EXHIBIT 32

Certification Pursuant to 18 U.S.C. Section 1350, As Adopted Pursuant to Section 906 of

the Sarbanes-Oxley Act of 2002

Roger G. Stoll, 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 Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that:

(1) the Quarterly Report on Form 10-Q of the Company for the three months ended March 31, 2004 (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:                 May 6, 2004	/s/    ROGER G. STOLL
	Roger G. Stoll, Ph.D.
	Chairman, President and Chief Executive Officer
Dated:                 May 6, 2004	/s/    MARIA S. MESSINGER
	Maria S. Messinger
	Vice President, Chief Financial Officer and Secretary