Exhibit 99.1

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

CORTEX REPORTS OPERATING RESULTS FOR DECEMBER 31, 2004

IRVINE, CA (March 21, 2005) — Cortex Pharmaceuticals, Inc. (AMEX: COR) reported a net loss of $2,535,000, or $0.09 per share for the quarter ended December 31, 2004 compared with net income of $512,000, or $0.02 per share for the corresponding prior year period. For the transitional six-month period ended December 31, 2004, Cortex reported a net loss of $4,046,000, or $0.14 per share compared to a net loss of $3,806,000, or $0.20 per share for the corresponding prior year period.

In November 2004 the Company’s Audit Committee, under authority from the Board of Directors, approved a change in the Company’s fiscal year from June 30 to December 31. A report covering the transitional period will be filed on a Form 10-K.

For both the three months and six months ended December 31, 2004, decreased revenues primarily resulted from the $2,000,000 milestone payment from Organon in late December 2003.

Operating expenses for both the three months and six months ended December 31, 2004 reflect increased development expenses for the AMPAKINE compound CX717, which is currently in Phase II clinical testing. Operating expenses for the prior year periods included technology access fees to the University of California triggered by the Organon milestone and significant non-cash stock compensation charges. Excluding these amounts from the prior year periods highlights the increased research and development expenses incurred during the six months ended December 31, 2004.

Other income for the current year periods included $499,000 related to the change in estimated value of warrants issued in Cortex’s December 2004 private placement. For the six months ended December 31, 2003, the related change for warrants issued in Cortex’s August 2003 private placement resulted in other expenses of $3,499,000. Neither of these non-cash amounts had any impact on Cortex’s working capital or its liquidity.

With its December 2004 private placement of common stock and warrants, Cortex further improved its balance sheet. The net proceeds from the financing approximated $10,400,000 and allow Cortex to advance its development plans for CX717, as well as other AMPAKINE compounds. Cortex’s cash and marketable securities increased to nearly $28,000,000 as of December 31, 2004.

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. The success of such activities depends on a number of factors, including the risks 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)

	Three months ended December 31,					Transitional Six months ended December 31,
	2004			2003		2004			2003
	(Unaudited)			(Unaudited)					(Unaudited)
Revenues	$	721		$	3,256	$	1,896		$	4,594
Operating expenses:
Research and development		2,885			1,837		4,926			2,870
General and administrative		866			695		1,530			1,155
Non-cash stock compensation charges		102			566		152			889
Total operating expenses		3,853			3,098		6,608			4,914
Income (loss) from operations		(3,132	)		158		(4,712	)		(320	)
Interest income, net		98			9		167			13
Change in fair value of common stock warrants		499			345		499			(3,499	)
Net income (loss)	$	(2,535	)	$	512	$	(4,046	)	$	(3,806	)
Income (loss) per share:
Basic and diluted	$	(0.09	)	$	0.02	$	(0.14	)	$	(0.20	)
Shares used in computing per share amounts
Basic		28,355			20,640		28,355			19,480
Diluted		28,355			23,909		28,355			19,480

Cortex Pharmaceuticals, Inc.

Condensed Balance Sheets

(in thousands)

	December 31, 2004		June 30, 2004
Assets:
Cash and cash equivalents	$	9,157	$	9,977
Marketable securities		18,838		12,211
Accounts receivable		42		133
Other current assets		318		268
		28,355		22,589
Furniture, equipment and leasehold improvements, net		388		269
Capitalized financing costs		1,136		—
Other		33		33
Total assets	$	29,912	$	22,891
Liabilities and Stockholders’ Equity:
Accounts payable and accrued expenses	$	1,907	$	1,815
Unearned revenue — current		377		206
Unearned revenue, other non-current		23		381
Common stock warrants		3,958		—
Stockholders’ equity		23,647		20,489
Total liabilities and stockholders’ equity	$	29,912	$	22,891

MORE INFORMATION AT WWW.CORTEXPHARM.COM

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