EXHIBIT 99.1

Investor Relations

eOn Communications

800-873-3194

investorrelations@eoncc.com

eOn Communications Reports Third Quarter Fiscal 2004 Results

ATLANTA (June 1, 2004) – eOn Communications Corporation^™ (NASDAQ: EONC), a leading provider of unified voice, e-mail and web-based communications solutions, today reported financial results for the third fiscal quarter ended April 30, 2004. Revenues for the quarter were $2,770,000, compared with $4,749,000 for the same period last year. Net loss for the quarter was $944,000, or ($0.07) per common share, compared with net income of $82,000, or $0.01 per share in the quarter ended April 30, 2003.

For the nine months ended April 30, 2004, revenues were $11,767,000, compared to $12,422,000 in the nine months ended April 30, 2003. Net loss for the nine months ended April 30, 2004 was $527,000, or ($0.04) per common share, an improvement of $1,185,000 from a net loss of $1,712,000, or ($0.14) per share in the prior-year period.

“The financial results for the quarter are clearly disappointing, given our previous four quarters of profitability,” said David Lee, eOn’s chairman and chief executive officer. “The decrease in revenues from the previous year quarter is entirely due to delays in orders for our eQueue product. As stated before, with a six to nine month sales cycle for the eQueue, these delays can be material and can affect our reported quarterly results quite dramatically. I am especially pleased, however, with the continued progress of our efforts to penetrate the Chinese market. We will continue to monitor the company’s expenses closely while focusing on becoming a leader in this rapidly expanding market.”

Third Quarter Operational Highlights

During the quarter, the Company signed an agreement with Hewlett-Packard (China), under which the two companies plan to work together to deliver advanced contact center solutions to the enterprise business market in China. The agreement allows HP (China) to market and incorporate eOn products into its solution portfolio. The two companies will also work closely together on joint marketing programs to build awareness of advanced contact center products and services in the Asian marketplace.

The Company also received its first orders for eQueue WorkForce Management from Aramark – Lake Powell and the University of Colorado Federal Credit Union. eQueue WorkForce Management, completely integrated with the eQueue Multi-media Contact Center Solution, allows

managers to more effectively manage agent labor costs – often the largest cost component in contact center operations. During the quarter, follow-on orders were also received from B&H Photo, Circuit City, the US Coast Guard, as well as from distribution partners Black Box Network Services and Professional Teledata.

The Company also participated in the 2004 Contact Center and Customer Relationship Management (CCM) Conference in Beijing, China. The Conference attracted contact center companies and participants to see the best solutions available today for China’s contact center industry. eOn received a service and product award for demonstrating core expertise and superior achievement in developing strategies and solutions for use in call centers and by customer interaction management professionals in mainland China.

Business Outlook

Lee concluded, “We believe that through the recognition we have gained and with the partnerships we have established, we are well positioned to capitalize on the emerging customer interaction management market in China. We are confident that with the addition of the predicted revenues originating from this emerging market, along with the expected rebound in order flow from our existing markets, we will resume profitable quarterly performance.”

Conference Call

The Company will host a conference call at 4:45 p.m. EDT today, June 1, 2004, to discuss its third quarter results. To hear the call, dial (913) 981-5559 or visit our investor relations website at investor.eoncc.com. A replay of the call will be posted to our investor relations website shortly following the call. A recording will also be available no later than noon on Friday, June 4, 2004, by direct dial at (678) 337-2001. These recordings will be available through June 18, 2004.

About eOn Communications^™

eOn Communications Corporation^™ is a leading provider of unified voice, e-mail and web-based communications systems for customer contact centers and general business applications. eOn helps enterprises communicate more effectively with customers, convert inquiries into sales, and increase customer satisfaction and loyalty. To find out more information about eOn Communications and its solutions, visit the World Wide Web at www.eoncommunications.com, or call 800-955-5321.

Note:

This press release may contain forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. These forward-looking statements involve risks and uncertainties, including technical and competitive factors, which could cause the Company’s results and the timing of certain events to differ materially from those discussed in the forward-looking statements. Such risks are detailed in eOn Communications Corporation’s most recent Form 10-Q filing with the Securities and Exchange Commission.

eOn Communications Corporation, the mark eOn, and eQueue are trademarks of eOn Communications Corporation.

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eOn Communications Corporation

Statements of Operations (Unaudited)

For the Three Months and Nine Months Ended April 30, 2004 and 2003

(Dollars in thousands, except per share data)

	Three Months Ended April 30,						Nine Months Ended April 30,
	2004			2003			2004			2003
Net revenues	$	2,770		$	4,749		$	11,767		$	12,422
Cost of revenues		1,259			1,780			4,950			5,180
Gross profit		1,511			2,969			6,817			7,242
Operating expenses:
Selling, general, and administrative		1,598			2,197			5,058			6,835
Research and development		855			686			2,248			2,166
Special charges		—			—			—			(63	)
Total operating expenses		2,453			2,883			7,306			8,938
Income (loss) from operations		(942	)		86			(489	)		(1,696	)
Interest income		(15	)		(16	)		(47	)		(80	)
Interest expense		9			9			26			26
Other expense, net		8			11			59			70
Income (loss) before income tax expense		(944	)		82			(527	)		(1,712	)
Income tax expense		—			—			—			—
Net income (loss)	$	(944	)	$	82		$	(527	)	$	(1,712	)
Net income (loss) per common share
Basic and diluted:	$	(0.07	)	$	0.01		$	(0.04	)	$	(0.14	)
Weighted average shares outstanding:
Basic and diluted		12,635			12,104			12,444			12,067

eOn Communications Corporation

Balance Sheets

April 30, 2004 and July 31, 2003

(Dollars in thousands)

	April 30, 2004			July 31, 2003
	(Unaudited)
ASSETS
Current assets:
Cash and cash equivalents	$	1,923		$	3,221
Marketable securities		4,200			4,200
Trade accounts receivable, net		3,163			2,849
Inventories		2,084			1,879
Other current assets		99			134
Total current assets		11,469			12,283
Property and equipment, net		763			1,149
Intangible assets, net		—			2
Total	$	12,232		$	13,434
LIABILITIES AND STOCKHOLDERS’ EQUITY
Current liabilities:
Trade accounts payable	$	1,218		$	1,361
Note payable – current		114			613
Accrued expenses and other		1,364			1,996
Total current liabilities		2,696			3,970
Commitments and contingencies		—			—
Stockholders’ equity:
Common stock		13			12
Additional paid-in capital		54,045			53,447
Treasury stock		(1,502	)		(1,502	)
Accumulated deficit		(43,020	)		(42,493	)
Total stockholders’ equity		9,536			9,464
Total	$	12,232		$	13,434