EXHIBIT 99.1

Press Release

Contacts:

Roger G. Stoll, Ph.D.	Shayne Payne/Gino de Jesus/Dian Griesel, Ph.D.
Chairman, President and CEO	The Investor Relations Group
Cortex Pharmaceuticals, Inc.	(212) 825-3210
(949) 727-3157

Cortex Announces Third Quarter Fiscal 2003 Results

IRVINE, CA, May 15, 2003 — Cortex Pharmaceuticals, Inc. (AMEX: COR) announced the results of its operations for the third fiscal quarter and the nine-month period ended March 31, 2003.

For the quarter ended March 31, 2003, Cortex reported a net loss of $140,000 ($0.01 per share) compared with a net loss of $839,000 ($0.05 per share) for the corresponding prior-year period. Results for the current year period reflect increased revenues from the agreement with Servier and reduced operating expenses.

In October 2002, Cortex expanded Servier’s rights to the AMPAKINE^® technology to include anxiety disorders in Servier’s licensed territories. In exchange, Servier is providing Cortex with $4,000,000 of additional research support, paid as $500,000 per quarter over a two-year period. Shortly after March 31, 2003, Cortex received approximately $1,000,000 of quarterly research support from Servier, including $500,000 from the October 2002 agreement and $500,000 from the original agreement with Servier signed in October 2000.

Operating expenses for the quarter ended March 31, 2003 decreased relative to the prior-year quarter primarily due to timing of clinical expenses. The prior-year period included costs related to the Phase II study in patients with Mild Cognitive Impairment, which began enrollment in March 2002. Servier is conducting this study along with Cortex and is paying nearly all of the associated costs.

For the nine months ended March 31, 2003, Cortex reported a net loss of $1,090,000 ($0.06 per share), compared with a net loss of $600,000 ($0.04 per share) for the corresponding prior-year period. Revenues for the prior year period included a $2,000,000 milestone from Cortex’s other partner, Organon, triggered when Organon elected to enter Phase II clinical studies of an AMPAKINE compound in schizophrenia. Operating expenses decreased in the current year period due to manpower and associated cost reductions, as well as technology access fees related to the Organon milestone in the prior-year period and the clinical expenses already mentioned.

“During the third quarter, we retained The Investor Relations Group of New York to assist us in broadening our shareholder base,” said Maria S. Messinger, Chief Financial Officer of Cortex. “Our concentrated efforts also include securing additional capital to allow us to advance new AMPAKINE compounds into clinical trials. By further developing these compounds, we believe that we enhance the value of new corporate partnerships that we may secure, while we continue our independent pursuit of other commercialization opportunities.”

Cortex’s business strategy includes developing licenses for drug indications that require substantial Phase III clinical trials and ultimately building large sales forces to successfully

market the drugs. At the same time, Cortex plans to develop internally a selected set of indications that typically require shorter development timelines, more modest investment in the development stages, and ultimately a more concentrated sales reach in the United States. Cortex believes that this combined approach may provide greater success for its technology.

Cortex is presently pursuing several financing avenues in order to increase its ability to carry out a sustained development program for its AMPAKINE technology. The Company is vigorously attempting to raise sufficient funds to adequately support three to four years of clinical development activity. Cortex is in discussions with traditional source of financing such as venture backed capital, but also is having discussions with various major pharmaceutical corporations regarding licensing opportunities. At the present time it is not possible to predict which event, if either, could occur more rapidly. Cortex intends that either option would accelerate the development of some of its second generation compounds, such as CX717.

Shortly after March 31, 2003, Cortex announced that it received an allowance in Europe for its broad method of use patent for drugs that improve memory and cognition. Similar patents already have issued in the United States, Mexico, Australia and New Zealand. With the issuance of these patents, Cortex may claim the use of any drug that works via the mechanism of its AMPAKINE compounds, namely AMPA type glutamate receptor up-modulation (AMPA-R) for enhancing memory encoding and cognition in humans.

“When this allowed patent issues, it will broaden what we believe are key patent rights for our AMPAKINE compounds — compounds that potentially may be useful in the treatment of some of the largest indications within our industry,” added Roger G. Stoll, Ph.D., Chairman, President and CEO of Cortex.

About Cortex Pharmaceuticals

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. (http://www.cortexpharm.com/)

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 Company may be unable to obtain additional capital needed to continue its operations; 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 yet been shown to have efficacy in the treatment of any disease.

(table follows)

Cortex Pharmaceuticals, Inc.

Condensed Statements of Operations

(in thousands, except per share data)

(Unaudited)

	Three months ended March 31,						Nine months ended March 31,
	2003			2002			2003			2002
Operating revenues	$	1,379		$	1,154		$	3,883		$	5,326
Operating expenses:
Research and development		968			1,417			2,924			4,023
General and administrative		553			586			2,062			1,965
Total operating expenses		1,521			2,003			4,986			5,988
Loss from operations		(142	)		(849	)		(1,103	)		(662	)
Interest income, net		2			10			13			62
Net loss	$	(140	)	$	(839	)	$	(1,090	)	$	(600	)
Basic and diluted loss per share:	$	(0.01	)	$	(0.05	)	$	(0.06	)	$	(0.04	)
Shares used in computing per share amounts
Basic and diluted		16,861			16,742			16,854			16,667

Cortex Pharmaceuticals, Inc.

Condensed Balance Sheets

(in thousands)

	March 31, 2003 (Unaudited)			June 30, 2002
Assets:
Cash, cash equivalents and short-term investments	$	173		$	1,849
Restricted cash		108			181
Other current assets		438			466
Total current assets		719			2,496
Furniture, equipment and leasehold improvements, net		340			451
Other assets		33			33
Total assets	$	1,092		$	2,980
Liabilities and stockholders’ deficit:
Current liabilities	$	1,056		$	658
Unearned revenues—current		988			2,187
Unearned revenues—non-current		494			727
Stockholders’ deficit		(1,446	)		(592	)
Total liabilities and stockholders’ deficit	$	1,092		$	2,980

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