Exhibit 99.1

Alexion Pharmaceuticals Reports Fourth Quarter and Year End Results & Fiscal 2005 Outlook

- Initiation of Three Phase III Programs Highlight the Quarter -

CHESHIRE, Conn., Sept. 24 /PRNewswire-FirstCall/ — Alexion Pharmaceuticals, Inc. (Nasdaq: ALXN) today announced the financial results for its fourth quarter and fiscal year ended July 31, 2004.

For the fourth quarter ended July 31, 2004, Alexion reported revenues of $4.15 million compared to $167,000 in the same quarterly period last year. In July 2004, the Company recognized a $4 million milestone payment from Procter & Gamble Pharmaceuticals (“P&G”) concurrent with the dosing of its first patient in the APEX-AMI trial. All other revenue in the fourth quarter of fiscal years 2004 and 2003 was primarily due to the amortization of the $10 million upfront fee paid in February 1999 to Alexion by P&G.

The Company’s research and development expenses for the quarter were $17.84 million compared to $18.59 million for the same period last year. The decrease for the quarter was due to lower manufacturing and manufacturing development costs associated with the lead C5 inhibitor candidates, eculizumab and pexelizumab, and lower discovery costs due principally to lower external license fees. These decreases were partially offset by higher clinical development costs. Clinical development costs in the fourth quarter of fiscal 2003 were lower than in 2004 primarily due to a shift to P&G in fiscal year 2003 of expenses associated with the PRIMO-CABG clinical trial. Per the Company’s revised collaboration agreement with P&G, P&G was responsible for the second 50% of costs associated with the Phase III PRIMO—CABG study.

General and administrative expenses were $4.78 million for the quarter compared to $3.14 million for the same period last year. The $1.64 million increase was principally due to increased costs of $1.1 million associated with pre-commercialization and business development activities in support of the Company’s PNH program as well as increased payroll costs, occupancy costs and professional fees to support continued growth of the Company’s operations.

The Company recorded an additional impairment of fixed assets charge of $760,000 during the quarter ended July 31, 2004 to write down the value of its subsidiary’s, Columbus Farming Corporation (“CFC”), UniGraft xenotransplantation facility (principally land, buildings and laboratory equipment), to its estimated fair market value of $450,000. Accordingly, total operating expenses for the quarter increased to $23.37 million compared to $21.73 million in the same three-month period ended July 31, 2003.

The Company recorded investment income for the quarter of $658,000 compared to $1.07 million for the same three-month period last year. The decrease was primarily due to reduced market interest rates and lower average cash balances. Interest expense for the quarter, primarily on the

- 1-

Company’s $120 million convertible subordinated notes, was $1.93 million as compared to $1.91 million for the same three-month period last year.

For the quarter ended July 31, 2004, Alexion recognized a $372,000 tax benefit resulting from exchanging its state of Connecticut research and development credits for cash.

As a result of the above factors, the Company incurred a net loss for the quarter of $20.12 million, or $0.88 per share, versus a net loss of $21.58 million or $1.18 per share for the same three-month period in 2003.

“Alexion achieved several critical milestones in the last several months, most notably reaching agreement with the FDA under the SPA process for the design of three independent pivotal Phase III clinical programs led by eculizumab in PNH which includes the TRIUMPH and SHEPHERD trials, and pexelizumab for the PRIMO-CABG2 and APEX-AMI trials,” said David W. Keiser, President and Chief Operating Officer of Alexion. “Also important has been our success in strengthening the Company’s financial picture through the recently completed $80.9 million financing. Our efforts and resources are now sharply focused on the timely and successful execution of these advanced clinical programs and on our preparations for the subsequent regulatory review and commercialization of these products.”

Year End Results

For the 12 months ended July 31, 2004, Alexion’s revenues were $4.61 million compared to $877,000 for last fiscal year. In July 2004, the Company recognized a $4 million milestone payment from P&G related to the dosing of its first patient in the APEX-AMI trial. Substantially all other revenue in fiscal year 2004 and 2003 was primarily from the amortization of the $10 million upfront fee paid to the Company in February 1999 by P&G.

Research and development expenditures were $59.84 million for the full year ended July 31, 2004, compared to $71.04 million last fiscal year. The $11.20 million decrease resulted primarily from i) lower clinical development costs of $4.7 million due to the completion of the pexelizumab Phase III PRIMO-CABG clinical trial; ii) lower costs for discovery research of $4.6 million due to lower external research and license fees and the termination of the Unigraft program at CFC; and iii) lower manufacturing and manufacturing development activities of $3.4 million resulting from the amended manufacturing agreement with Lonza and the timing of costs related to the manufacture of pexelizumab. These lower expenses were partially offset by increased payroll and benefits costs and increased occupancy and depreciation costs.

General and administrative expenses were $14.46 million for the year compared to $10.87 million for last fiscal year. The increase in general and administrative expenses of $3.59 million in fiscal year 2004 as compared to 2003 was due principally to increased pre-commercialization and business development activities of approximately $1.8 million in support of the Company’s PNH program, as well as continued growth of its operations of $1.8 million.

- 2 -

The Company recorded an impairment of fixed assets charge of $760,000 in fiscal 2004 and $2.56 million in fiscal 2003 related to the decision to terminate the UniGraft xenotransplantation program and write down the value of CFC’s assets to fair market value. Accordingly, total operating expenses decreased to $75.06 million for the fiscal year compared to $84.47 million in the 12 months ended July 31, 2003.

Alexion recorded investment income for the 12 months ended July 31, 2003 of $3.37 million compared to $5.81 million for last fiscal year. The decrease was primarily due to reduced market interest rates and lower average cash balances. Interest expense was $7.70 million for the 12 months ended July 31, 2004 versus $7.69 million for last fiscal year. A state tax benefit of $691,000 was recognized in fiscal year 2004 as compared to $1.0 million for fiscal year 2003.

Net loss for the 12 months decreased to $74.10 million or $3.43 per share from a net loss of $84.47 million or $4.64 per share recorded for last fiscal year.

As of July 31, 2004, Alexion had approximately $266.5 million in cash, cash equivalents and marketable securities. In July 2004, the Company sold 5.5 million shares of common stock at a price of $15.50 per share resulting in net proceeds of approximately $80.9 million, net of underwriting discounts, fees and other expenses of approximately $4.4 million related to the transaction. In September 2003, the Company sold 3.6 million shares of common stock at a price of $13.00 per share resulting in net proceeds of approximately $43.9 million, net of underwriting discounts, fees and other expenses of approximately $2.9 million related to the transaction. The Company expects to use the net proceeds of these sales of common stock to fund working capital and other general corporate purposes, including additional clinical trials of eculizumab and pexelizumab, as well as other research and product development activities.

Fiscal year 2005 outlook: For Alexion’s 2005 fiscal year, which began August 1, 2004, guidance with respect to the projected net loss is $105 - $115 million. Our financial results and the amount of our loss may vary depending upon many factors, including the extent and speed with which the Company can advance the Phase III clinical development programs for eculizumab in PNH, and for pexelizumab in CABG and acute myocardial infarction (“AMI”). Any delays may cause expenses to increase and/or to be extended into fiscal year 2006. This guidance also excludes any impact of any potential business development activities that may occur during the year.

Alexion is engaged in the discovery and development of therapeutic products aimed at treating patients with a wide array of severe disease states, including hematologic and cardiovascular disorders, autoimmune diseases and cancer. Alexion’s two lead product candidates, pexelizumab and eculizumab, are currently undergoing evaluation in several clinical development programs. Alexion has completed a Phase III clinical study with pexelizumab in coronary artery bypass graft (“CABG”) surgery patients undergoing cardiopulmonary bypass (“CPB”), and two large Phase II studies with pexelizumab in acute myocardial infarction (“AMI”) patients. The

- 3 -

Phase III trial and the Phase II trials were conducted in collaboration with Procter and Gamble Pharmaceuticals. Separately, after completing agreements with the FDA under the Special Protocol Assessment (“SPA”) process for the design of Phase III pivotal trials of pexelizumab in CABG patients undergoing CPB and in AMI patients treated with primary percutaneous intervention, Alexion has commenced Phase III pivotal trials in CABG and in AMI patients. In addition, Alexion has completed a pilot clinical trial using eculizumab for the treatment of patients with paroxysmal nocturnal hemoglobinuria (“PNH”). Under the Special Protocol Assessment process, the FDA has agreed to protocols for the two trials constituting the pivotal Phase III program of eculizumab in PNH. Eculizumab is also in development in rheumatoid arthritis and membranous nephritis. Alexion is engaged in discovering and developing a pipeline of additional antibody therapeutics targeting severe unmet medical needs, through its wholly owned subsidiary, Alexion Antibody Technologies, Inc. This press release and further information about Alexion Pharmaceuticals, Inc. can be found on the World Wide Web at: http://www.alexionpharm.com.

ALEXION PHARMACEUTICALS, INC

Selected Financial Data

Statement of Operations

(dollars in thousands except per share data)

	Quarter ended July 31,						Year ended July 31,
	2004			2003			2004			2003
Contract research revenues	$	4,147		$	167		$	4,609		$	877
Operating expenses
Research and development		17,836			18,588			59,840			71,042
General and administrative		4,776			3,142			14,459			10,869
Impairment of fixed assets		760			—			760			2,560
Total operating expenses		23,372			21,730			75,059			84,471
Operating loss		(19,225	)		(21,563	)		(70,450	)		(83,594	)
Other income and expense
Investment income		658			1,074			3,373			5,809
Investment expense		(1,928	)		(1,911	)		(7,709	)		(7,694	)
Loss before benefit from state tax benefit		(20,495	)		(22,400	)		(74,786	)		(85,479	)
State tax benefit		372			816			691			1,012
Net loss	$	(20,123	)	$	(21,584	)	$	(74,095	)	$	(84,467	)
Basic and diluted net loss per share	$	(0.88	)	$	(1.18	)	$	(3.43	)	$	(4.64	)
Shares used in computing basic and diluted net loss per common share		21,677			18,215			21,622			18,209

-4-

Balance Sheet Data

(dollars in thousands)

	July 31, 2004		July 31, 2003
Cash, cash equivalents and marketable securities	$	266,501	$	215,410
Total assets	$	319,575	$	267,227
Net stockholders’ equity	$	172,522	$	120,286

This news release contains forward-looking statements. Such statements are subject to factors that may cause Alexion’s results and plans to differ from those expected, including the results of pre-clinical or clinical studies (including termination or delay in clinical programs), the need for additional research and testing, delays in arranging satisfactory manufacturing capability, inability to acquire funding on timely and satisfactory terms, delays in developing or adverse changes in commercial relationships, the possibility that results of earlier clinical trials are not predictive of safety and efficacy results in later clinical trials, dependence on Procter & Gamble Pharmaceuticals for development and commercialization of pexelizumab, the risk that third parties won’t agree to license any necessary intellectual property to us on reasonable terms, and a variety of other risks set forth from time to time in Alexion’s filings with the Securities and Exchange Commission, including but not limited to the risks discussed in Alexion’s Annual Report on Form 10-K for the year ended July 31, 2003 and in our other filings with the Securities and Exchange Commission. P&GP retains the development rights and the termination rights discussed in Alexion’s Form 10-K and other filings referred to above. Alexion does not intend to update any of these forward-looking statements to reflect events or circumstances after the date hereof, except when a duty arises under law.

Contact: Alexion Pharmaceuticals, Inc.

       David Keiser

       President & COO

       203-272-2596

       Euro RSCG Life NRP

       Ernie Knewitz (Media)

       212-845-4253

       Rx Communications

       Rhonda Chiger (Investor)

       917-322-2569

- 5 -