Subscription Agreement

Exhibit 1.2

Subscription Agreement

This subscription (this “Subscription”) is dated August 24, 2007, by and between the investor identified on the signature page hereto (the “Investor”) and Cortex Pharmaceuticals, Inc., a Delaware corporation (the “Company”), whereby the parties agree as follows:

1. Subscription.

(a) Investor agrees to buy and the Company agrees to sell and issue to Investor (i) such number of shares (the “Shares”) of the Company’s common stock, $0.001 par value per share (the “Common Stock”), and (ii) such number of warrants to purchase Common Stock (the “Warrants”, and together with the Shares, the “Securities”), as set forth on the signature page hereto, for an aggregate purchase price set forth on the signature page hereto (the “Purchase Price”).

(b) The Securities have been registered on a Registration Statement on Form S-3, Registration No. 333-138844, which registration statement has been declared effective by the Securities and Exchange Commission and is effective on the date hereof (together with any registration statement filed by the Company pursuant to Rule 462(b) under the Securities Act, the “Registration Statement”). A final prospectus supplement will be delivered as required by law.

(c) On the closing date, which, in accordance with Rule 15c6-1 promulgated under the Securities Exchange Act of 1934, as amended, is expected to occur on or about August 29, 2007 (the “Closing Date”), upon satisfaction or waiver of all the conditions to closing set forth in the Placement Agency Agreement (the “Placement Agreement”) dated August 24, 2007 by and among the Company and the placement agents named therein (the “Placement Agents”), (i) the Company shall cause its transfer agent to release to the Investor or the Placement Agents (in the event the Investor chooses to settle the Shares via DVP by checking the appropriate space on the Signature Page hereto), as the case may be, the number of Shares being purchased by the Investor (such release of Shares shall be made through the facilities of The Depository Trust Company’s DWAC system), (ii) the Company shall deliver to the Investor the Warrants being purchased by the Investor, and (iii) the aggregate purchase price for the Securities being purchased by the Investor will be delivered by or on behalf of the Investor to the Company. If the Investor chooses to settle the Shares via DWAC (by checking the appropriate space on the Signature Page hereto), the provisions set forth in Exhibit A hereto shall be incorporated herein by reference as if set forth fully herein.

2. Company Representations and Warranties. The Company represents and warrants that: (a) it has full corporate power and authority to enter into this Subscription and to perform all of its obligations hereunder; (b) this Subscription has been duly authorized and executed by and, when delivered in accordance with the terms hereof, will constitute a valid and binding agreement of the Company enforceable in accordance with its terms, except as such enforceability may be limited by bankruptcy, insolvency, reorganization, moratorium or similar laws affecting the rights and remedies of creditors generally or subject to general principles of equity; (c) the execution and delivery of this Subscription and the consummation of the transactions contemplated hereby do not conflict with or result in a breach of (i) the Company’s Certificate of Incorporation or Bylaws, or (ii) any material agreement to which the Company is a party or by which any of its property or assets is bound; (d) the Shares when issued and paid for in accordance with the terms of this Subscription will be duly authorized, validly issued, fully paid and non-assessable, the Warrants when issued and paid for in accordance with the terms of this Subscription will be duly and validly authorized by the Company and upon delivery to the Investors at the Closing Date will be valid and binding obligations of the Company, enforceable in accordance with their terms, except as such enforceability may be limited by bankruptcy, insolvency, reorganization, moratorium or similar laws affecting the rights and remedies of creditors generally or subject to general principles of equity, and the shares of Common Stock issuable upon exercise of the

Warrants when issued and paid for in accordance with the terms thereof will be duly authorized, validly issued, fully paid and non-assessable; (e) the Registration Statement and any post-effective amendment thereto, at the time it became effective, did not contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein not misleading; (f) the prospectus contained in the Registration Statement, as amended or supplemented, did not contain as of the effective date thereof, and as of the date hereof does not contain, any untrue statement of a material fact or omit to state a material fact necessary in order to make the statements therein, in light of the circumstances under which they were made, not misleading; and (g) all preemptive rights or rights of first refusal held by stockholders of the Company and applicable to the transactions contemplated hereby have been duly satisfied or waived in accordance with the terms of the agreements between the Company and such stockholders conferring such rights.

In addition, the Placement Agreement contains certain representations and warranties of the Company. The Company acknowledges and agrees that the Investor may rely on the representations and warranties made by it to the Placement Agents in Section 3 of the Placement Agreement, to the same extent as if such representations and warranties had been incorporated in full herein and made directly to the Investor.

3. Investor Representations, Warranties and Acknowledgments.

(a) The Investor represents and warrants that: (i) it has full right, power and authority to enter into this Subscription and to perform all of its obligations hereunder; (ii) this Subscription has been duly authorized and executed by the Investor and , when delivered in accordance with the terms hereof, will constitute a valid and binding agreement of the Investor enforceable against the Investor in accordance with its terms, except as such enforceability may be limited by bankruptcy, insolvency, reorganization, moratorium or similar laws affecting the rights and remedies of creditors generally or subject to general principles of equity; (iii) the execution and delivery of this Subscription and the consummation of the transactions contemplated hereby do not conflict with or result in a breach of (A) the Investor’s certificate of incorporation or by-laws (or other governing documents), or (B) any material agreement or any law or regulation to which the Investor is a party or by which any of its property or assets is bound; (iv) it has had full access to the base prospectus included in the Registration Statement and the Company’s periodic reports and other information incorporated by reference therein, and was able to read, review, download and print such materials; (v) in making its investment decision in this offering, the Investor and its advisors, if any, have relied solely on the Company’s public filings with the Securities and Exchange Commission; (vi) it is knowledgeable, sophisticated and experienced in making, and is qualified to make, decisions with respect to investments in securities representing an investment decision like that involved in the purchase of the Securities; (vii) the Investor has had no position, office or other material relationship within the past three years with the Company or persons known to it to be affiliates of the Company and (viii), except as set forth below, the Investor is not a, and it has no direct or indirect affiliation or association with any, National Association of Securities Dealers, Inc. member as of the date hereof.

(If no exceptions, write “none.” If left blank, response will be deemed to be “none.”)

(b) The Investor also represents and warrants that, other than the transactions contemplated hereunder, the Investor has not directly or indirectly, nor has any person acting on behalf of or pursuant to any understanding with the Investor, executed any disposition, including “short sales” as defined in Rule 200 of Regulation SHO under the Securities Exchange Act of 1934 (the “Short Sales”), in the securities of the Company during the period commencing from the time that the Investor first became aware of the proposed transactions contemplated hereunder until the date hereof (“Discussion Time”). The Investor has maintained the confidentiality of all disclosures made to it in connection with this transaction (including the existence and terms of this transaction).

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4. Investor Covenant Regarding Short Sales and Confidentiality. The Investor covenants that neither it nor any affiliates acting on its behalf or pursuant to any understanding with it will execute any Short Sales or other disposition of securities of the Company during the period after the Discussion Time and ending at the time that the transactions contemplated by this Subscription are first publicly announced through a press release. The Investor covenants that until such time as the transactions contemplated by this Subscription are publicly disclosed by the Company through a press release, the Investor will maintain the confidentiality of all disclosures made to it in connection with this transaction (including the existence and terms of this transaction).

5. Public Disclosure. The Company shall (i) before the opening of trading on the American Stock Exchange on the next trading day after the date hereof, issue a press release, disclosing all material aspects of the transactions contemplated hereby, to the extent permitted by applicable law, and (ii) make such other filings and notices in the manner and time required by the Securities and Exchange Commission with respect to the transactions contemplated hereby. The Company shall not identify the Investor by name in any press release or public filing, or otherwise publicly disclose the Investor’s name, without the Investor’s prior written consent, unless required by law or the rules and regulations of any self-regulatory organization or exchange to which the Company or its securities are subject.

6. Miscellaneous.

(a) This Subscription constitutes the entire understanding and agreement between the parties with respect to its subject matter, and there are no agreements or understandings with respect to the subject matter hereof which are not contained in this Subscription. This Subscription may be modified only in writing signed by the parties hereto.

(b) This Subscription may be executed in any number of counterparts, all of which taken together shall constitute one and the same instrument and shall become effective when counterparts have been signed by each party and delivered to the other parties hereto, it being understood that all parties need not sign the same counterpart. Execution may be made by delivery by facsimile.

(c) The provisions of this Subscription are severable and, in the event that any court or officials of any regulatory agency of competent jurisdiction shall determine that any one or more of the provisions or part of the provisions contained in this Subscription shall, for any reason, be held to be invalid, illegal or unenforceable in any respect, such invalidity, illegality or unenforceability shall not affect any other provision or part of a provision of this Subscription and this Subscription shall be reformed and construed as if such invalid or illegal or unenforceable provision, or part of such provision, had never been contained herein, so that such provisions would be valid, legal and enforceable to the maximum extent possible, so long as such construction does not materially adversely effect the economic rights of either party hereto.

(d) All communications hereunder, except as may be otherwise specifically provided herein, shall be in writing and shall be mailed, hand delivered, sent by a recognized overnight courier service such as Federal Express, or sent via facsimile and confirmed by letter, to the party to whom it is addressed at the following addresses or such other address as such party may advise the other in writing:

To the Seller: as set forth on the signature page hereto.

To the Buyer: as set forth on the signature page hereto.

All notices hereunder shall be effective upon receipt by the party to which it is addressed.

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(e) This Subscription shall be governed by and interpreted in accordance with the laws of the State of New York for contracts to be wholly performed in such state and without giving effect to the principles thereof regarding the conflict of laws. To the extent determined by such court, the prevailing party shall reimburse the other party for any reasonable legal fees and disbursements incurred in enforcement of, or protection of any of its rights under this Subscription.

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If the foregoing correctly sets forth our agreement, please confirm this by signing and returning to us the duplicate copy of this Subscription.

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EXHIBIT A

TO BE COMPLETED BY INVESTOR

SETTLING VIA DWAC

Delivery through the facilities of The Depository Trust Company’s (“DTC”) DWAC system, registered in the Investor’s name and address as set forth on the Signature Page of the Agreement to which this Exhibit A is attached, and released by American Stock Transfer & Trust Company, the Company’s transfer agent (the “Transfer Agent”), to the Investor at the Closing.

NO LATER THAN ONE (1) BUSINESS DAY AFTER THE EXECUTION OF THE AGREEMENT TO WHICH THIS EXHIBIT A IS ATTACHED BY THE INVESTOR AND THE COMPANY, THE INVESTOR SHALL:

Such funds shall be held in escrow pursuant to an escrow agreement entered into between JPMorgan Chase Bank, NA (the “Escrow Agent”), the Placement Agents and the Company (the “Escrow Agreement”) until the Closing and delivered by the Escrow Agent on behalf of the Investor to the Company.

EXHIBIT B

TO BE COMPLETED BY INVESTOR

SETTLING VIA DVP

Delivery versus payment (“DVP”) (i.e., the Company shall deliver Shares registered in the Investor’s name and address as set forth on the Signature Page of the Agreement to which this Exhibit B is attached and released by the Transfer Agent through DTC’s DWAC system to the Investor at the Closing directly to the account(s) at the Placement Agents identified by the Investor and simultaneously therewith payment shall be made by the Placement Agents from such account(s) to the Company). NO LATER THAN ONE (1) BUSINESS DAY AFTER THE EXECUTION OF THE AGREEMENT TO WHICH THIS EXHIBIT B IS ATTACHED BY THE INVESTOR AND THE COMPANY, THE INVESTOR SHALL:

If the Shares are to be further credited to an account held elsewhere than at the Placement Agents, please complete the information requested below in order to facilitate such further credit: