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 First Quarter Fiscal 2005 Results

IRVINE, CA (November 15, 2004) — Cortex Pharmaceuticals, Inc. (AMEX: COR) reported a net loss of $1,511,000 ($0.05 per share) for the quarter ended September 30, 2004. This compares with a net loss of $4,319,000 ($0.24 per share) for the corresponding prior year period, which included non-cash charges of $3,844,000 related to warrants issued in the Company’s private placement of common stock in August 2003.

Operating expenses increased from $1,816,000 to $2,756,000 for the quarter ended September 30, 2004 compared to the corresponding prior year period, reflecting increased research and development expenses, including costs for Phase I clinical testing of the second generation AMPAKINE^® compound, CX717.

“With the encouraging results from the Phase I studies, our plans include advancing CX717 into several pilot Phase IIa studies in selected indications in early 2005,” commented Roger G. Stoll, Ph.D., Chairman, President and Chief Executive Officer of Cortex.

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.

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 obtain sufficient funding to develop AMPAKINE compounds for indications it wishes to retain; that the Company may be unable to arrive at additional corporate partnerships with other pharmaceutical companies for other indications 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.

(table follows)

Cortex Pharmaceuticals, Inc.

Condensed Statements of Operations

(in thousands, except per share data)

(Unaudited)

	Three months ended September 30,
	2004			2003
Research, license and grant revenues	$	1,175		$	1,337
Operating expenses:
Research and development		2,042			1,033
General and administrative		664			460
Non-cash, stock compensation charges		50			323
Total operating expenses		2,756			1,816
Loss from operations		(1,581	)		(479	)
Interest income, net		70			4
Increase in fair value of common stock warrants		—			(3,844	)
Net loss	$	(1,511	)	$	(4,319	)
Net loss per share, basic and diluted	$	(0.05	)	$	(0.24	)
Shares used in computing per share amounts
Basic and diluted		28,355			18,321

Cortex Pharmaceuticals, Inc.

Condensed Balance Sheets

(in thousands)

	September 30, 2004 (Unaudited)		June 30, 2004
Assets:
Cash and cash equivalents	$	11,414	$	9,977
Marketable securities		8,699		12,211
Accounts receivable		10		133
Other current assets		254		268
		20,377		22,589
Furniture, equipment and leasehold improvements, net		337		269
Other assets		33		33
Total assets	$	20,747	$	22,891
Liabilities and stockholders’ equity:
Current liabilities	$	1,627	$	2,021
Non-current liabilities		81		381
Stockholders’ equity		19,039		20,489
Total liabilities and stockholders’ equity	$	20,747	$	22,891

More information at www.cortexpharm.com

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