EXHIBIT 32

Certification of Chief Executive Officer and Chief Financial Officer Pursuant to Rule 13a-14(b)/15d-14(b) of the Securities Exchange Act of 1934

and 18 U.S.C. Section 1350

Mark A. Varney, Ph.D., President and Chief Executive Officer of Cortex Pharmaceuticals, Inc. (the “Company”), and Maria S. Messinger, Chief Financial Officer of the Company, each certifies, pursuant to Rule 13a-14(b) or Rule 15d-14(b) of the Securities Exchange Act of 1934 and 18 U.S.C. Section 1350, that:

(1) the Quarterly Report on Form 10-Q of the Company for the quarterly period ended June 30, 2012 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 780(d)); and

(2) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: August 16, 2012	/s/ Mark A. Varney
	Mark A. Varney, Ph.D.
	President and Chief Executive Officer
Dated: August 16, 2012	/s/ Maria S. Messinger
	Maria S. Messinger
	Vice President, Chief Financial Officer and Secretary

This certification accompanies the Quarterly Report pursuant to Rule 13a-14(b) or Rule 15d-14(b) under the Securities Exchange Act of 1934 and 18 U.S.C. Section 1350 and shall not be deemed filed by the Company for purposes of Section 18 of the Securities Exchange Act of 1934.