Exhibit 99.1

CORTEX REPORTS THIRD QUARTER RESULTS

IRVINE, CA (November 14, 2005) — Cortex Pharmaceuticals, Inc. (AMEX: COR) reported a net loss of $2,530,000 ($0.08 per share) for the quarter ended September 30, 2005, compared with a net loss of $1,511,000 ($0.05 per share) for the corresponding prior year period. For the nine months ended September 30, 2005, Cortex reported a net loss of $7,867,000 ($0.24 per share) compared with a net loss of $3,699,000 ($0.14 per share) for the corresponding prior year period. Increased net losses in the current year periods primarily reflect research and development expenses, including amounts for the AMPAKINE^® compound, CX717, which is currently in Phase IIa studies in Attention Deficit Hyperactivity Disorder, mild to moderate Alzheimer’s disease and a shift work protocol being conducted by DARPA (Defense Advanced Research Projects Agency). Results from these studies are anticipated during the first quarter of 2006. The enrollment phase of the ADHD study was completed before the end of October 2005, while the shift work protocol is just being initiated by DARPA.

Increased net losses relative to the prior year periods also reflect decreased research revenues due to the end of research support from the October 2002 amendment to Cortex’s collaborative agreement with Servier. Cortex continues to receive research support approximating $2,220,000 per year from Servier under the October 2000 collaborative agreement, as extended in late 2003.

Increased administrative expenses related to fees for preparing the Company’s assessment of its internal control system as of December 31, 2005, as required by The Sarbanes-Oxley Act of 2002.

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.

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Cortex Pharmaceuticals, Inc.

Condensed Statements of Operations

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Cortex Pharmaceuticals, Inc.

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MORE INFORMATION AT WWW.CORTEXPHARM.COM

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