Exhibit 99.1

PRESS RELEASE

CORTEX REPORTS SECOND QUARTER RESULTS

IRVINE, CA (August 15, 2005) — Cortex Pharmaceuticals, Inc. (AMEX: COR) reported a net loss of $2,689,000 ($0.08 per share) for the quarter ended June 30, 2005, compared with a net loss of $1,314,000 ($0.05 per share) for the corresponding prior year period. For the six months ended June 30, 2005, Cortex reported a net loss of $5,337,000 ($0.16 per share) compared with a net loss of $2,188,000 ($0.08 per share) for the corresponding prior year period. Increased net losses in the current year periods reflect development expenses for the AMPAKINE^® compound, CX717 and increased preclinical research and development of the AMPAKINE technology. Cortex expects that the increased pace of research and development will continue to impact its expense levels throughout 2005.

As recently reported, Cortex has begun enrollment in its second and third Phase IIa studies with CX717: one in Attention Deficit Hyperactivity Disorder and the other in mild to moderate Alzheimer’s disease. These studies follow results from the first Phase IIa trial with CX717 that suggest that when compared to placebo, the compound increased wakefulness in a dose-related manner and improved cognitive performance in healthy male subjects that were deprived of sleep. A fourth Phase IIa study in simulated night shift work is scheduled to start enrollment at the end of August. Cortex anticipates that information relative to the outcome of these studies will be available toward the end of 2005 or sooner, depending on patient enrollment.

Revenues of $647,000 and $1,346,000 for the three months and six months ended June 30, 2005, respectively, decreased relative to the prior year periods due to the end of research support under the October 2002 amendment to Cortex’s collaborative agreement with Servier. Revenues for the current year periods primarily represent the research support that Cortex continues to receive from Servier under the October 2000 collaborative agreement, as extended in late 2003.

A conference call to discuss the quarterly results and the continuing developments within Cortex’s research and development is scheduled for August 17 at 3:00 pm EDT. Participants are asked to call the following numbers 5-10 minutes prior to the starting time:

A replay will be available for 45 days after the call by dialing 1-888-203-0820 (US and Canada) or 1-719-457-0820 (International) and entering access code 9450020 when prompted.

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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