Exhibit 99.1

PRESS RELEASE

CORTEX ANNOUNCES APPOINTMENT OF HASKELL & WHITE LLP AS

INDEPENDENT AUDITORS AND CHANGE IN FISCAL YEAR END TO DECEMBER 31

IRVINE, CA (November 10, 2004) — Cortex Pharmaceuticals, Inc. (AMEX: COR) announced that it has engaged Haskell & White LLP as its new independent auditors and that it has changed its fiscal year end from June 30 to December 31.

Haskell & White replaces Ernst & Young LLP prospectively effective following the filing of the Company’s quarterly report on Form 10-Q for September 30, 2004. The change in auditors was not a result of any disagreements with Ernst & Young on any matter of accounting principles or practices, financial statement disclosure, or auditing scope or procedures.

“Our audit committee sought to engage a firm that is more commensurate with our size, scope and service needs in today’s accounting environment,” commented Roger G. Stoll, Ph.D., Chairman, President and Chief Executive Officer of Cortex. “The increased demand for audit services due to the Sarbanes-Oxley Act of 2002 and related Section 404 requirements are straining the resources of all audit firms. We believe that the selection of Haskell & White will accommodate our increasing audit needs, while at the same time remaining cost-effective for Cortex.”

“Going forward, we believe that harmonizing our fiscal year with the calendar year will facilitate communications with the investor community and many of the service organizations who work with us to develop our products,” added Dr. Stoll. “As a result of this change, we will file a report on Form 10-K for the six months ending December 31, 2004 in early 2005.”

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.

MORE INFORMATION AT WWW.CORTEXPHARM.COM

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