Company Institute

Member:	1	Audit Committee
	2	Trustee Nominating Committee
	3	Board Operations Committee

Executive Officers

William C. Morris

Chairman

Brian T. Zino

President and Chief Executive Officer

Christopher J. Mahony

Vice President

Thomas G. Rose

Vice President

Lawrence P. Vogel

Vice President and Treasurer

Frank J. Nasta

Secretary

20

Seligman

140 Years of Investment Experience

J. & W. Seligman & Co. Incorporated is a firm with a long tradition of investment expertise, offering a broad array of investment choices to help today’s investors seek their long-term financial goals.

Established in 1864, Seligman has a history of providing financial services marked not by fanfare, but rather by a quiet and firm adherence to financial prudence. While the world has changed dramatically in the 140 years since Seligman first opened its doors, the firm has continued to offer its clients high-quality investment solutions through changing times.

In the late 19th century, as the country grew, Seligman helped finance the westward expansion of the railroads, the construction of the Panama Canal, and the launching of urban transit systems. In the early 20th century, the firm helped fund the growing capital needs of new industries, including the nascent automobile and steel industries.

With the formation of Tri-Continental Corporation in 1929 — today, one of the nation’s largest diversified publicly-traded closed-end equity investment companies — Seligman began shifting its emphasis to investment management. In 1930, Seligman established what would be the first in an impressive lineup of mutual funds.

Seligman is proud of its distinctive past and of the traditional values that continue to shape the firm’s business decisions and investment judgment. While much has changed over the years, the firm’s commitment to providing prudent investment management that seeks to build wealth for clients over time is an enduring value that will continue to guide Seligman.

Table of Contents
To The Shareholders	1
Performance Overview	2
Portfolio Overview	4
Portfolio of Investments	6
Statement of Assets and Liabilities	13
Statement of Operations	14
Statements of Changes in Net Assets	15
Notes to Financial Statements	16
Financial Highlights	22
Report of Independent Registered Public Accounting Firm	27
Trustees and Executive Officers	28
For More Information	back cover

To The Shareholders

Your mid-year shareholder report for Seligman High-Yield Bond Series follows this letter. This report contains the Fund’s investment results and financial statements, including a portfolio of investments.

For the six months ended June 30, 2004, the Fund posted a total return of –0.49% based on the net asset value of Class A shares. During the same time period, the Lipper High Current Yield Average returned 1.16%, and the Citigroup High Yield Bond Index returned 1.19%.

We appreciate your continued support of Seligman High-Yield Bond Series and look forward to serving your investment needs for many years to come.

By Order of the Trustees,

William C. Morris

Chairman

Brian T. Zino

President

August 13, 2004

1

Performance Overview

Investment Results

Total Returns
For the Six Months Ended June 30, 2004
				Average Annual
	Six Months*			One Year			Five Years			Ten Years			Class B Since Inception 4/22/96			Class C Since Inception 5/27/99			Class I Since Inception 11/30/01			Class R Since Inception 4/30/03
Class A**
With Sales Charge		(5.30	)%		3.22	%		(3.80	)%		3.05	%		n/a			n/a			n/a			n/a
Without Sales Charge		(0.49	)		8.40			(2.87	)		3.55			n/a			n/a			n/a			n/a
Class B**
With CDSC†		(5.65	)		2.29			(3.90	)		n/a			n/a			n/a			n/a			n/a
Without CDSC		(0.88	)		7.28			(3.66	)		n/a			0.45	%		n/a			n/a			n/a
Class C**
With Sales Charge and CDSCø		(2.92	)		5.35			(3.82	)		n/a			n/a			(3.85	)%		n/a			n/a
Without Sales Charge and CDSC		(0.87	)		7.27			(3.61	)		n/a			n/a			(3.66	)		n/a			n/a
Class D**
With 1% CDSC		(1.82	)		6.27			n/a			n/a			n/a			n/a			n/a			n/a
Without CDSC		(0.87	)		7.27			(3.61	)		2.72			n/a			n/a			n/a			n/a
Class I**		(0.29	)		8.81			n/a			n/a			n/a			n/a			5.45	%		n/a
Class R**
With 1% CDSC		(1.58	)		7.12			n/a			n/a			n/a			n/a			n/a			n/a
Without CDSC		(0.62	)		8.12			n/a			n/a			n/a			n/a			n/a			8.73	%
Lipper High Current Yield Average***		1.16			9.66			3.28			5.37			4.68	#		3.20			8.57			13.64
Citigroup High Yield Bond Index***		1.19			10.35			5.29			7.62			6.65	††		5.15	†††		10.46			12.30

										Dividend and Capital Gain
										Per Share and Yield Information
Net Asset Value Per Share										For the Six Months Ended June 30, 2004
	6/30/04			12/31/03			6/30/03			Dividends Paidøø			SEC Yieldsøøø			Capital Gain‡
Class A		$	3.39		$	3.55		$	3.39		$	0.1424		6.68	%		Realized	$	0.002
Class B			3.39			3.55			3.40			0.1294		6.27			Unrealized		0.103	‡‡
Class C			3.40			3.56			3.41			0.1294		6.20
Class D			3.40			3.56			3.41			0.1294		6.27
Class I			3.39			3.55			3.39			0.1493		7.54
Class R			3.39			3.55			3.39			0.1379		6.63

(Continued on page 3.)

2

Performance Overview

(Continued from page 2.)

The rates of return will vary and the principal value of an investment will fluctuate so that shares, if redeemed, may be worth more or less than their original cost. Performance data quoted does not reflect the deduction of taxes that an investor may pay on Fund distributions or the redemption of Fund shares. Performance data quoted represents past performance. Past performance is not indicative of future investment results. Current performance may be higher or lower than the performance shown above. With respect to Class I shares, the Manager voluntarily reimbursed certain expenses in 2002 and 2001. Absent reimbursement, returns that include these periods would be lower.

*	Returns for periods of less than one year are not annualized.
**	Return figures reflect any change in price per share and assume the reinvestment of all distributions. Returns for Class A shares are calculated with and without the effect of the initial 4.75% maximum sales charge. Returns for Class B shares are calculated with and without the effect of the maximum 5% contingent deferred sales charge (“CDSC”), charged on redemptions made within one year of purchase, declining to 1% in the sixth year and 0% thereafter.
	Returns for Class C shares are calculated with and without the effect of the initial 1% maximum sales charge and the 1% CDSC that is charged on redemptions made within 18 months of purchase. Returns for Class D and R shares are calculated with and without the effect of the 1% CDSC, charged on certain redemptions made within one year of purchase. Returns for Class I shares are calculated without any sales charges.
***	The Citigroup High Yield Bond Index and the Lipper High Current Yield Average are unmanaged benchmarks that assume reinvestment of all distributions and exclude the effect of taxes and sales charges, and the Citigroup High Yield Bond Index also excludes the effect of fees. Investors cannot invest directly in an average or an index.
ø	The CDSC is 1% for periods up to 18 months.
øø	Represents per share amount paid or declared during the six months ended June 30, 2004, or in the case of Class R, for the period April 30, 2003 to December 31, 2003.
øøø	Current yield, representing the annualized yield for the 30-day period ended June 30, 2004, has been computed in accordance with SEC regulations and will vary.
†	The CDSC is 5% for periods of one year or less and 2% for the five-year period.
††	From April 30, 1996.
†††	From May 31, 1999.
#	From April 25, 1996.
‡	Information does not reflect effect of capital loss carryforwards that are available to offset these and future net realized capital gains. See Note 5 to Financial Statements.
‡‡	Represents the per share amount of net unrealized appreciation of portfolio securities as of June 30, 2004.

3

Portfolio Overview

Largest Industries

June 30, 2004

Percent of
Net Assets

Largest Portfolio Changes During Past Six Months
Largest Purchases	Largest Sales
Corporate Bonds:	Corporate Bonds:
Nextel Communications 9.375%, 1/15/2009*	Georgia-Pacific 8.875%, 5/15/2031
SBA Telecommunications 0% (9.75%†) 12/15/2011*	SBA Communications 10.25%, 2/1/2009**
Crown Castle International 10.75%, 8/1/2011*	Triton PCS 8.75%, 11/15/2011**
Pilgrims Pride 9.25%, 11/15/2013*	Millennium America 7.625%, 11/15/2026**
Nalco 0% (9%†), 2/1/2014*	NBC Acquisition 10.75, 2/15/2009**
Georgia-Pacific 7.5%, 5/15/2006*	Crown Cork & Seal 8%, 4/15/2023
Echostar DBS 10.375%, 10/1/2011*	Bally Total Fitness 10.5%, 7/15/2011
Centenial Communications 8.125%, 2/1/2014*	Dobson Communications 8.875%, 10/01/2013
Calpine 8.75%, 7/15/2013*	Northwest Airlines 9.875%, 3/15/2007**
Tembec Industries 8.5%, 2/1/2011*	Dresser 9.375%, 4/15/2011**

Largest portfolio changes from the previous period to the current period are based on cost of purchases and proceeds from sales of securities, listed in descending order.

*	Position added during the period.
**	Position eliminated during the period.

4

Portfolio Overview

Top Ten Companies June 30, 2004
Security	Value		Percent of Net Assets
Charter Communications	$	14,992,875	2.3
Qwest		13,893,250	2.2
Nextel Communications		12,428,656	1.9
SBA Telecommunications		10,225,125	1.6
Calpine		10,208,063	1.6
Owens-Illinois		10,189,750	1.6
Georgia-Pacific		10,152,187	1.6
Dex Media East		9,782,500	1.5
Huntsman ICI Chemicals		9,763,125	1.5
American Tower		9,668,751	1.5

The amounts shown for the top ten companies represent the value of the Fund’s investments in securities of all types issued by the companies or their affiliates.

Ratings §
June 30, 2004
	Moody’s		S&P
Ba/BB	8.8	%	16.3	%
B/B	56.4		59.6
Caa/CCC	31.3		23.3
Ca/CC	3.0		—
Non-rated	0.5		0.8

Weighted

Average Maturity

6.79 years

§ Percentages based on current market values of long-term holdings.

5

Portfolio of Investments
June 30, 2004

	Principal Amount		Value
Corporate Bonds 93.3%
Aerospace 3.0%
BE Aerospace 9.5%, 11/1/2008	$	7,275,000	$	7,056,750
K&F Industries 9.625%,12/15/2010		3,600,000		3,964,500
Sequa 9%, 8/1/2009		5,375,000		5,737,813
TD Funding 8.375%, 7/15/2011		2,650,000		2,703,000
				19,462,063
Auto 4.0%
Cummings 9.5%, 12/1/2010		750,000		853,125
Dura Operating 9%, 5/1/2009		4,450,000		4,383,250
Foamex 10.75%, 4/1/2009		6,175,000		6,144,125
Goodyear Tire & Rubber 7.857%, 8/15/2011		3,575,000		3,280,063
Stoneridge 11.5%, 5/1/2012		3,575,000		4,227,437
Tenneco Automotive 10.25%, 7/15/2013*		4,425,000		5,022,375
TRW Automotive Acquisition 11.0%, 2/15/2013		1,203,000		1,425,555
				25,335,930
Broadcasting 3.1%
Granite Broadcasting 9.75%, 12/1/2010*		5,300,000		4,955,500
Nextmedia Operating 10.75%, 7/1/2011		3,625,000		4,064,531
Paxson Communications 0% (12.25%†), 1/15/2009		4,175,000		3,653,125
Sinclair Broadcasting Group 8%, 3/15/2012		2,300,000		2,363,250
Spanish Broadcasting System 9.625%, 11/1/2009		2,100,000		2,226,000
Young Broadcasting 10%, 3/1/2011		2,675,000		2,735,188
				19,997,594
Building Products 1.7%
Associated Materials 9.75%, 4/15/2012		2,775,000		3,094,125
Euramax International 8.5%, 8/15/2011*		3,575,000		3,735,875
Texas Industries 10.25%, 6/15/2011*		3,600,000		4,032,000
				10,862,000
Cable 3.8%
Charter Communications:
10.25%, 9/15/2010*		8,750,000		8,859,375
0% (11.75%†), 5/15/2011		9,400,000		6,133,500
CSC Holdings 7.875%, 12/15/2007		3,725,000		3,892,625
Insight Midwest/Insight Capital 10.5%, 11/1/2010		2,625,000		2,874,375
Mediacom Broadband 11%, 7/15/2013		2,200,000		2,354,000
				24,113,875

See footnotes on page 12.

6

Portfolio of Investments
June 30, 2004

	Principal Amount		Value
Capital Goods 3.8%
Blount 13%, 8/1/2009	$	5,275,000	$	5,677,219
Columbus McKinnon 10%, 8/1/2010		3,500,000		3,727,500
JLG Industries 8.375%, 6/15/2012		3,525,000		3,604,313
NMHG Holding 10%, 5/15/2009		2,875,000		3,176,875
Norcross Safety Products 9.875%, 8/15/2011		3,100,000		3,363,500
Park-Ohio Industries 9.25%, 12/1/2007		4,425,000		4,524,562
				24,073,969
Chemicals 10.6%
Arco Chemical 9.8%, 2/1/2020		6,775,000		6,673,375
Equistar Chemicals 10.125%, 9/1/2008		4,225,000		4,647,500
FMC 10.25%, 11/1/2009		750,000		866,250
Hines Nurseries 10.25%, 10/1/2011		1,750,000		1,916,250
Huntsman ICI Chemicals 10.125%, 7/1/2009		9,525,000		9,763,125
International Specialty Holdings 10.625%, 12/15/2009		5,825,000		6,436,625
Koppers 9.875%, 10/15/2013		1,750,000		1,925,000
Lyondell Chemical 11.125%, 7/15/2012		5,350,000		5,951,875
Millennium America 9.25%, 6/15/2008		3,775,000		4,077,000
Nalco 0% (9%†), 2/1/2014*		8,850,000		5,907,375
Polyone 10.625%, 5/15/2010		3,500,000		3,727,500
Resolution Performance Products 9.5%, 4/15/2010		3,525,000		3,648,375
Rockwood Specialties Group 10.625%, 5/15/2011		3,525,000		3,771,750
Terra Capital 11.5%, 6/1/2010		5,050,000		5,555,000
UAP Holding		4,175,000		3,356,700
				68,223,700
Consumer Products 2.6%
Jostens 0%, 12/1/2013		6,200,000		4,247,000
Playtex Products 9.375%, 6/1/2011		3,500,000		3,421,250
Rayovac 8.5%, 10/1/2013		3,575,000		3,771,624
Remington Arms 10.5%, 2/1/2011		1,750,000		1,706,250
Simmons 7.875%, 1/15/2014		3,500,000		3,587,500
				16,733,624
Containers 3.9%
Anchor Glass Container 11%, 2/15/2013		2,650,000		3,044,188
BWAY 10%, 10/15/2010		2,675,000		2,822,125
Crown Cork & Seal 8%, 4/15/2023		1,900,000		1,662,500
Crown European Holdings 9.5%, 3/1/2011 (France)*		2,825,000		3,093,374
Owens-Illinois:
7.5%, 5/15/2010		8,150,000		8,027,750
7.8%, 5/15/2018		2,350,000		2,162,000

See footnotes on page 12.

7

Portfolio of Investments
June 30, 2004

	Principal Amount		Value
Containers (continued)
Pliant:
0% (11.125†), 6/15/2009	$	2,900,000	$	2,457,750
11.125%, 9/1/2009		1,875,000		2,015,625
				25,285,312
Diversified Telecommunications 2.2%
Qwest 13.5%, 12/15/2010*		11,900,000		13,893,250
Electric 0.9%
CMS Energy 9.875%, 10/15/2007		1,775,000		1,921,437
MSW Energy Holdings 8.5%, 9/1/2010*		3,600,000		3,825,000
				5,746,437
Energy 3.9%
Dynegy Holdings 8.75%, 2/15/2012		6,825,000		6,517,875
El Paso 7.875%, 6/15/2012		5,375,000		4,850,938
El Paso Production Holdings 7.75%, 6/1/2013*		4,550,000		4,197,375
Williams Companies:
6.75%, 4/15/2009*		4,200,000		4,147,500
8.125%, 3/15/2012		4,650,000		4,987,125
				24,700,813
Environmental 0.4%
Allied Waste North America 7.875%, 4/15/2013		2,400,000		2,520,000
Finance 0.9%
Western Financial Bank 9.625%, 5/15/2012		5,075,000		5,607,875
Food and Beverage 2.4%
Dean Foods 8.15%, 8/1/2007		750,000		811,875
Land O’ Lakes 8.75%, 11/15/2011		5,300,000		4,902,500
Pilgrim’s Pride 9.25%, 11/15/2013		5,725,000		6,125,750
Seminis Vegetable Seeds 10.25%, 10/1/2013		3,525,000		3,851,063
				15,691,188
Food and Drug 2.1%
General Nutrition Center 8.5%, 12/1/2010		1,300,000		1,355,250
Rite Aid:
8.125%, 5/1/2010		2,700,000		2,855,250
7.7%, 2/15/2027		6,350,000		5,651,500
Roundy’s (Series B) 8.875%, 6/15/2012		3,125,000		3,328,125
				13,190,125

See footnotes on page 12.

8

Portfolio of Investments
June 30, 2004

	Principal Amount		Value
Gaming 1.4%
Harrah’s Operating 7.875%, 12/15/2005	$	3,675,000	$	3,890,906
Mandalay Resort Group 9.375%, 2/15/2010		2,675,000		2,929,125
MGM Mirage 9.75%, 6/1/2007		2,000,000		2,195,000
				9,015,031
Health Care Facilities and Supplies 2.1%
Alliance Imaging 10.375%, 4/15/2011		3,625,000		3,815,313
Medex 8.875%, 5/15/2013*		3,550,000		3,763,000
Province Healthcare 7.5%, 6/1/2013		2,275,000		2,206,750
Universal Hospital Services 10.125%, 11/1/2011		3,525,000		3,595,500
				13,380,563
Industrials 0.3%
Sensus Metering Systems 8.625%, 12/15/2013		1,750,000		1,688,750
Leisure 1.7%
Bally Total Fitness 10.5%, 7/15/2011*		3,650,000		3,449,250
Intrawest 7.5%, 10/15/2013		2,775,000		2,726,438
Six Flags 8.875%, 2/1/2010		4,925,000		4,900,374
				11,076,062
Lodging 1.6%
Host Marriot (Series I) 9.5%, 1/15/2007		2,400,000		2,634,000
John Q. Hammons Hotels (Series B) 8.875%, 5/15/2012		2,325,000		2,534,250
MeriStar Hospitality 9.125%, 1/15/2011		4,750,000		4,821,250
				9,989,500
Metals and Mining 4.3%
AK Steel:
7.875%, 2/15/2009		3,550,000		3,337,000
7.75%, 6/15/2012		1,700,000		1,542,750
Earle M. Jorgesen 9.75%, 6/1/2012		3,050,000		3,355,000
Gerdau AmeriSteel 10.375%, 7/15/2011		3,500,000		3,920,000
IMCO Recycling 10.375%, 10/15/2010		5,250,000		5,696,250
Neenah Foundry 11%, 9/30/2010		3,950,000		4,206,750
United States Steel 10.75%, 8/1/2008		4,666,000		5,354,235
				27,411,985
Paper and Forest Products 5.7%
Buckeye Technologies 8%, 10/15/2010		3,550,000		3,274,875
Caraustar Industries 9.875%, 4/1/2011		3,450,000		3,450,000

See footnotes on page 12.

9

Portfolio of Investments
June 30, 2004

	Principal Amount		Value
Paper and Forest Products (continued)
Georgia-Pacific:
7.5%, 5/15/2006	$	4,875,000	$	5,191,875
8.875%, 5/15/2031		4,625,000		4,960,312
Jefferson Smurfit 8.25%, 10/1/2012		3,625,000		3,788,125
Longview Fibre 10%, 1/15/2009		3,600,000		3,906,000
Newark Group 9.75%, 3/15/2014*		3,500,000		3,368,750
Potlatch 10%, 7/15/2011		3,800,000		4,237,000
Tembec Industries 8.5%, 2/1/2011		4,450,000		4,516,750
				36,693,687
Property and Real Estate Development 0.1%
Forest City Enterprises 7.625%, 6/1/2015		850,000		858,500
Publishing 4.1%
Dex Media East 0% (9%†), 11/15/2013*		15,050,000		9,782,500
Houghton Mifflin 9.875%, 2/1/2013		4,425,000		4,447,124
Primedia 8.875%, 5/15/2011		5,400,000		5,373,000
Vertis:
9.75%, 4/1/2009		1,775,000		1,917,000
10.875%, 6/15/2009		2,575,000		2,781,000
13.5%, 12/7/2009*		1,750,000		1,758,750
				26,059,374
Restaurants 0.6%
Buffets 11.25%, 7/15/2010		1,750,000		1,837,500
Domino’s 8.25%, 7/1/2011*		1,900,000		2,023,500
				3,861,000
Satellite 1.4%
Echostar DBS:
10.375%, 10/1/2007		4,450,000		4,778,188
6.375%, 10/1/2012		4,225,000		4,182,750
				8,960,938
Services 2.1%
Mail-Well 7.875%, 12/1/2013		2,600,000		2,379,000
Mobile Mini 9.5%, 7/1/2013		1,350,000		1,485,000
Perry-Judd’s Holdings 10.625%, 12/15/2007		3,925,000		3,493,250
URS 11.5%, 9/15/2009		1,170,000		1,348,425
Williams Scotsman:
9.875%, 6/1/2007		3,475,000		3,466,313
10%, 8/15/2008		1,325,000		1,450,875
				13,622,863

See footnotes on page 12.

10

Portfolio of Investments
June 30, 2004

	Principal Amount		Value
Stores 1.8%
Asbury Auto Group:
9%, 6/15/2012	$	1,775,000	$	1,819,375
8%, 3/15/2014		1,725,000		1,656,000
Central Garden & Pet 9.125%, 2/1/2013		2,675,000		2,915,750
Hollywood Entertainment 9.625%, 3/15/2011		4,625,000		5,341,875
				11,733,000
Technology 1.1%
AMI Semiconductor 10.75%, 2/1/2013		3,559,000		4,172,928
Xerox 9.75%, 1/15/2009		2,625,000		2,999,062
				7,171,990
Textile and Apparel 0.6%
Russell 9.25%, 5/1/2010		3,800,000		4,056,500
Tower 4.1%
American Tower:
9.375%, 2/1/2009		4,425,000		4,745,813
7.5%, 5/1/2012*		4,450,000		4,327,625
Crown Castle International 10.75%, 8/1/2011		6,175,000		6,946,875
SBA Telecommunications 0% (9.75%†) 12/15/2011*		13,725,000		10,225,125
				26,245,438
Utilities 4.1%
AES 9.375%, 9/15/2010		6,400,000		6,856,000
Calpine:
8.5%, 7/15/2010*		7,000,000		5,775,000
8.75%, 7/15/2013*		5,325,000		4,433,063
Edison Mission Energy 7.73%, 6/15/2009		5,525,000		5,400,687
National Waterworks (Series B) 10.5%, 12/1/2012		1,775,000		1,979,125
NRG Energy 8%, 12/15/2013		1,750,000		1,776,250
				26,220,125
Wireless 6.9%
Alamosa Holdings 11%, 7/31/2010		7,150,000		7,829,250
Centenial Cellular Operating 10.75%, 12/15/2008		2,352,000		2,446,080
Centenial Communications 8.125%, 2/1/2014*		4,725,000		4,406,062
Dobson Communications 8.875%, 10/1/2013		3,275,000		2,505,375
Nextel Communications 9.375%, 11/15/2009		11,575,000		12,428,656
Nextel Partners:
12.5%, 11/15/2009		1,750,000		1,793,750
8.125%, 7/1/2011		895,000		1,047,150

See footnotes on page 12.

11

Portfolio of Investments
June 30, 2004

	Principal Amount, Shares or Warrants			Value
Wireless (continued)
Rural Cellular:
9.75%, 1/15/2010	$	2,825,000		$	2,577,813
9.875%, 2/1/2010		3,550,000			3,541,125
Western Wireless 9.25%, 7/15/2013		5,350,000			5,537,250
					44,112,511
Total Corporate Bonds (Cost $578,017,337)					597,595,572
Preferred Stocks 1.1%
Broadcasting 0.6%
Paxson Communications 14.25%		41,700	shs.		3,664,388
Publishing 0.5%
Primedia 8.625%		37,000			3,200,500
Total Preferred Stocks (Cost $7,385,534)					6,864,888
Asset-Backed Securities 0.7%
Utilities 0.7%
Midland Funding (Series A) 11.75%, 7/23/2005 (Cost $4,153,590)	$	4,078,166			4,241,293
Warrants 0.1%
Tower 0.1%
American Tower (Cost $238,723)		3,125	wts.		595,313
Fixed-Time Deposit 3.4%
Rabobank Nederland 1.43%, 7/1/2004 (Cost $21,890,000)	$	21,890,000			21,890,000
Total Investments (Cost $611,685,184) 98.6%					631,187,066
Other Assets Less Liabilities 1.4%					8,993,038
Net Assets 100.0%				$	640,180,104

* Rule 144A security.

† Deferred-interest debentures pay no interest for a stipulated number of years, after which they pay the indicated coupon rate.

See Notes to Financial Statements.

12

Statement of Assets and Liabilities
June 30, 2004

Assets:
Investments, at value:
Corporate bonds (cost $578,017,337)	$	597,595,572
Preferred stocks (cost $7,385,534)		6,864,888
Asset-backed securities (cost $4,153,590)		4,241,293
Warrants (cost $238,723)		595,313
Fixed Time Deposit (cost $21,890,000)		21,890,000
Total investments (cost $611,685,184)		631,187,066
Cash		293,234
Receivable for interest and dividends		13,402,546
Receivable for securities sold		1,649,128
Expenses prepaid to shareholder service agent		170,511
Receivable for shares of Beneficial Interest sold		72,310
Other		96,735
Total Assets		646,871,530
Liabilities:
Payable for shares of Beneficial Interest repurchased		2,605,322
Dividends payable		1,724,581
Payable for securities purchased		1,479,807
Distribution and service fees payable		393,046
Management fee payable		343,464
Accrued expenses and other		145,206
Total Liabilities		6,691,426
Net Assets	$	640,180,104
Composition of Net Assets:
Shares of Beneficial Interest, at par (unlimited shares authorized; $0.001 par value; 188,701,899 shares outstanding):
Class A	$	62,470
Class B		77,015
Class C		15,281
Class D		31,976
Class I		1,787
Class R		173
Additional paid-in capital		2,080,528,360
Dividends in excess of net investment income		(2,188,300	)
Accumulated net realized loss		(1,457,850,540	)
Net unrealized appreciation of investments		19,501,882
Net Assets	$	640,180,104

Net Asset Value Per Share:
Class A ($211,504,857 ÷ 62,470,492 shares)	$	3.39	Class D ($108,685,283 ÷ 31,975,558 shares)	$	3.40
Class B ($261,410,829 ÷ 77,014,897 shares)	$	3.39	Class I ($6,050,511 ÷ 1,786,764 shares)	$	3.39
Class C ($51,942,767 ÷ 15,281,120 shares)	$	3.40	Class R ($585,857 ÷ 173,068 shares)	$	3.39

See Notes to Financial Statements.

13

Statement of Operations
For the Six Months Ended June 30, 2004

Investment Income:
Interest	$	32,964,319
Dividends		774,128
Total Investment Income		33,738,447
Expenses:
Distribution and service fees		2,611,766
Management fees		2,274,055
Shareholder account services		1,027,724
Custody and related services		102,878
Registration		80,094
Shareholder reports and communications		45,557
Auditing and legal fees		38,229
Directors’ fees and expenses		12,091
Miscellaneous		23,146
Total Expenses		6,215,540
Net Investment Income		27,522,907
Net Realized and Unrealized Gain (Loss) on Investments:
Net realized gain on investments		313,593
Net change in unrealized appreciation of investments		(33,035,020	)
Net Loss on Investments		(32,721,427	)
Decrease in Net Assets from Operations	$	(5,198,520	)

See Notes to Financial Statements.

14

Statements of Changes in Net Assets

	Six Months Ended June 30, 2004				Year Ended December 31, 2003
Operations:
Net investment income		$	27,522,907			$	57,838,777
Net realized gain on investments			313,593				52,924,456
Net change in unrealized appreciation of investments			(33,035,020	)			39,644,062
Increase (Decrease) in Net Assets from Operations			(5,198,520	)			150,407,295
Distributions to Shareholders:
Net investment income:
Class A			(9,353,053	)			(20,541,568	)
Class B			(10,866,824	)			(23,309,524	)
Class C			(2,112,498	)			(4,052,841	)
Class D			(4,428,146	)			(9,584,885	)
Class I			(254,464	)			(349,882	)
Class R			(14,752	)			(77	)
Total			(27,029,737	)			(57,838,777	)
Dividends in excess of net investment income:
Class A			—				(972,847	)
Class B			—				(1,103,937	)
Class C			—				(191,942	)
Class D			—				(453,939	)
Class I			—				(16,570	)
Class R			—				(4	)
Total			—				(2,739,239	)
Decrease in Net Assets from Distributions			(27,029,737	)			(60,578,016	)
Capital Share Transactions:
Net proceeds from sales of shares			20,977,168				91,960,373
Investment of dividends			13,950,268				30,359,362
Exchanged from associated funds			20,240,033				132,697,242
Total			55,167,469				255,016,977
Cost of shares repurchased			(107,391,811	)			(221,949,382	)
Exchanged into associated funds			(37,450,382	)			(133,080,952	)
Total			(144,842,193	)			(355,030,334	)
Decrease in Net Assets from Capital Share Transactions			(89,674,724	)			(100,013,357	)
Decrease in Net Assets			(121,902,981	)			(10,184,078	)
Net Assets:
Beginning of period			762,083,085				772,267,163
End of Period (includes dividends in excess of net investment income    of $2,188,300 and $3,398,362, respectively)		$	640,180,104			$	762,083,085

See Notes to Financial Statements.

15

Notes to Financial Statements

1.	Multiple Classes of Shares— Seligman High-Yield Bond Series (the “Fund”) is a series of Seligman High Income Fund Series (the “Series”). The Fund offers the following six classes of shares:
	Class A shares are sold with an initial sales charge of up to 4.75% and a continuing service fee of up to 0.25% on an annual basis. Class A shares purchased in an amount of $1,000,000 or more are sold without an initial sales charge but are subject to a contingent deferred sales charge (“CDSC”) of 1% on redemptions within 18 months of purchase.
	Class B shares are sold without an initial sales charge but are subject to a distribution fee of 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 5% on redemptions in the first year of purchase, declining to 1% in the sixth year and 0% thereafter. Class B shares will automatically convert to Class A shares approximately eight years after their date of purchase.
	Class C shares are sold primarily with an initial sales charge of up to 1%, and a CDSC, if applicable, of 1% imposed on redemptions made within 18 months of purchase. Shares purchased through certain financial intermediaries may be bought without an initial sales charge and with a 1% CDSC on redemptions made within 12 months of purchase. All Class C shares are subject to a distribution fee of up to 0.75% and a service fee of up to 0.25% on an annual basis.
	Class D shares are sold without an initial sales charge but are subject to a distribution fee of up to 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 1% imposed on redemptions made within one year of purchase.
	Class I shares are offered to certain institutional clients. Class I shares are sold without any sales charges and are not subject to distribution and service fees.
	Class R shares are offered to certain employee benefit plans and are not available to all investors. They are sold without an initial sales charge, but are subject to a distribution fee of up to 0.25% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 1% on redemptions made within one year of a plan’s initial purchase of Class R shares.
	All classes of shares represent interests in the same portfolio of investments, have the same rights and are generally identical in all respects except that each class bears its own class-specific expenses, and has exclusive voting rights with respect to any matter on which a separate vote of any class is required.
2.	Significant Accounting Policies— The financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America which require management to make certain estimates and assumptions at the date of the financial statements. Actual results may differ from these estimates. These interim financial statements reflect all adjustments which are, in the opinion of management, necessary to a fair statement of the results for the interim period presented. All such adjustments are of a normal recurring nature. The following summarizes the significant accounting policies of the Fund:
	a.	Security Valuation— Securities traded on an exchange are valued at the last sales price on the primary exchange or market on which they are traded. Securities not listed on an exchange or security market are valued by independent pricing services based on bid prices, which consider such factors as coupons, maturities, credit ratings, liquidity, specific terms and features, and the US Treasury yield curve, or are valued by J. & W. Seligman & Co. Incorporated (the “Manager”) based on quotations provided by primary market makers in such securities. Securities for which market quotations are not readily available are valued at fair value determined in accordance with procedures approved by the Trustees. This can occur in the event of, among other things, natural disasters, acts of terrorism,
16

Notes to Financial Statements

		market disruptions, intra-day trading halts, and extreme market volatility in the US markets. Short-term holdings maturing in 60 days or less are valued at amortized cost.
	b.	Federal Taxes— There is no provision for federal income tax. The Fund has elected to be taxed as a regulated investment company and intends to distribute substantially all taxable net income and net gain realized.
	c.	Security Transactions and Related Investment Income— Investment transactions are recorded on trade dates. Identified cost of investments sold is used for both financial reporting and federal income tax purposes. Dividends receivable and payable are recorded on ex-dividend dates. Interest income is recorded on an accrual basis. The Fund amortizes discount and premium on portfolio securities for financial reporting purposes.
	d.	Repurchase Agreements— The Fund may enter into repurchase agreements with commercial banks and with broker/dealers deemed to be creditworthy by the Manager. Securities received as collateral subject to repurchase agreements are deposited with the Fund’s custodian and, pursuant to the terms of the repurchase agreement, must have an aggregate market value greater than or equal to the repurchase price plus accrued interest at all times. Procedures have been established to monitor, on a daily basis, the market value of repurchase agreements’ underlying securities to ensure the existence of the proper level of collateral.
	e.	Multiple Class Allocations— All income, expenses (other than class-specific expenses), and realized and unrealized gains or losses are allocated daily to each class of shares based upon the relative value of shares of each class. Class-specific expenses, which include distribution and service fees and any other items that are specifically attributable to a particular class, are charged directly to such class. For the six months ended June 30, 2004, distribution and service fees, shareholder account services and registration expenses were class-specific expenses.
	f.	Distributions to Shareholders— Dividends are declared daily and paid monthly. Other distributions paid by the Fund are recorded on ex-dividend dates. The treatment for financial statement purposes of distributions made to shareholders during the year from net investment income or net realized gains may differ from their ultimate treatment for federal income tax purposes. These differences are caused primarily by differences in the timing of the recognition of certain components of income, expense, or realized capital gain for federal income tax purposes. Where such differences are permanent in nature, they are reclassified in the components of net assets based on their ultimate characterization for federal income tax purposes. Any such reclassification will have no effect on net assets, results of operations, or net asset values per share of the Fund.
3.	Purchases and Sales of Securities— Purchases and sales of portfolio securities, excluding short-term investments, for the six months ended June 30, 2004, amounted to $210,803,168 and $313,425,951, respectively.
	At June 30, 2004, the cost of investments for federal income tax purposes was $613,770,972. The tax basis cost was greater than the cost for financial reporting purposes due to tax deferral of losses on wash sales in the amount of $532,428 and the amortization of premium for financial reporting purposes of $1,553,360. The tax basis gross unrealized appreciation and depreciation of portfolio securities amounted to $25,563,452 and $8,147,358, respectively.
4.	Management Fee, Distribution Services, and Other Transactions— The Manager manages the affairs of the Fund and provides the necessary personnel and facilities. Compensation of all officers of the Fund, all trustees of the Fund who are employees of the Manager, and all personnel of the Fund and the Manager is paid by the Manager. The Manager receives a fee, calculated daily and payable monthly, equal
17

Notes to Financial Statements

	to 0.65% per annum of the first $1 billion of the Fund’s average daily net assets and 0.55% per annum of the Fund’s average daily net assets in excess of $1 billion. The management fee reflected in the Statement of Operations represents 0.65% per annum of the Fund’s average daily net assets.
	Seligman Advisors, Inc. (the “Distributor”), agent for the distribution of the Fund’s shares, and an affiliate of the Manager, received concessions of $9,473 from sales of Class A shares. Commissions of $75,528 and $18,659 were paid to dealers from sales of Class A and Class C shares, respectively.
	The Fund has an Administration, Shareholder Services and Distribution Plan (the “Plan”) with respect to distribution of its shares. Under the Plan, with respect to Class A shares, service organizations can enter into agreements with the Distributor and receive a continuing fee of up to 0.25% on an annual basis, payable monthly, of the average daily net assets of the Class A shares attributable to the particular service organizations for providing personal services and/or the maintenance of shareholder accounts. The Distributor charges such fees to the Fund pursuant to the Plan. For the six months ended June 30, 2004, fees incurred under the Plan aggregated $281,351 or 0.25% per annum of the average daily net assets of Class A shares.
	Under the Plan, with respect to Class B shares, Class C shares, Class D shares, and Class R shares, service organizations can enter into agreements with the Distributor and receive a continuing fee for providing personal services and/or the maintenance of shareholder accounts of up to 0.25% on an annual basis of the average daily net assets of the Class B, Class C, Class D, and Class R shares for which the organizations are responsible; and, for Class C and Class D shares, fees for providing other distribution assistance of up to 0.75% (0.25%, in the case of Class R shares) on an annual basis of such average daily net assets. Such fees are paid monthly by the Fund to the Distributor pursuant to the Plan.
	With respect to Class B shares, a distribution fee of 0.75% on an annual basis of average daily net assets is payable monthly by the Fund to the Distributor; however, the Distributor has sold its rights to this fee with respect to a substantial portion of Class B shares to third parties (the “Purchasers”), which provide funding to the Distributor to enable it to pay commissions to dealers at the time of the sale of the related Class B shares.
	For the six months ended June 30, 2004, fees incurred under the Plan, equivalent to 1% per annum of the average daily net assets of Class B, Class C, and Class D shares, and 0.50% per annum of average daily net assets of Class R shares, amounted to $1,453,423, $283,047, $593,043, and $902, respectively.
	The Distributor is entitled to retain any CDSC imposed on certain redemptions of Class A , Class C, Class D and Class R shares. For the six months ended June 30, 2004, such charges amounted to $59,125.
	The Distributor has sold its rights to collect any CDSC imposed on redemptions of Class B shares to the Purchasers. In connection with the sale of its rights to collect any CDSC and the distribution fees with respect to Class B shares described above, the Distributor receives payments from the Purchasers based on the value of Class B shares sold. The aggregate of such payments and distribution fees retained by the Distributor, for the six months ended June 30, 2004, amounted to $8,693.
	Seligman Services, Inc., an affiliate of the Manager, is eligible to receive commissions from certain sales of shares of beneficial interest of the Fund, as well as distribution and service fees pursuant to the Plan. For the six months ended June 30, 2004, Seligman Services, Inc. received commissions of $1,840 from the sales of shares of the Fund. Seligman Services, Inc. also received distribution and service fees of $11,130, pursuant to the Plan.
	Seligman Data Corp., which is owned by certain associated investment companies, charged the Fund at cost $1,027,724 for shareholder account services in accordance with a methodology approved by the
18

Notes to Financial Statements
	Fund’s trustees. Class I shares receive more limited shareholder services than the Fund’s other classes of shares (the “Retail Classes”). Seligman Data Corp. does not allocate to Class I the costs of any of its departments that do not provide services to the Class I shareholders.
	Costs of Seligman Data Corp. directly attributable to the Retail Classes of the Fund were charged to those classes in proportion to their respective net asset values. Costs directly attributable to Class I shares were charged to Class I. The remaining charges were allocated to the Retail Classes and Class I by Seligman Data Corp. pursuant to a formula based on their net assets, shareholder transaction volumes and number of shareholder accounts.
	The Series and certain other associated investment companies (together, the “Guarantors”) have severally but not jointly guaranteed the performance and observance of all the terms and conditions of two leases entered into by Seligman Data Corp., including the payment of rent by Seligman Data Corp. (the “Guaranties”). The leases and the Guaranties expire in September 2008 and January 2009. The obligation of the Series to pay any amount due under either Guaranty is limited to a specified percentage of the full amount, which generally is based on the Series’ percentage of the expenses billed by Seligman Data Corp. to all Guarantors in the preceding calendar quarter. As of June 30, 2004, the Series’ potential obligation under the Guaranties is $541,800. As of June 30, 2004, no event has occurred which would result in the Series becoming liable to make any payment under a Guaranty. The Fund would bear a portion of any payments made by the Series under the Guaranties. A portion of rent paid by Seligman Data Corp. is charged to the Fund as part of Seligman Data Corp.’s shareholder account services cost.
	Certain officers and trustees of the Fund are officers or directors of the Manager, the Distributor, Seligman Services, Inc., and/or Seligman Data Corp.
	The Fund has a compensation arrangement under which trustees who receive fees may elect to defer receiving such fees. Trustees may elect to have their deferred fees accrue interest or earn a return based on the performance of the Fund or other funds in the Seligman Group of Investment Companies. The cost of such fees and earnings/loss accrued thereon is included in trustees’ fees and expenses, and the accumulated balance thereof at June 30, 2004, of $25,063 is included in accrued expenses and other liabilities. Deferred fees and related accrued earnings are not deductible by the Fund for federal income tax purposes until such amounts are paid.
5.	Capital Loss Carryforward and Other Adjustments — At December 31, 2003, the Fund had a net capital loss carryforward for federal income tax purposes of $1,457,014,138, which is available for offset against future taxable net capital gains, with $88,447,879 expiring in 2007, $255,659,981 expiring in 2008, $668,622,539 expiring in 2009, and $444,283,739 expiring in 2010. The amount was determined after adjustments for certain differences between financial reporting and tax purposes, such as wash sale losses. Accordingly, no capital gain distributions are expected to be paid to shareholders until net capital gains have been realized in excess of the available capital loss carryforwards.
6.	Committed Line of Credit— The Fund is a participant in a joint $425 million committed line of credit that is shared by substantially all open-end funds in the Seligman Group of Investment Companies. The trustees have currently limited the Fund’s borrowings to 10% of its net assets. Borrowings pursuant to the credit facility are subject to interest at a rate equal to the overnight federal funds rate plus 0.50%. The Fund incurs a commitment fee of 0.10% per annum on its share of the unused portion of the credit facility. The credit facility may be drawn upon only for temporary purposes and is subject to certain other customary restrictions. The credit facility commitment expires in June 2005, but is renewable annually with the consent of the participating banks. For the six months ended June 30, 2004, the Fund did not borrow from the credit facility.

19

Notes to Financial Statements

7. Transactions in Shares of Beneficial Interest— The Fund has authorized unlimited shares of $0.001 par value Shares of Beneficial Interest. Transactions in Shares of Beneficial Interest were as follows:

	Six Months Ended June 30, 2004						Year Ended December 31, 2003
Class A	Shares			Amount			Shares			Amount
Net proceeds from sales of shares		3,690,171		$	12,971,592			19,750,005		$	64,845,052
Investment of dividends		1,420,499			4,927,896			3,372,353			11,257,976
Exchanged from associated funds		4,520,401			15,630,243			29,714,802			98,511,770
Converted from Class B**		1,265,803			4,325,842			—			—
Total		10,896,874			37,855,573			52,837,160			174,614,798
Cost of shares repurchased		(11,494,461	)		(40,040,487	)		(30,635,465	)		(102,529,746	)
Exchanged into associated funds		(7,127,280	)		(24,690,406	)		(32,468,232	)		(107,935,587	)
Total		(18,621,741	)		(64,730,893	)		(63,103,697	)		(210,465,333	)
Decrease		(7,724,867	)	$	(26,875,320	)		(10,266,537	)	$	(35,850,535	)
Class B	Shares			Amount			Shares			Amount
Net proceeds from sales of shares		626,788		$	2,203,106			2,392,996		$	8,001,358
Investment of dividends		1,444,529			5,024,882			3,241,500			10,864,949
Exchanged from associated funds		713,239			2,502,846			7,082,946			23,575,331
Total		2,784,556			9,730,834			12,717,442			42,441,638
Cost of shares repurchased		(11,690,075	)		(40,687,760	)		(20,972,117	)		(70,334,266	)
Exchanged into associated funds		(2,649,683	)		(9,205,577	)		(4,978,261	)		(16,519,189	)
Converted to Class A**		(1,261,695	)		(4,321,717	)		—			—
Total		(15,601,453	)		(54,215,054	)		(25,950,378	)		(86,853,455	)
Decrease		(12,816,897	)	$	(44,484,220	)		(13,232,936	)	$	(44,411,817	)
Class C	Shares			Amount			Shares			Amount
Net proceeds from sales of shares		781,649		$	2,774,085			4,172,255		$	13,957,406
Investment of dividends		339,333			1,181,433			635,232			2,132,580
Exchanged from associated funds		195,762			687,665			1,534,952			5,162,235
Total		1,316,744			4,643,183			6,342,439			21,252,221
Cost of shares repurchased		(2,413,795	)		(8,392,389	)		(4,832,192	)		(16,224,882	)
Exchanged into associated funds		(450,132	)		(1,560,856	)		(1,301,150	)		(4,330,091	)
Total		(2,863,927	)		(9,953,245	)		(6,133,342	)		(20,554,973	)
Increase (decrease)		(1,547,183	)	$	(5,310,062	)		209,097		$	697,248
Class D		Shares			Amount			Shares			Amount
Net proceeds from sales of shares		447,484		$	1,560,949			971,003		$	3,242,054
Investment of dividends		733,037			2,552,773			1,714,869			5,744,394
Exchanged from associated funds		399,455			1,419,279			1,631,198			5,447,906
Total		1,579,976			5,533,001			4,317,070			14,434,354
Cost of shares repurchased		(5,158,868	)		(18,006,231	)		(9,663,490	)		(32,471,269	)
Exchanged into associated funds		(576,472	)		(1,993,543	)		(1,276,564	)		(4,296,085	)
Total		(5,735,340	)		(19,999,774	)		(10,940,054	)		(36,767,354	)
Decrease		(4,155,364	)	$	(14,466,773	)		(6,622,984	)	$	(22,333,000	)

See footnotes on page 21.

20

Notes to Financial Statements

	Six Months Ended June 30, 2004						Year Ended December 31, 2003
Class I	Shares			Amount			Shares			Amount
Net proceeds from sales of shares		245,815		$	863,501			575,349		$	1,913,003
Investment of dividends		72,684			251,430			107,251			359,386
Total		318,499			1,114,931			682,600			2,272,389
Cost of shares repurchased		(75,080	)		(256,942	)		(115,864	)		(389,219	)
Increase		243,419		$	857,989			566,736		$	1,883,170
							April 30, 2003* to December 31, 2003
Class R	Shares			Amount			Shares			Amount
Net proceeds from sales of shares		171,454		$	599,810			445		$	1,500
Investment of dividends		3,490			11,854			23			77
Total		174,944			611,664			468			1,577
Cost of shares repurchased		(2,344	)		(8,002	)		—			—
Increase		172,600		$	603,662			468		$	1,577

*	Commencement of offering of shares
**	Automatic conversion of Class B shares to Class A shares approximately eight years after the initial purchase date

8.	Other Matters — The Manager has conducted an extensive internal review in response to developments regarding disruptive or illegal trading practices within the mutual fund industry. As of September 2003, the Manager had one arrangement that permitted frequent trading in the Seligman registered investment companies (“Seligman Funds”). This arrangement was in the process of being closed down by the Manager before the first proceedings relating to trading practices within the mutual fund industry were publicly announced. Based on a review of the Manager’s records for 2001 through 2003, the Manager identified three other arrangements that had permitted frequent trading in the Seligman Funds. All three had already been terminated prior to the end of September 2002. The Securities and Exchange Commission (the “SEC”), the NASD and the Attorney General of the State of New York also are reviewing these matters.
	The Manager also has reviewed its practice of placing some of the Seligman Funds’ orders to buy and sell portfolio securities with brokerage firms in recognition of their sales of Seligman Funds. This practice is permissible when done properly; however, the Manager believes that it may have violated applicable requirements for certain of such orders as a result of compensation arrangements the Manager had with certain brokerage firms. The Manager discontinued this practice entirely in October 2003. The Manager is confident that the execution of all such orders was consistent with its best execution obligations and that the Seligman Funds did not pay higher brokerage commissions than they would otherwise have paid for comparable transactions. The Manager has also responded fully to information requests from the SEC and the NASD relating to the Manager’s use of revenue sharing and fund portfolio brokerage commissions and will continue to provide additional information if, and as, requested.
	The results of the Manager’s internal reviews were presented to the Independent Trustees of the Seligman Funds. In order to resolve matters with the Independent Trustees relating to the four arrangements that permitted frequent trading, which did not adversely affect Seligman High-Yield Bond Series, the Manager has made payments to three funds and has agreed to waive a portion of its management fee with respect to another fund. In order to resolve matters with the Independent Trustees with regard to portfolio brokerage commissions, in May 2004, the Manager made payments to each of twenty-four funds in an amount equal to the commissions paid by each such fund during the period from 1998 through 2003 to certain brokerage firms in recognition of sales of fund shares. Seligman High-Yield Bond Series generally does not pay brokerage commissions and thus did not receive any payment from the Manager.

21

Financial Highlights

The tables below are intended to help you understand each Class’s financial performance for the past five and one-half years or from its inception if less than five and one-half years. Certain information reflects financial results for a single share of Beneficial Interest of a Class that was held throughout the periods shown. Per share amounts are calculated using average shares outstanding. “Total return” shows the rate that you would have earned (or lost) on an investment in each Class, assuming you reinvested all your dividends and capital gain distributions. Total returns do not reflect any taxes or sales charges and are not annualized for periods of less than one year.

CLASS A
	Six Months Ended 6/30/04				Year Ended December 31,
					2003			2002			2001ø			2000			1999
Per Share Data:
Net Asset Value, Beginning of Period		$	3.55		$	3.16		$	3.69		$	4.99		$	6.26		$	6.95
Income (Loss) from
Investment Operations:
Net investment income			0.14			0.26			0.28			0.47			0.64			0.69
Net realized and unrealized gain (loss)
on investments			(0.16	)		0.40			(0.47	)		(1.21	)		(1.21	)		(0.68	)
Total from Investment Operations			(0.02	)		0.66			(0.19	)		(0.74	)		(0.57	)		0.01
Less Distributions:
Dividends from net investment income			(0.14	)		(0.26	)		(0.28	)		(0.47	)		(0.64	)		(0.70	)
Dividends in excess of
net investment income			—			(0.01	)		—			—			(0.02	)		—
Return of capital			—			—			(0.06	)		(0.09	)		(0.04	)		—
Total Distributions			(0.14	)		(0.27	)		(0.34	)		(0.56	)		(0.70	)		(0.70	)
Net Asset Value, End of Period		$	3.39		$	3.55		$	3.16		$	3.69		$	4.99		$	6.26
Total Return:			(0.49	)%		21.84	%		(5.35	)%		(15.91	)%		(10.02	)%		0.09	%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	211,505		$	248,869		$	254,191		$	360,394		$	584,944		$	923,395
Ratio of expenses to average net assets			1.28	%†		1.30	%		1.31	%		1.16	%		1.09	%		1.08	%
Ratio of net investment income to
average net assets			8.36	%†		7.88	%		8.53	%		10.61	%		11.08	%		10.30	%
Portfolio turnover rate			31.19	%		141.00	%		117.82	%		53.04	%		27.45	%		40.60	%

See footnotes on page 26.

22

Financial Highlights

CLASS B
	Six Months Ended 6/30/04
					Year Ended December 31,
					2003			2002			2001ø			2000			1999
Per Share Data:
Net Asset Value, Beginning of Period		$	3.55		$	3.17		$	3.70		$	5.00		$	6.26		$	6.95
Income (Loss) from Investment Operations:
Net investment income			0.13			0.24			0.26			0.43			0.59			0.64
Net realized and unrealized gain (loss) on investments			(0.16	)		0.39			(0.48	)		(1.21	)		(1.20	)		(0.68	)
Total from Investment Operations			(0.03	)		0.63			(0.22	)		(0.78	)		(0.61	)		(0.04	)
Less Distributions:
Dividends from net investment income			(0.13	)		(0.24	)		(0.25	)		(0.43	)		(0.59	)		(0.65	)
Dividends in excess of net investment income			—			(0.01	)		—			—			(0.02	)		—
Return of capital			—			—			(0.06	)		(0.09	)		(0.04	)		—
Total Distributions			(0.13	)		(0.25	)		(0.31	)		(0.52	)		(0.65	)		(0.65	)
Net Asset Value, End of Period		$	3.39		$	3.55		$	3.17		$	3.70		$	5.00		$	6.26
Total Return:			(0.88	)%		20.64	%		(6.07	)%		(16.58	)%		(10.66	)%		(0.69	)%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	261,411		$	319,267		$	326,688		$	483,041		$	723,751		$	1,073,910
Ratio of expenses to average net assets			2.03	%†		2.05	%		2.06	%		1.91	%		1.84	%		1.83	%
Ratio of net investment income
to average net assets			7.61	%†		7.13	%		7.78	%		9.86	%		10.33	%		9.55	%
Portfolio turnover rate			31.19	%		141.00	%		117.82	%		53.04	%		27.45	%		40.60	%

See footnotes on page 26.

23

Financial Highlights

CLASS C
	Six Months Ended 6/30/04				Year Ended December 31,
					2003			2002			2001ø			2000			1999
Per Share Data:
Net Asset Value, Beginning of Period		$	3.56		$	3.17		$	3.70		$	5.00		$	6.27		$	6.75
Income (Loss) from
Investment Operations:
Net investment income			0.13			0.24			0.26			0.43			0.59			0.32
Net realized and unrealized gain (loss)    on investments			(0.16	)		0.40			(0.48	)		(1.21	)		(1.21	)		(0.41	)
Total from Investment Operations			(0.03	)		0.64			(0.22	)		(0.78	)		(0.62	)		(0.09	)
Less Distributions:
Dividends from net investment income			(0.13	)		(0.24	)		(0.25	)		(0.43	)		(0.59	)		(0.39	)
Dividends in excess of    net investment income			—			(0.01	)		—			—			(0.02	)		—
Return of capital			—			—			(0.06	)		(0.09	)		(0.04	)		—
Total Distributions			(0.13	)		(0.25	)		(0.31	)		(0.52	)		(0.65	)		(0.39	)
Net Asset Value, End of Period		$	3.40		$	3.56		$	3.17		$	3.70		$	5.00		$	6.27
Total Return:			(0.87	)%		20.98	%		(6.08	)%		(16.59	)%		(10.81	)%		(1.71	)%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	51,943		$	59,892		$	52,709		$	78,721		$	87,204		$	51,815
Ratio of expenses to average net assets			2.03	%†		2.05	%		2.06	%		1.91	%		1.84	%		1.81	%†
Ratio of net investment income to average net assets			7.61	%†		7.13	%		7.78	%		9.86	%		10.33	%		9.78	%†
Portfolio turnover rate			31.19	%		141.00	%		117.82	%		53.04	%		27.45	%		40.60	%**

See footnotes on page 26.

24

Financial Highlights

CLASS D
	Six Months Ended 6/30/04				Year Ended December 31,
					2003			2002			2001ø			2000			1999
Per Share Data:
Net Asset Value, Beginning of Period		$	3.56		$	3.17		$	3.70		$	5.00		$	6.27		$	6.95
Income (Loss) from Investment Operations:
Net investment income			0.13			0.24			0.26			0.43			0.59			0.64
Net realized and unrealized gain (loss    on investments			(0.16	)		0.40			(0.48	)		(1.21	)		(1.21	)		(0.67	)
Total from Investment Operations			(0.03	)		0.64			(0.22	)		(0.78	)		(0.62	)		(0.03	)
Less Distributions:
Dividends from net investment income			(0.13	)		(0.24	)		(0.25	)		(0.43	)		(0.59	)		(0.65	)
Dividends in excess of    net investment income			—			(0.01	)		—			—			(0.02	)		—
Return of capital			—			—			(0.06	)		(0.09	)		(0.04	)		—
Total Distributions			(0.13	)		(0.25	)		(0.31	)		(0.52	)		(0.65	)		(0.65	)
Net Asset Value, End of Period		$	3.40		$	3.56		$	3.17		$	3.70		$	5.00		$	6.27
Total Return:			(0.87	)%		20.98	%		(6.08	)%		(16.59	)%		(10.81	)%		(0.54	)%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	108,685		$	128,582		$	135,595		$	217,133		$	369,286		$	656,727
Ratio of expenses to average net assets			2.03	%†		2.05	%		2.06	%		1.91	%		1.84	%		1.83	%
Ratio of net investment income    to average net assets			7.61	%†		7.13	%		7.78	%		9.86	%		10.33	%		9.55	%
Portfolio turnover rate			31.19	%		141.00	%		117.82	%		53.04	%		27.45	%		40.60	%

See footnotes on page 26.

25

Financial Highlights

CLASS I															CLASS R
	Six Months Ended 6/30/04				Year Ended December 31,						11/30/01* to 12/31/01ø				Six Months Ended 6/30/04				4/30/03* to 12/31/03
					2003			2002
Per Share Data:
Net Asset Value, Beginning of Period		$	3.55		$	3.16		$	3.69			$	3.77			$	3.55		$	3.37
Income (Loss) from Investment Operations:
Net investment income			0.15			0.28			0.29				0.02				0.14			0.17
Net realized and unrealized gain (loss)    on investments			(0.16	)		0.40			(0.47	)			(0.05	)			(0.16	)		0.19
Total from Investment Operations			(0.01	)		0.68			(0.18	)			(0.03	)			(0.02	)		0.36
Less Distributions:
Dividends from net investment income			(0.15	)		(0.28	)		(0.29	)			(0.01	)			(0.14	)		(0.17	)
Dividends in excess of    net investment income			—			(0.01	)		—				—				—			(0.01	)
Return of capital			—			—			(0.06	)			(0.04	)			—			—
Total Distributions			(0.15	)		(0.29	)		(0.35	)			(0.05	)			(0.14	)		(0.18	)
Net Asset Value, End of Period		$	3.39		$	3.55		$	3.16			$	3.69			$	3.39		$	3.55
Total Return:			(0.29	)%		22.38	%		(5.02	)%			(0.91	)%			(0.62	)%		10.99	%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)		$	6,051		$	5,472		$	3,085			$	53			$	586		$	2
Ratio of expenses to average net assets			0.85	%†		0.95	%		0.93	%			0.78	%†			1.53	%†		1.56	%†
Ratio of net investment income    to average net assets			8.80	%†		8.23	%		8.91	%			11.48	%†			8.11	%†		7.64	%†
Portfolio turnover rate			31.19	%		141.00	%		117.82	%			53.04	%***			31.19	%		141.00	%‡
Without expense reimbursement:‡‡    Ratio of expenses to average net assets									0.98	%			1.43	%†
Ratio of net investment income    to average net assets									8.86	%			10.83	%†

†	Annualized.
*	Commencement of offering of shares.
**	For the year ended December 31, 1999.
***	For the year ended December 31, 2001.
‡	For the year ended December 31, 2003.
‡‡	The Manager, at its discretion, reimbursed certain expenses of Class I shares.
ø	As required, effective January 1, 2001, the Fund adopted the provisions of the AICPA Audit and Accounting Guide for Investment Companies and began amortizing premium on debt securities. The effect of this change for the year ended December 31, 2001, was to decrease net investment income per share by $0.01 for Classes A, B, C and D, decrease net realized and unrealized loss on investments per share by $0.01 for Classes A, B, C and D, and decrease the ratios of net investment income to average net assets from 10.77% to 10.61% for Class A, from 10.02% to 9.86% for Classes B, C, and D, and from 11.53% to 11.48% for Class I. The effect of this change per share for Class I was less than $0.01. The ratios for periods prior to January 1, 2001, have not been restated.

See Notes to Financial Statements.

26

Report of Independent Registered
Public Accounting Firm

The Trustees and Shareholders,
Seligman High-Yield Bond Series of
Seligman High Income Fund Series:

We have audited the accompanying statement of assets and liabilities of Seligman High-Yield Bond Series (the “Fund”), including the portfolio of investments, as of June 30, 2004, and the related statement of operations for the six months then ended, the statements of changes in net assets for the six months then ended and for the year ended December 31, 2003, and the financial highlights for each of the periods presented. These financial statements and financial highlights are the responsibility of the Fund’s management. Our responsibility is to express an opinion on these finan-cial statements and financial highlights based on our audits.

We conducted our audits in accordance with auditing standards of the Public Company Accounting Oversight Board (United States). Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements and financial highlights are free of material misstatement. An audit includes examining, on a test basis, evidence supporting the amounts and disclosures in the financial statements. Our procedures included confirmation of securities owned as of June 30, 2004, by correspondence with the Fund’s custodian and brokers. An audit also includes assessing the accounting principles used and significant estimates made by management, as well as evaluating the overall financial statement presentation. We believe that our audits provide a reasonable basis for our opinion.

In our opinion, the financial statements and financial highlights referred to above present fairly, in all material respects, the financial position of Seligman High-Yield Bond Series as of June 30, 2004, the results of its operations for the six months then ended, the changes in its net assets for the six months then ended and for the year ended December 31, 2003, and the financial highlights for the respective stated periods, in conformity with accounting principles generally accepted in the United States of America.

DELOITTE & TOUCHE LLP
New York, New York
August 13, 2004

27

Trustees

Robert B. Catell 2, 3
•	Chairman, Chief Executive Officer and Director, KeySpan Corporation
John R. Galvin 1, 3
•	Dean Emeritus,
•	Fletcher School of Law and Diplomacy at Tufts University
Alice S. Ilchman 2, 3
•	President Emerita, Sarah Lawrence College
•	Director, Jeannette K. Watson Summer Fellowship
•	Trustee, Committee for Economic Development
Frank A. McPherson 2, 3
•	Retired Chairman of the Board and Chief Executive Officer, Kerr-McGee Corporation
•	Director, ConocoPhillips
•	Director, Integris Health
John E. Merow 1, 3
•	Retired Chairman and Senior Partner, Sullivan & Cromwell LLP
•	Director, Commonwealth Industries, Inc.
•	Trustee, New York-Presbyterian Hospital
Betsy S. Michel 1, 3
•	Trustee, The Geraldine R. Dodge Foundation
William C. Morris
•	Chairman, J. & W. Seligman & Co. Incorporated
•	Chairman, Carbo Ceramics Inc.
Leroy C. Richie 1, 3
•	Chairman and Chief Executive Officer, Q Standards Worldwide, Inc.
•	Director, Kerr-McGee Corporation
Robert L. Shafer 2, 3
•	Retired Vice President, Pfizer Inc.
James N. Whitson 1, 3
•	Retired Executive Vice President and Chief Operating Officer, Sammons Enterprises, Inc.
•	Director, CommScope, Inc.
Brian T. Zino
•	Director and President, J. & W. Seligman & Co. Incorporated
•	Chairman, Seligman Data Corp.
•	Director, ICI Mutual Insurance Company
•	Member of the Board of Governors, Investment Company Institute

Member:	1	Audit Committee
	2	Trustee Nominating Committee
	3	Board Operations Committee

Executive Officers

William C. Morris

Chairman

Brian T. Zino

President and Chief Executive Officer

Kendall C. Peterson

Vice President

Thomas G. Rose

Vice President

Lawrence P. Vogel

Vice President and Treasurer

Frank J. Nasta

Secretary

28

ITEM 2. CODE OF ETHICS.
Not applicable.

ITEM 3. AUDIT COMMITTEE FINANCIAL EXPERT.
Not applicable.

ITEM 4. PRINCIPAL ACCOUNTANT FEES AND SERVICES.
Not applicable.

ITEM 5. AUDIT COMMITTEE OF LISTED REGISTRANTS.
Not applicable.

ITEM 6. SCHEDULE OF INVESTMENTS.
Not applicable.

ITEM 7. DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END MANAGEMENT INVESTMENT COMPANIES.
Not applicable.

ITEM 8. PURCHASES OF EQUITY SECURITIES BY CLOSED-END MANAGEMENT INVESTMENT COMPANY AND AFFILIATED PURCHASERS.
Not applicable.

ITEM 9. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.
Not applicable.

ITEM 10. CONTROLS AND PROCEDURES.

(a)   The registrant’s principal executive officer and principal financial officer have concluded, based upon their evaluation of the registrant’s disclosure controls and procedures as conducted within 90 days of the filing date of this report, that these disclosure controls and procedures provide reasonable assurance that material information required to be disclosed by the registrant in the report it files or submits on Form N-CSR is recorded, processed, summarized and reported, within the time periods specified in the Commission’s rules and forms and that such material information is accumulated and communicated to the registrant’s management, including its principal executive officer and principal financial officer, as appropriate, in order to allow timely decisions regarding required disclosure.

(b)   The registrant’s principal executive officer and principal financial officer are aware of no changes in the registrant’s internal control over financial reporting that occurred during the registrant’s most recent fiscal half-year that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting.

ITEM 11. EXHIBITS.

(a)(1) Not applicable.

(a)(2) Certifications of principal executive officer and principal financial officer as required by Rule 30a-2(a) under the Investment Company Act of 1940.

(a)(3) Not applicable.

(b)     Certifications of chief executive officer and chief financial officer as required by Rule 30a-2(b) under the Investment Company Act of 1940.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

SELIGMAN HIGH INCOME FUND SERIES:

By: /S/  BRIAN T. ZINO
Brian T. Zino
President and Chief Executive Officer

Date:  September 1, 2004

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed below by the following persons on behalf of the registrant in the capacities and on the dates indicated.

By: /S/  BRIAN T. ZINO
Brian T. Zino
President and Chief Executive Officer

Date:  September 1, 2004

By: /S/  LAWRENCE P. VOGEL
Lawrence P. Vogel
Vice President, Treasurer and Chief Financial Officer

Date:  September 1, 2004

SELIGMAN HIGH INCOME FUND SERIES:

EXHIBIT INDEX

(a)(2) Certifications of principal executive officer and principal financial officer as required by Rule 30a-2(a) under the Investment Company Act of 1940.

(b)     Certification of chief executive officer and chief financial officer as required by Rule 30a-2(b) of the Investment Company Act of 1940.