Exhibit 99.1

PRESS RELEASE

Contacts: Roger G. Stoll, Ph.D. Chairman, President and CEO Cortex Pharmaceuticals, Inc. (949) 727-3157 Damian R. McIntosh / Dian Griesel, Ph.D. Media Contact: Janet Vasquez / Lynn Granito The Investor Relations Group (212) 825-3210

MARK A. VARNEY, Ph.D. NAMED CHIEF OPERATING

OFFICER AND CHIEF SCIENTIFIC OFFICER OF CORTEX

PHARMACEUTICALS

IRVINE, CA (January 31, 2006) — Cortex Pharmaceuticals, Inc (AMEX: COR) has named Mark Varney, Ph.D. as Chief Operating Officer and Chief Scientific Officer. In his new position Dr. Varney, who has spent over 15 years in the pharmaceutical industry, will join the company’s expert team as they develop the AMPAKINE^® technology. Initially he will concentrate largely on the company’s research and development processes in an effort to help speed new compounds into clinical trials.

Prior to joining Cortex, Dr. Varney held senior level positions at Sepracor, Inc., where he was Vice President and head of Discovery, and at Bionomics, Ltd., where he was Vice President of Drug Discovery. Prior to that, Dr. Varney held positions of increasing responsibilities over his six-year tenure at SIBIA Neuroscience, Inc., including his most recent position as Director of Neuropharmacology. Upon the acquisition of SIBIA by Merck, Inc in 1999, he was appointed a Director of SIBIA’s San Diego facility. Prior to SIBIA, he held research positions at Servier in France and Merck Sharp & Dohme in the U.K. Dr. Varney received his B.Sc. in Biochemistry with honors from Surrey University, U.K. and completed his Ph.D. and postdoctoral training at Oxford University, U.K.

Dr. Varney’s career has focused on drug discovery programs for treating schizophrenia, depression, cognitive disorders, anxiety, epilepsy and insomnia. He has been successful in developing drug candidates in several of these disease areas. He has extensive publications in peer-reviewed journals; is the Editor-in-Chief of the journal “CNS & Neurological Disorders-Drug Targets,” and has filed numerous patent applications relating to new chemical entities and methods of use.

“Dr. Varney brings to Cortex an outstanding background in drug discovery and development,” stated Dr. Roger Stoll, President and Chief Executive Officer of Cortex. “Dr. Varney will strengthen significantly the process used with our R&D organization and we believe will thereby improve our efficiency in bringing new products to market. Dr. Varney, along with Dr. Hank Mansbach,

our Chief Medical Officer, and Dr. Gary Rogers, our Senior Vice President of Pharmaceutical Research, bring together substantial expertise in both research and development that should pay dividends in maturing our capabilities as a developer of CNS drugs and enhance our leadership position in the technology of AMPAKINE therapy.”

“I am excited by the opportunity at Cortex and am very much looking forward to contributing to the Company’s future success,” said Dr. Varney. “Cortex has made tremendous progress in the AMPAKINE field, and I believe that it is in a strong position to translate these discoveries into meaningful therapies to treat patients and to increase shareholder value.”

In connection with his employment, Dr. Varney will be granted options to purchase an aggregate of 750,000 shares of Cortex common stock with an exercise price equal to the closing sale price of the common stock as reported on the AMEX on January 30, 2006.

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. The success of such activities depends on a number of factors, including the risks that the Company’s proposed compounds may at any time be found to be unsafe or ineffective for the indications under clinical test 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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