Prospectus Supplement No. 4
PROSPECTUS SUPPLEMENT NO. 4    Filed Pursuant to Rule 424(b)(3)

(To Prospectus Dated March 18, 2004)

   Registration No. 333-112043

CORTEX PHARMACEUTICALS, INC.

11,743,710 Shares of Common Stock

($0.001 par value)

This prospectus supplement supplements information contained in that certain prospectus dated March 18, 2004 of Cortex Pharmaceuticals, Inc. (the “Company”), relating to the offer and sale from time to time of up to 6,909,091 shares of the Company’s outstanding common stock, and up to 4,834,619 shares of the Company’s common stock issuable upon exercise of warrants, which are held by certain stockholders and warrant holders named in the prospectus under the section entitled “Selling Stockholders.” This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the prospectus, including any amendments or supplements thereto.

The following amends and supplements the information set forth in the prospectus under the caption “Selling Stockholders” with respect to the selling stockholders named below and the respective shares of common stock beneficially owned by such selling stockholders that may be offered pursuant to the prospectus:

 

Name

   Common
Stock Owned
Prior to the
Offering
   Common
Stock Being
Offered
Pursuant to
this
Prospectus
  

Common

Stock Owned
Upon
Completion of
this Offering

   Percentage of
Common Stock
Owned Upon
Completion of
this Offering

Perceptive Life Sciences Master Fund, Ltd.(22)

   600,000    600,000    0    0

Xmark Opportunity Fund, L.P.(50)

   254,361    179,361    75,000    *

Xmark Opportunity Fund, Ltd.(51)

   285,639    210,639    75,000    *

* Indicates less than 1%.
(22) Joseph Edelman, whose business address is c/o Perceptive Advisors, LLC, 7284 W. Palmetto Park Rd., Suite 306, Boca Raton, FL 33433, is the Chief Executive Officer and Managing Member of Perceptive Advisors, LLC, the Investment Manager to Perceptive Life Sciences Master Fund, Ltd., and as such, Mr. Edelman possesses the power to vote and direct the disposition of the securities held by Perceptive Life Sciences Master Fund, Ltd.
(50) Consists of 254,361 shares subject to warrants held prior to the offering that are currently exercisable, of which 179,361 shares subject to warrants are being offered pursuant to this prospectus. Mitchell D. Kaye, whose business address is c/o Xmark Funds, 301 Tresser Blvd., Suite 1320, Stamford, CT 06901, is the Chief Investment Officer of Xmark Opportunity Fund, L.P., and as such, Mr. Kaye possesses the power to vote and direct the disposition of the securities held by Xmark Opportunity Fund, L.P. Perceptive Life Sciences Master Fund, Ltd. assigned the foregoing warrants to Xmark Opportunity Fund, L.P. in March 2006.
(51) Consists of 285,639 shares subject to warrants held prior to the offering that are currently exercisable, of which 210,639 shares subject to warrants are being offered pursuant to this prospectus. Mitchell D. Kaye, whose business address is c/o Xmark Funds, 301 Tresser Blvd., Suite 1320, Stamford, CT 06901, is the Chief Investment Officer of Xmark Opportunity Fund, Ltd., and as such, Mr. Kaye possesses the power to vote and direct the disposition of the securities held by Xmark Opportunity Fund, Ltd. Perceptive Life Sciences Master Fund, Ltd. assigned the foregoing warrants to Xmark Opportunity Fund, Ltd. in March 2006.

All information in this prospectus supplement is as of March 30, 2006.

The date of this prospectus supplement is March 30, 2006.