Exhibit 99.1

PRESS RELEASE

Company Contact:

Mark A. Varney, Ph.D.

President and CEO

Cortex Pharmaceuticals, Inc.

949.727.3157

CORTEX REPORTS FIRST QUARTER OPERATING RESULTS

IRVINE, CA (May 15, 2012) — Cortex Pharmaceuticals, Inc. (OTCBB (CORX)) reported a net loss of approximately $934,000, or $0.01 per share, for the quarter ended March 31, 2012, compared with a net loss of approximately $1,556,000, or $0.02 per share, for the corresponding prior year period, with the difference including expenses incurred in the prior year period to reacquire the respiratory depression project that Biovail purchased from the Company in March 2010.

For the quarter ended March 31, 2012, the Company’s total operating expenses decreased to approximately $935,000 from approximately $1,584,000 for the corresponding prior year period. Along with the $200,000 upfront payment related to the March 2011 transaction with Biovail, the decreased operating expenses reflect the Company’s previously announced decrease in its internal staffing levels in its efforts to conserve its financial resources. Cortex will continue to outsource a substantial amount of its research and development activities to qualified vendors.

The repurchase of AMPAKINE compounds, patents and rights from Biovail reinforces the Company’s renewed focus on the discovery and development of innovative pharmaceuticals for the treatment of breathing disorders, including respiratory depression and sleep apnea.

During the quarter ended March 31, 2012, Cortex announced the issuance by The United States Patent and Trademark Office (USPTO) of two key patents that protect the next generation of AMPAKINE^® compounds, including the lead preclinical compounds, CX2007 and CX2076. The USPTO issued both a composition-of-matter patent and a divisional patent covering methods of use, including the treatment for a broad range of breathing disorders such as opioid-induced respiratory depression and sleep apneas. These issued patents will provide protection from competitors through August 2028.

Cortex Pharmaceuticals, Inc.

Cortex, located in Irvine, California, is a clinical-stage specialty pharmaceutical company focused primarily on the discovery, development and commercialization of positive AMPA-type glutamate receptor modulators. Cortex has pioneered a class of proprietary pharmaceuticals called AMPAKINE compounds, which act to increase the strength of signals at connections between brain cells. Recent research has focused on the use of AMPAKINE compounds for the potential treatment or prevention of respiratory depression induced by opioid analgesics, anesthetic agents and benzodiazepines, as well as the potential treatment for central sleep apnea. For additional information regarding Cortex, please visit the Company’s website at http://www.cortexpharm.com.

Forward-Looking Statement

Note — This press release contains forward-looking statements concerning the Company’s research and development activities. Words such as “believes,” “anticipates,” “plans,” “expects,” “indicates,” “will,” “intends,” “potential,” “suggests,” “assuming,” “designed” and similar expressions are intended to identify forward-looking statements. These statements are based on the Company’s current beliefs and expectations. 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 patents may not issue from the Company’s patent applications; that competitors may challenge or design around the Company’s patents or develop competing technologies; that the Company may have insufficient resources to undertake proposed clinical studies or continue its operations and that preclinical or 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 preclinical and clinical testing and regulatory approval. AMPAKINE compounds are investigational drugs and have not been approved for the treatment of any disease. Readers are cautioned not to place undue reliance on these forward-looking statements that speak only as of the date of this press release. The Company undertakes no obligation to update publicly any forward-looking statements to reflect new information, events or circumstances after the date of this press release or to reflect the occurrence of unanticipated events.

(tables follow)

Cortex Pharmaceuticals, Inc.

Condensed Statements of Operations

(in thousands, except per share data)

Cortex Pharmaceuticals, Inc.

Condensed Balance Sheets

(in thousands)

MORE INFORMATION AT WWW.CORTEXPHARM.COM

#  #  #  #  #