THIS CERTIFICATE AND THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"), OR ANY
STATE SECURITIES LAW, AND MAY NOT BE SOLD, TRANSFERRED, PLEDGED, HYPOTHECATED OR
OTHERWISE DISPOSED OF  UNTIL EITHER (i) A REGISTRATION STATEMENT UNDER THE
SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS SHALL HAVE BECOME EFFECTIVE
WITH REGARD THERETO, OR (ii) THE CORPORATION SHALL HAVE RECEIVED AN OPINION OF
COUNSEL ACCEPTABLE TO THE CORPORATION AND ITS COUNSEL THAT AN EXEMPTION FROM
REGISTRATION UNDER THE SECURITIES ACT OR APPLICABLE STATE SECURITIES LAWS IS
AVAILABLE IN CONNECTION WITH SUCH OFFER, SALE OR TRANSFER.

Warrant to Purchase
106,195 shares


                        WARRANT TO PURCHASE COMMON STOCK
                                       OF
                          CORTEX PHARMACEUTICALS, INC.

     THIS CERTIFIES that Swartz Investments, Inc. ("Holder") or any subsequent
holder hereof, has the right to purchase from Cortex Pharmaceuticals, Inc., a
Delaware Corporation (the "Company"), not more than 106,195 fully paid and
nonassessable shares of the Company's Common Stock, $.001 par value  ("Common
Stock"), at a price of $2.825 per share subject to adjustment as provided below
(the "Exercise Price"), at any time on or before 5:00 p.m., Atlanta, Georgia
time, on December 6, 2000.

     The holder of this Warrant agrees with the Company that this Warrant is
issued and all rights hereunder shall be held subject to all of the conditions,
limitations and provisions set forth herein.

     1.   EXERCISE.

     This Warrant may be exercised as to all or any lesser number of full shares
of Common Stock covered hereby upon surrender of this Warrant, with the
Subscription Form attached hereto duly executed, together with the full Exercise
Price (as hereinafter defined) in cash, or by certified or official bank check
payable in New York Clearing House Funds for each share of Common Stock as to
which this Warrant is exercised, at the office of the Company, Attn: President,
Cortex Pharmaceuticals, Inc., 15241 Barranca Parkway Irvine, CA 92718, or at
such other office or agency as the Company may designate in writing, by
overnight mail, with an advance copy of the Subscription Form by facsimile (such
surrender and payment hereinafter called the "Exercise of this Warrant").  The
"Date of Exercise" of the Warrant shall be defined as the date that the advance
copy of the Subscription Form is sent by facsimile to the Company, provided that
the original  Warrant and Subscription Form are received by the Company within
five business days  thereafter.



The original Warrant and Subscription Form must be received within 5 business
days of the Date of Exercise, or the Subscription Form MAY, AT THE COMPANY'S
OPTION, be considered void.  This Warrant shall be canceled upon its Exercise,
and, as soon as practical AFTER THE DATE OF EXERCISE, the holder hereof shall be
entitled to receive a certificate or certificates for the number of shares of
Common Stock purchased upon such Exercise and a new Warrant or Warrants
(containing terms identical to this Warrant) representing any unexercised
portion of this Warrant.  Each person in whose name any certificate for shares
of Common Stock is issued shall, for all purposes, be deemed to have become the
holder of record of such shares on the Date of Exercise of this Warrant,
irrespective of the date of delivery of such certificate.  Nothing in this
Warrant shall be construed as conferring upon the holder hereof any rights as a
shareholder of the Company.

     2.   PAYMENT OF WARRANT EXERCISE PRICE.

     Payment of the Exercise Price may be made by any of the following, or a
combination thereof, at the election of Holder:

          (i)  cash, certified check or cashiers check or wire transfer; or

          (ii) surrender of this Warrant at the principal office of the Company
together with notice of election, in which event the Company shall issue Holder
a number of shares of Common Stock computed using the following formula:

               X = Y (A-B)/A

where:    X = the number of shares of Common Stock to be issued to Holder (not
              to exceed the number of shares set forth on the cover page of this
              Warrant, as adjusted pursuant to the provisions of Section 4 of
              this Warrant).

          Y = the number of shares of Common Stock for which this Warrant
              is being exercised.

          A = the Market Price of one share of Common Stock (for purposes of
          this Section 2(ii), the "Market Price" shall be defined as the average
          closing bid price of the Common Stock for the five trading days prior
          to the Date of Exercise of this Warrant (the "Average Closing Bid
          Price"), as reported by the National Association of Securities Dealers
          Automated Quotation System ("NASDAQ"), or if the Common Stock is not
          traded on NASDAQ, the Average Closing Bid Price in the over-the-
          counter market; provided, however, that if the Common Stock is listed
          on a stock exchange, the Market Price shall be the Average Closing Bid
          Price on such exchange).

          B = the Exercise Price.

It is intended that the Common Stock issuable upon exercise of this Warrant in a
cashless exercise transaction shall be deemed to have been acquired at the time
this Warrant was



issued, for purposes of Rule 144(d)(3)(ii).

     3.   TRANSFER AND REGISTRATION.

     Subject to the provisions of Section 7 of this Warrant, this Warrant may be
transferred on the books of the Company, wholly or in part, in person or by
attorney, upon surrender of this Warrant properly endorsed, with signature
guaranteed.  This Warrant shall be canceled upon such surrender and, as soon as
practicable thereafter, the person to whom such transfer is made shall be
entitled to receive a new Warrant or Warrants as to the portion of this Warrant
transferred, and the holder of this Warrant shall be entitled to receive a new
Warrant or Warrants as to the portion hereof retained. The Common Stock issuable
upon the exercise of this Warrant constitute "Registrable Securities" under that
certain Registration Rights Agreement dated on or about December  6, 1995
between the Company and certain investors and, accordingly, has the benefit of
the registration rights pursuant to that agreement.

     4.   ANTI-DILUTION ADJUSTMENTS.

          (a)  If the Company shall at any time declare a dividend payable in
shares of Common Stock, then the holder hereof, upon Exercise of this Warrant
after the record date for the determination of holders of Common Stock entitled
to receive such dividend, shall be entitled to receive upon Exercise of this
Warrant, in addition to the number of shares of Common Stock as to which this
Warrant is Exercised, such additional shares of Common Stock as such holder
would have received had this Warrant been Exercised immediately prior to such
record date.

          (b)  If the Company shall at any time effect a recapitalization or
reclassification of such character that the shares of Common Stock shall be
changed into or become exchangeable for a larger or smaller number of shares,
then upon the effective date thereof, the number of shares of Common Stock which
the holder hereof shall be entitled to purchase upon Exercise of this Warrant
shall be increased or decreased, as the case may be, in direct proportion to the
increase or decrease in the number of shares of Common Stock by reason of such
recapitalization or reclassification, and the Exercise Price shall be, in the
case of an increase in the number of shares, proportionately decreased and, in
the case of a decrease in the number of shares, proportionally increased.

          (c)  If the Company shall at any time distribute to holders of Common
Stock cash, evidences of indebtedness or other securities or assets (other than
cash dividends or distributions payable out of earned surplus or net profits
for the current or preceding year) then, in any such case, the holder of this
Warrant shall be entitled to receive, upon exercise of this Warrant, with
respect to each share of Common Stock issuable upon such Exercise, the amount of
cash or evidences of indebtedness or other securities or assets which such
holder would have been entitled to receive with respect to each such share of
Common Stock as a result of the happening of such event had this Warrant been
Exercised immediately prior to the record date or other date fixing shareholders
to be affected by such event (the "Determination Date") or, in lieu thereof, if
the Board of Directors of the Company should so determine at the time of such
distribution, a reduced



Exercise Price determined by multiplying the Exercise Price on the Determination
Date by a fraction, the numerator of which is the result of such Exercise Price
reduced by the value of such distribution applicable to one share of Common
Stock (such value to be determined by the Board in its discretion) and the
denominator of which is such Exercise Price.

          (d)  If the Company shall at any time consolidate or merge with any
other corporation or transfer all or substantially all of its assets, then the
Company shall deliver written notice to the Holder of such merger, consolidation
or sale of assets at least thirty (30) days prior to the closing of such merger,
consolidation or sale of assets and this Warrant shall terminate and expire
immediately prior to the closing of such merger, consolidation or sale of
assets.

          (e)  As used in this Warrant, the term "Exercise Price" shall mean the
purchase price per share specified in this Warrant until the occurrence of an
event stated in subsection (b) or (c) of this Section 4 and thereafter shall
mean said price as adjusted from time to time in accordance with the provisions
of said subsection.  No such adjustment shall be made unless such adjustment
would change the Exercise Price at the time by $.01 or more; provided, however,
that all adjustments not so made shall be deferred and made when the aggregate
thereof would change the Exercise Price at the time by $.01 or more. No
adjustment made pursuant to any provision of this Section 4 shall have the
effect of increasing the total consideration payable upon Exercise of this
Warrant in respect of all the Common Stock  as to which  this Warrant may be
exercised.

          (f)  In the event that at any time, as a result of an adjustment made
pursuant to this Section 4, the holder of this Warrant shall, upon Exercise of
this Warrant, become entitled to receive shares and/or other securities or
assets (other than Common Stock) then, wherever appropriate, all references
herein to shares of Common Stock shall be deemed to refer to and include such
shares and/or other securities or assets; and thereafter the number of such
shares and/or other securities or assets shall be subject to adjustment from
time to time in a manner and upon terms as nearly equivalent as practicable to
the provisions of this Section 4.

     5.   FRACTIONAL INTERESTS.

          No fractional shares or scrip representing fractional shares shall be
issuable upon the Exercise of this Warrant, but on Exercise of this Warrant, the
holder hereof may purchase only a whole number of shares of Common Stock. The
Company shall make a payment in cash in respect of any fractional shares which
might otherwise be issuable upon Exercise of this Warrant, calculated by
multiplying the fractional share amount by the market price of the Company's
Common Stock on the Date of Exercise as reported by the Nasdaq National Market
or such other exchange as Company's Common Stock is traded on.

     6.   RESERVATION OF SHARES.

          The Company shall at all times reserve for issuance such number of



authorized and unissued shares of Common Stock (or other securities substituted
therefor as herein above provided) as shall be sufficient for Exercise of this
Warrant. The Company covenants and agrees that upon Exercise of this Warrant,
all shares of Common Stock issuable upon such Exercise shall be duly and validly
issued, fully paid, nonassessable and not subject to preemptive rights of any
shareholders.

     7.   RESTRICTIONS ON TRANSFER.

          This Warrant and the Common Stock issuable on Exercise hereof have not
been registered under the Securities Act of 1933, as amended, and may not be
sold, transferred, pledged, hypothecated or otherwise disposed of in the absence
of registration or the availability of an exemption  from registration under
said Act, and, in the event a holder believes an exemption from the registration
requirements of the Act is available, the holder must deliver a legal opinion
satisfactory in form and substance, to the Issuer and its counsel, stating that
such exemption is available. All shares of Common Stock issued upon Exercise of
this Warrant shall bear an appropriate legend to such effect.

     8.   BENEFITS OF THIS WARRANT.

          Nothing in this Warrant shall be construed to confer upon any person
other than the Company and the holder of this Warrant any legal or equitable
right, remedy or claim under this Warrant and this Warrant shall be for the sole
and exclusive benefit of the Company and the holder of this Warrant.

     9.   APPLICABLE LAW.

          This Warrant is issued under and shall for all purposes be governed by
and construed in accordance with the laws of the state of Delaware.
Jurisdiction for any dispute regarding this Warrant lies in Delaware.

     10.  LOSS OF WARRANT.

          Upon receipt by the Company of evidence of the loss, theft,
destruction or mutilation of this Warrant, and (in the case of loss, theft or
destruction) of indemnity or security reasonably satisfactory to the Company,
and upon surrender and cancellation of this Warrant, if mutilated, the Company
shall execute and deliver a new Warrant of like tenor and date.

     11.  NOTICE TO COMPANY.

          Notices or demands pursuant to this Warrant to be given or made by the
holder of this Warrant to or on the Company shall be sufficiently given or made
if sent by certified or registered mail, return receipt requested, postage
prepaid, and addressed, until another address is designated in writing by the
Company, Attn: President, Cortex Pharmaceuticals, Inc., 15241 Barranca Parkway
Irvine, CA 92718.  Notices or demands pursuant to this Warrant to be given or
made by the Company to or on the holder of this Warrant shall be sufficiently
given or made if sent by certified or registered mail, return receipt requested,
postage prepaid, and addressed, until another address is designated in



writing by the holder, Attn:  Mr. Eric Swartz, Swartz Investments, Inc., 1080
Holcomb Bridge Road, 200 Roswell Summit, Suite 285, Roswell, GA 30076 until
another address is designated in writing by Swartz Investments, Inc.

     IN WITNESS WHEREOF, this Warrant is hereby executed effective as of the
date set forth below.


Dated as of:  December 8, 1995


                              CORTEX PHARMACEUTICALS, INC.



                                        By: /s/ D. SCOTT HAGEN
                                           ------------------------------------

                                        Print Name: D. SCOTT HAGEN
                                                   ----------------------------

                                        Title: Acting President and CEO
                                              ---------------------------------



                                SUBSCRIPTION FORM

                        TO:  CORTEX PHARMACEUTICALS, INC.

     The undersigned hereby irrevocably exercises the right to purchase
____________ of the shares of Common Stock of Cortex Pharmaceuticals, Inc., a
Delaware corporation, evidenced by the attached Warrant, and herewith makes
payment of the Exercise Price with respect to such shares in full, all in
accordance with the conditions and provisions of said Warrant.

     The undersigned agrees not to offer, sell, transfer or otherwise dispose of
any of such Common Stock, except in accordance with the provisions of Section 7
of the Warrant, and consents that the following legend may be affixed to the
certificates for the Common Stock hereby subscribed for, if such legend is
applicable:

     "The securities represented by this certificate have not been registered
     under the Securities Act of 1933, as amended (the "Securities Act"), or any
     state securities law, and may not be sold, transferred, pledged,
     hypothecated or otherwise disposed of until either (i) a registration
     statement under the Securities Act and applicable state securities laws
     shall have become effective with regard thereto, or (ii) the corporation
     shall have received an opinion of counsel acceptable to the corporation and
     its counsel that an exemption from registration under the Securities Act or
     applicable state securities laws is available in connection with such
     offer, sale or transfer."

     The undersigned requests that certificates for such shares be issued, and a
warrant representing any unexercised portion thereof be issued, pursuant to the
Warrant in the name of  the Registered Holder and delivered to the undersigned
at the address set forth below:


Dated:


- --------------------------------------------------------------------------------
                         Signature of Registered Holder

- --------------------------------------------------------------------------------
                        Name of Registered Holder (Print)


- --------------------------------------------------------------------------------
                                     Address
- --------------------------------------------------------------------------------
The attached Warrant and the securities issuable on exercise thereof have not
been registered under the Securities Act of 1933, as amended, and may not be
sold, transferred, pledged, hypothecated or otherwise disposed of in the absence
of registration or the availability of an exemption from registration under said
Act.
- --------------------------------------------------------------------------------



                                   ASSIGNMENT

                    (To be executed by the registered holder
                        desiring to transfer the Warrant)

     FOR VALUE RECEIVED, the undersigned holder of the attached Warrant hereby
sells, assigns and transfers unto the person or persons below named the right to
purchase ___________ shares of the Common Stock of CORTEX PHARMACEUTICALS, INC.
evidenced by the attached Warrant and does hereby irrevocably constitute and
appoint _______________________ attorney to transfer the said Warrant on the
books of the Company, with full power of substitution in the premises.

Dated:                                        __________________________________
                                             Signature

Fill in for new Registration of Warrant:

___________________________________
               Name


___________________________________
             Address


___________________________________
Please print name and address of
assignee (including zip code number)


- --------------------------------------------------------------------------------

NOTICE

The signature to the foregoing Subscription Form or Assignment must correspond
to the name as written upon the face of the attached Warrant in every
particular, without alteration or enlargement or any change whatsoever.

- --------------------------------------------------------------------------------