Exhibit 99.1

Press Release

Company Contact:	Investor Contact:
Roger G. Stoll, Ph.D.	Jane Lin/ Dian Griesel, Ph.D.
Chairman, President and CEO	The Investor Relations Group
Cortex Pharmaceuticals, Inc.	212.825.3210
949.727.3157

Cortex Reports Third Quarter Operating Results

— Balance Sheet Reflects $17.5 Million Net Proceeds from January 2004 Private Placement —

IRVINE, CA (May 10, 2004) — Cortex Pharmaceuticals, Inc. (AMEX: COR) reported a net loss of $874,000 ($0.03 per share) for the quarter ended March 31, 2004, compared with a net loss of $140,000 ($0.01 per share) for the corresponding prior year period, with the difference representing decreased licensing and grant revenues, as well as increased personnel-related expenses and non-cash stock compensation charges in the current year period.

For the nine-month period ended March 31, 2004, Cortex reported a net loss of $4,680,000 ($0.22 per share), compared to a net loss of $1,090,000 ($0.06 per share) for the corresponding prior year period, with the increase reflecting non-cash charges of $3,600,000 primarily related to warrants issued in Cortex’s August 2003 private placement.

Revenues for the nine-month period ended March 31, 2004 include the $2,000,000 milestone payment received from Organon, as previously reported. Organon paid the milestone in order to retain its rights to Cortex’s AMPAKINE^® technology in the field of depression.

Excluding non-cash stock compensation charges, operating expenses for the nine months ended March 31, 2004 increased relative to costs for the corresponding prior year period mostly due to preclinical expenses to advance the AMPAKINE compound, CX717.

“As planned, we will be initiating Phase I human testing with CX717 this month,” said Roger Stoll, Ph.D., President and CEO of Cortex. “We anticipate preliminary results from this study by the end of August 2004. With the proceeds from the private placements, we have been able to accelerate the development of CX717 as well as other follow-on compounds.”

Non-cash charges recorded during the nine months ended March 31, 2004 include amounts required by EITF 00-19, “Accounting for Derivative Financial Instruments Indexed To, and Potentially Settled In a Company’s Own Stock”. The charges relate to the increase in Black-Scholes value of warrants issued in the August 2003 private placement from the closing date of the transaction until the date that the registration statement covering the underlying common shares was declared effective by the Securities and Exchange Commission. The non-cash charges had no impact on Cortex’s working capital or its liquidity.

Cortex Pharmaceuticals, Inc.

Cortex, located in Irvine, California, is a neuroscience company focused on novel drug therapies for neurological and psychiatric disorders. The Company is pioneering a class of proprietary pharmaceuticals called AMPAKINE compounds, which act to increase the strength of signals at connections between brain cells. The loss of these connections is thought to be responsible for memory and behavior problems in Alzheimer’s disease. Many psychiatric diseases, including schizophrenia, occur as a result of imbalances in the brain’s neurotransmitter system. These imbalances may be improved by using the AMPAKINE technology. Cortex has alliances with N.V. Organon for the treatment of schizophrenia and depression and with Les Laboratoires Servier for the development of AMPAKINE compounds to treat the neurodegenerative effects associated with aging and disease, including Mild Cognitive Impairment, Alzheimer’s disease and anxiety disorders. Cortex is currently developing CX717, a second generation AMPAKINE compound, for the Alzheimer’s disease and Mild Cognitive Impairment indications.

Forward-Looking Statement

Note — This press release contains forward-looking statements concerning the Company’s research and development activities, clinical trials and business development plans. Actual results may differ materially, depending on a number of risk factors, including the risks that the agreements with Organon and Servier will not result in any commercial products or that any additional milestone payments will be earned by the Company; that the Company may be unable to arrive at additional corporate partnerships with other pharmaceutical companies on acceptable terms and therefore be required to independently fund clinical development of AMPAKINE compounds through the sale of additional equity securities or otherwise; that the Company’s proposed products may at any time be found to be unsafe or ineffective for any or all of their proposed indications; that competitors may challenge or design around the Company’s patents or develop competing technologies; and that clinical studies may at any point be suspended or take substantially longer than anticipated to complete. As discussed in the Company’s Securities and Exchange Commission filings, the Company’s proposed products will require additional research, lengthy and costly clinical testing and regulatory approval. AMPAKINE compounds are investigational drugs and have not been approved for the treatment of any disease.

(tables follow)

Cortex Pharmaceuticals, Inc.

Condensed Statements of Operations

(in thousands, except per share data)

(Unaudited)

	Three months ended March 31,						Nine months ended March 31,
	2004			2003			2004			2003
Operating revenues	$	1,166		$	1,379		$	5,759		$	3,883
Operating expenses:
Research and development		1,164			959			4,033			2,908
General and administrative		622			498			1,777			1,943
Non-cash stock compensation charges		182			64			1,071			135
Total operating expenses		1,968			1,521			6,881			4,986
Loss from operations		(802	)		(142	)		(1,122	)		(1,103	)
Interest income, net		32			2			45			13
Change in fair value of common stock warrants		(104	)		—			(3,603	)		—
Net loss	$	(874	)	$	(140	)	$	(4,680	)	$	(1,090	)
Loss per share:
Basic and diluted	$	(0.03	)	$	(0.01	)	$	(0.22	)	$	(0.06	)
Shares used in computing per share amounts
Basic and diluted		25,553			16,861			21,490			16,854

Cortex Pharmaceuticals, Inc.

Condensed Balance Sheets

(in thousands)

	March 31, 2004 (Unaudited)		June 30, 2003
Assets:
Cash and cash equivalents	$	20,067	$	1,125
Marketable securities		2,600		—
Restricted cash		—		84
Accounts receivable		236		428
Other current assets		331		211
		23,234		1,848
Furniture, equipment and leasehold improvements, net		270		298
Other assets		33		33
Total assets	$	23,537	$	2,179
Liabilities and stockholders’ equity (deficit):
Accounts payable and accrued expenses	$	1,116	$	1,335
Unearned revenue — current		309		2,017
Unearned revenue — non-current		378		247
Stockholders’ equity (deficit)		21,734		(1,420	)
Total liabilities and stockholders’ equity (deficit)	$	23,537	$	2,179

More information at www.cortexpharm.com

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