CORTEX PHARMACEUTICALS INC/DE/
PRE 14A, 1998-10-16
PHARMACEUTICAL PREPARATIONS
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<PAGE>
 
                           SCHEDULE 14A INFORMATION
                                        
          Proxy Statement Pursuant to Section 14(a) of the Securities
                             Exchange Act of 1934

                             [Amendment No. ____]


Filed by the Registrant  [X]
Filed by a Party other than the Registrant [_]

Check the appropriate box:

[X]    Preliminary Proxy Statement
[_]    Confidential, for Use of the Commission Only (as permitted by Rule 14a-
       6(e)(2))
[_]    Definitive Proxy Statement
[_]    Definitive Additional Materials
[_]    Soliciting Material Pursuant to (S) 240.14a-11(c) or (S) 240.14a-12


                         CORTEX PHARMACEUTICALS, INC.
               (Name of Registrant as Specified in Its Charter)

                                      N/A
                  (Name of Person(s) Filing Proxy Statement)

Payment of filing fee (Check the appropriate box):

[X]    No fee required
[_]    Fee computed on table below per Exchange Act Rules 14a-6(i)(1) and 0-11.

       (1)  Title of each class of securities to which transaction applies:

       (2)  Aggregate number of securities to which transaction applies:

       (3)  Per unit price or other underlying value of transaction computed
            pursuant to Exchange Act Rule 0-11 (set forth the amount on which
            the filing fee is calculated and state how it was determined):

       (4)  Proposed maximum aggregate value of transaction:

       (5)  Total fee paid:
 

[_]    Fee paid previously by written preliminary materials.
[_]    Check box if any part of the fee is offset as provided by Exchange Act
       Rule 0-11(a)(2) and identify the filing for which the offsetting fee was
       paid previously. Identify the previous filing by registration statement
       number, or the Form or Schedule and the date of its filing.

       (1)  Amount Previously Paid:

       (2)  Form, Schedule or Registration Statement No.:

       (3)  Filing Party:

       (4)  Date Filed:
<PAGE>
 
                          CORTEX PHARMACEUTICALS, INC.
                             15241 Barranca Parkway
                            Irvine, California 92618
                                        

                    NOTICE OF ANNUAL MEETING OF STOCKHOLDERS

                               December 15, 1998



To the Stockholders of Cortex Pharmaceuticals, Inc.:

     The Annual Meeting of Stockholders of Cortex Pharmaceuticals, Inc., a
Delaware corporation (the "Company"), will be held at the offices of the
Company, 15241 Barranca Parkway, Irvine, California, on Tuesday, December 15,
1998 at 9:00 a.m. Pacific Time, to consider and vote on the following matters
described in the attached Proxy Statement:

     (1) The election of six (6) directors to serve until the next Annual
Meeting of Stockholders or until their successors are elected and duly qualified
(Proposal 1);

     (2) The approval (recommended by the Board of Directors) of an Amendment to
the Company's Restated Certificate of Incorporation to increase the authorized
number of shares of the Company's Common Stock (which Amendment may be deemed to
have anti-takeover effects) from 20,000,000 to 30,000,000 (Proposal 2);

     (3) To ratify the appointment of Ernst & Young LLP as independent auditors
of the Company for the fiscal year ending June 30, 1999 (Proposal 3); and

     (4) Such other business as may properly come before the meeting or any
adjournment thereof.

     The Board of Directors has fixed the close of business on October 27, 1998,
as the record date for the determination of stockholders entitled to notice of
and to vote at the meeting or any postponement and adjournment thereof.  The
stock transfer books will not be closed.

     The Board of Directors welcomes the personal attendance of stockholders at
the meeting. However, please sign and return the enclosed proxy, which you may
revoke at any time prior to its use, whether or not you expect to attend the
meeting. A self-addressed, postage prepaid envelope is enclosed for your
convenience. Your proxy will not be used if you attend the meeting and choose to
vote in person.


                                 By Order of the Board of Directors



                                 /s/ Vincent F. Simmon, Ph.D.
                                 Secretary


Irvine, California
November 5, 1998
<PAGE>
 
                          CORTEX PHARMACEUTICALS, INC.
                                        
                             15241 Barranca Parkway
                           Irvine, California  92618

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

                                PROXY STATEMENT
                         ANNUAL MEETING OF STOCKHOLDERS
                          To Be Held December 15, 1998
                                   9:00 a.m.

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



Solicitation and Revocation of Proxies

     The accompanying proxy is solicited by and on behalf of the Board of
Directors of Cortex Pharmaceuticals, Inc., a Delaware corporation (the
"Company"), and the Company will bear the cost of such solicitation.
Solicitation of proxies will be primarily by mail, although some of the
officers, directors and employees of the Company may solicit proxies personally
or by telephone. The Company will reimburse brokerage houses and other
custodians, nominees or fiduciaries for their expenses in sending proxy
materials to their principals.

     The persons named as proxies were designated by the Board of Directors and
are directors of the Company.  All properly executed proxies will be voted
(except to the extent that authority to vote has been withheld) and where a
choice has been specified by the stockholder as provided in the proxy it will be
voted in accordance with the specification so made.  Proxies submitted without
specification will be voted FOR the election as directors of the nominees
                            ---                                          
proposed by the Board of Directors, FOR the approval of an Amendment to the
                                    ---                                    
Company's Restated Certificate of Incorporation to increase the authorized
number of shares of Common Stock from 20,000,000 to 30,000,000 and FOR the
                                                                   ---    
ratification of Ernst & Young LLP as the Company's independent auditors.

     Any stockholder may revoke a proxy at any time before it is voted at the
meeting by a proxy bearing a later date.  A proxy may also be revoked by any
stockholder by delivering written notice of revocation to the Secretary of the
Company or by voting in person at the meeting.

     This Proxy Statement and proxy are being mailed to stockholders of the
Company on or about November 5, 1998.  The mailing address of the executive
offices of the Company is 15241 Barranca Parkway, Irvine, California 92618.


Voting at the Meeting

     Only record holders of Common Stock of the Company at the close of business
on October 27, 1998, will be entitled to notice of, and to vote at, the meeting.
As of the record date, there were 10,237,126 shares of the Company's Common
Stock outstanding.  Each share is entitled to one vote at the meeting.
Abstentions and broker non-votes are counted for purposes of determining the
presence or absence of a quorum for the transaction of business.  Abstentions
are counted in tabulating the votes cast on proposals presented to stockholders,
whereas broker non-votes are not counted for purposes of determining whether a
proposal has been approved.

                                       1
<PAGE>
 
                                  PROPOSAL ONE

                             ELECTION OF DIRECTORS
                                        
     The persons named in the enclosed proxy will vote to elect the six (6)
proposed nominees named below unless contrary instructions are given in the
proxy.  The election of directors shall be by the affirmative vote of the
holders of a plurality of the shares voting in person or by proxy at the
meeting.  Each director is to hold office until the next annual meeting and
until his successor is elected and qualified.

     The names and certain information concerning the persons nominated by the
Board of Directors to become directors at the meeting are set forth below.  The
Company's Board of Directors recommends that you vote FOR the election of each
                                                      ---                     
of the nominees named below.  It is intended that shares represented by the
proxies will be voted FOR the election to the Board of Directors of the persons
                      ---                                                      
named below unless authority to vote for nominees has been withheld in the
proxy.  Although each of the persons named below has consented to serve as a
director if elected and the Board of Directors has no reason to believe that any
of the nominees named below will be unable to serve as a director, if any
nominee withdraws or otherwise becomes unavailable to serve, the persons named
as proxies will vote for any substitute nominee designated by the Board of
Directors.  The following information regarding the nominees is relevant to your
consideration of the slate proposed by the Board of Directors:


Nominees for Director

     Robert F. Allnutt, 63, was elected a director in December 1995.  Since
February 1995, Mr. Allnutt has been a senior counselor for APCO Associates,
Inc., a public affairs and strategic communications company.  Mr. Allnutt was
Executive Vice President of the Pharmaceutical Manufacturers Association from
May 1985 until February 1995 and was Vice President for Government Relations of
Communications Satellite Corporation from May 1984 until May 1985.  Prior to
1984, Mr. Allnutt held numerous positions in the Federal Government for 25
years, including 15 years at NASA, where his positions included Associate Deputy
Administrator, the third ranking position in the agency.  Mr. Allnutt is a
director of Cypros Pharmaceuticals, Inc., a developer and marketer of
prescription pharmaceuticals.  Mr. Allnutt also serves as a member of the Board
of Directors of the National Health Council.  Mr. Allnutt holds a B.S. in
Industrial Engineering from the Virginia Polytechnic Institute and J.D. and
L.L.M. degrees from George Washington University.

     Charles J. Casamento, 53, was elected to the Board of Directors of the
Company in July 1997.  Since June 1993, Mr. Casamento has been Chairman,
President and Chief Executive Officer of RiboGene, Inc., a biopharmaceutical
company based in Hayward, California.  Prior to that, he was President and Chief
Executive Officer of Interneuron Pharmaceuticals, a neuropharmaceutical company,
from its founding in March 1989 until May 1993.  From January 1986 to March
1989, he was Senior Vice President and General Manager, Pharmaceuticals &
Biochemicals at Genzyme Corp., a biotechnology company.  From 1970 through 1985,
Mr. Casamento held senior management positions in marketing, finance and
business development at Sandoz, Johnson & Johnson and American Hospital Supply
Corp., where he was Vice President, Business Development and Strategic Planning
for the Critical Care Division.  He holds a B.S. degree in Pharmacy and an
M.B.A. from Fordham University and is a licensed pharmacist.

                                       2
<PAGE>
 
     Carl W. Cotman, Ph.D., 58, has been a Scientific Director of and consultant
to the Company since October 1987, served as a director of the Company from
March 1989 to October 1990, and was reelected as a director in November 1991.
Dr. Cotman has been a Professor of Psychobiology, Neurology, and Psychiatry at
the University of California, Irvine since 1985.  He was a Professor of
Psychobiology and Neurology at that University from 1983 to 1985, and has held
various other teaching and research positions at that University since 1968.  He
chaired the Scientific Advisory Council of the American Paralysis Association
and is a member of numerous professional associations and committees, including
the Council of the American Society for Neurochemistry, the National Institute
of Aging Task Force, the American Association for the Advancement of Science and
the International Society for Neurochemistry.  Dr. Cotman has served on the
editorial boards of numerous scientific journals and has authored or co-authored
seven books and over 400 articles in the fields of neurobiology, memory and
cognition, and the recovery of function after brain injury.  Dr. Cotman holds a
B.A. in Chemistry from Wooster College, an M.A. in Analytical Chemistry from
Wesleyan University, and a Ph.D. in Biochemistry from Indiana University.

     Michael G. Grey, 45, has been a director of the Company since September
1994.  From November 1994 until August 1998, Mr. Grey served as President of
BioChem Therapeutic, Inc., a wholly owned subsidiary of BioChem Pharma, an
international biopharmaceutical company.  From January 1994 to October 1994, Mr.
Grey was Senior Vice President, Corporate Development of Titan Pharmaceuticals,
Inc., a biopharmaceutical holding company, and President and Chief Operating
Officer at Ansan, Inc., an early stage biopharmaceutical company.  From 1991
until 1993, Mr. Grey served as Vice President, Corporate Development of Glaxo,
Inc., and from 1989 until 1991, Mr. Grey served as Director of International
Licensing of Glaxo Holdings p.l.c., where he was responsible for the worldwide
licensing activities of Glaxo, Inc.  Mr. Grey holds a B.Sc. degree in Chemistry
from the University of Notingham.

     Vincent F. Simmon, Ph.D., 55, was appointed President and Chief Executive
Officer and a director of the Company in May 1996 and has been the acting Chief
Financial Officer and Secretary of the Company since October 13, 1998.  From
November 1994 until December 1995, Dr. Simmon served as Chairman, President and
Chief Executive Officer of Prototek, Inc., a privately-held biopharmaceutical
company focusing on the development of protease inhibitors.  From March 1990 to
November 1994, Dr. Simmon served as President, Chief Executive Officer and a
director at Alpha I Biomedicals, Inc., a biotechnology company.  From February
1985 to March 1990, Dr. Simmon served as Vice President for Biomedical and
Biotechnology Research at W. R. Grace and Co. From 1979 to 1985, Dr. Simmon
served in varying capacities including Senior Vice President of Research and
Development for Genex Corporation, a genetic engineering company, and from 1973
to 1979 in varying capacities including Assistant Director, Department of
Technology for SRI International, a consulting company.  Dr. Simmon has served
as a governor of the Emerging Companies Section of BIO (Biotechnology Industrial
Organization) and a director of the Chemical  Industries Institute for
Toxicology (Research Triangle Park).  Dr. Simmon holds a B.A. degree in Biology
and Chemistry from Amherst College, an M.S. degree from the University of Toledo
in Plant Physiology and a Ph.D. degree in Molecular Biology from Brown
University.  Dr. Simmon was a post-doctoral fellow at Stanford University from
1971 to 1973.

                                       3
<PAGE>
 
     Davis L. Temple, Jr., Ph.D., 55, has been a director of and consultant to
the Company since March 1994 and served as co-member of the Office of the Chief
Executive of the Company from October 1995 to May 1996.  In April 1997, Dr.
Temple was appointed as Chairman and Chief Executive Officer of Cognetix Inc., a
privately-held biopharmaceutical drug discovery and development company.  From
November 1995 until April 1997, he was a Senior Consultant for Kaufman Brothers,
a New York investment bank.  Prior to that, from January 1994 to November 1995
he was Managing Director at Stover Haley Burns, Inc., a life science advisory
group.  From 1990 until 1993, Dr. Temple served as Vice President, CNS Drug
Discovery for Bristol-Myers Squibb and from 1984 to 1990 he served as Senior
Vice President, CNS Research at Bristol-Myers Company. Dr. Temple holds a B.S.
degree in Pharmacy from Louisiana State University and a Ph.D. degree in
Medicinal Chemistry and Pharmacology from the University of Mississippi.


Director Not Standing for Reelection

     Harvey S. Sadow, Ph.D., 76, has been a director of the Company since March
1988 and Chairman of the Board of Directors since January 1991.  Dr. Sadow has
informed the Company that he will retire from his position as Chairman of the
Board upon expiration of his term at the 1998 Annual Meeting of Stockholders and
will not stand for reelection to the Board.  Dr. Sadow was President and Chief
Executive Officer of Boehringer Ingelheim Corporation, a major health care
company, from 1971 until his retirement in January 1988 and was Chairman of the
Board of that company from 1988 through December 1990.  Dr. Sadow was Chairman
of the University of Connecticut Foundation, the President's Council of the
American Lung Association, and the Connecticut Law Enforcement Foundation and
was a member of the Board of Directors of the Pharmaceutical Manufacturers
Association ("PMA") and Chairman of the Board of the PMA Foundation.  Dr. Sadow
is also a member of several other professional committees and societies,
including the American Society for Clinical Pharmacology and Therapeutics.  He
has published extensively in the field of treatment of diabetes mellitus.  Dr.
Sadow is Chairman of Cholestech Corporation, a developer, manufacturer and
seller of lipid measuring diagnostic products; a director of Penederm, Inc., a
developer and marketer of specialized dermatologic products; and a director of
several privately-held companies in the health care field, including Trega
Biosciences, Inc., a drug development company.  Dr. Sadow holds a B.S. from the
Virginia Military Institute, an M.S. from the University of Kansas, and a Ph.D.
from the University of Connecticut.


Executive Officer

     Dr. Simmon is the only executive officer of the Company.

                                       4
<PAGE>
 
Scientific Director

     In addition to Dr. Cotman, the other Scientific Director of the Company is
Gary S. Lynch, Ph.D.

     Gary S. Lynch, Ph.D., 55, has been a Scientific Director of and consultant
to the Company since October 1987 and served as a director of the Company from
March 1988 to March 1989 and from December 1994 to December 1995.  Dr. Lynch has
been a Professor in the Department of Psychobiology at the University of
California, Irvine since 1981, and has held various other teaching and research
positions at that University since 1969.  He is a Professor at the University's
Center for the Neurobiology of Learning and Memory.  Dr. Lynch is a member of
the Neuroscience Society and the International Brain Research Organization.  He
also serves on the Advisory Board of the Cognitive Neurosciences Institute.  Dr.
Lynch has authored or co-authored over 400 articles and a number of books in the
areas of neurobiology, cognition and memory.  Dr. Lynch holds a B.A. in
Psychology from the University of Delaware and a Ph.D. in Psychology from
Princeton University.


Board Committees

     The Board of Directors of the Company has a standing Compensation Committee
and Audit Committee.  The Board of Directors does not have a standing nominating
committee.  The functions of the Compensation Committee include administering
the Company's stock plans and advising the Board of Directors on officer
compensation and on employee compensation generally.  The Compensation Committee
held two meetings during fiscal 1998 and is comprised of Dr. Cotman as Chairman
of the Committee, Mr. Grey and Dr. Temple.  The Audit Committee has the
responsibility of recommending to the Board of Directors the appointment of the
Company's outside auditors, examining the results of audits and reviewing
internal accounting controls.  The Audit Committee held one meeting during
fiscal 1998 and is comprised of Dr. Sadow as Chairman of the Committee, Mr.
Allnutt and Mr. Casamento.


Attendance at Meetings

     During the fiscal year ended June 30, 1998, the Board of Directors held a
total of four meetings. No member of the Board of Directors attended fewer than
75% of the meetings of the Board and of the committees of which he was a member.

                                       5
<PAGE>
 
Executive Compensation

     The following table sets forth summary information concerning compensation
paid or accrued by the Company for services rendered during the three fiscal
years ended June 30, 1998, to the Company's Chief Executive Officer and to the
other executive officer employed by the Company as of June 30, 1998.


                          Summary Compensation Table

<TABLE> 
<CAPTION> 
                                                                                       Long Term
                                                 Annual Compensation              Compensation Awards     
                                         ---------------------------------     ------------------------  
                                                                               Securities
                                                                               Underlying
Name and                                                      Other Annual      Options/     All Other
Principal Position                Year    Salary     Bonus    Compensation (2)   SARs(#)   Compensation($)
- ----------------------------------------------------------------------------------------------------------
<S>                               <C>    <C>        <C>           <C>             <C>           <C>     
Vincent F. Simmon, Ph.D. (1)      1998   $203,178   $    --       $14,996              --       $ --    
President, Chief                  1997    200,000    53,138        50,005              --         -- 
Executive Officer                 1996     25,000    20,410         3,613         180,000         -- 
and Acting Chief                                                                                      
Financial Officer                                                                                     
and Secretary                                                                                         
                                                                                                      
D. Scott Hagen (3)                1998   $149,900   $    --       $ 8,939              --         $ -- 
                                  1997    139,677    11,024        10,282          40,000           -- 
                                  1996    128,751    18,750        14,663          11,000           -- 
 
</TABLE>
_______________________
(1)  Dr. Simmon was appointed President and Chief Executive Officer on May 15,
     1996 and became the acting Chief Financial Officer and Secretary of the
     Company on October 13, 1998.
(2)  Represents accrued or paid-out vacation pay, sick pay and/or relocation
     reimbursements.
(3)  Mr. Hagen resigned as Vice President, Chief Financial Officer and Secretary
     of the Company on October 13, 1998.

                                       6
<PAGE>
 
Option Matters

          There were no grants of stock options to the Company's executive
officers named in the Summary Compensation Table during the fiscal year ended
June 30, 1998.  The following table sets forth certain information concerning
the exercise of options by each of the Company's executive officers named in the
Summary Compensation Table during the fiscal year ended June 30, 1998, including
the aggregate value of gains on the date of exercise.  In addition, the table
includes the number of shares covered by both exercisable and unexercisable
stock options as of June 30, 1998.  Also reported are the values for "in the
money" options which represent the positive spread between the exercise prices
of any such existing stock options and $1.875, the last sale price of Common
Stock on June 30, 1998, as reported by Nasdaq.


                Aggregated Option Exercises in Last Fiscal Year
                       and Fiscal Year-End Option Values

<TABLE>
<CAPTION>
                                              Value Realized($)
                                                 (market price       Number of Securities          Value of Unexercised
                                                   at exercise       Underlying Unexercised             In-the-Money
                           Shares Acquired       less exercise       Options at FY-End(#)          Options at FY-End($)
Name                        on Exercise(#)               price)   Exercisable   Unexercisable   Exercisable   Unexercisable
- ---------------------------------------------------------------------------------------------------------------------------
<S>                        <C>                <C>                 <C>           <C>             <C>           <C> 
Vincent F. Simmon, Ph.D.                --                $ --        124,999          55,001          $ --            $ --

D. Scott Hagen                          --                  --         36,918          34,028            --              --
</TABLE> 
_________________________


Employment and Consulting Agreements

     Vincent F. Simmon joined the Company as President and Chief Executive
Officer in May 1996.  His employment agreement calls for a base salary of
$200,000 per year with an annual bonus, at the discretion of the Board of
Directors of the Company, in cash and/or equity equal to between 15% and 50% of
his base salary, subject to annual review by the Compensation Committee.  In
connection with his employment, Dr. Simmon was granted options to purchase
180,000 shares of Common Stock at an exercise price of $5.625 per share,
representing 100% of the fair market value as of the date of grant.  The options
vest monthly over a three-year period commencing one month from the date of
grant and have a ten-year term.

     Mr. Hagen entered into a three-year employment agreement with the Company,
commencing September 1, 1988.  The employment agreement was extended for
additional terms, most recently as of January 1, 1998 for a term ending December
31, 1998; however, Mr. Hagen resigned from the Company on October 13, 1998.  The
agreement provided for a base salary of $150,000 with an annual bonus of between
$10,000 and $30,000.  Because Mr. Hagen's employment was terminated as a result
of his voluntary resignation, he is not entitled to receive any severance
payment under the employment agreement.

     Drs. Carl W. Cotman and Gary S. Lynch (both of whom are co-founders and
Scientific Directors of the Company) have each entered into a consulting
agreement with the Company. Dr. Lynch receives a consulting fee of $30,000 per
year and Dr. Cotman receives a consulting fee of $23,000 per year.  The term of
each consulting agreement commenced in November 1987 and will continue until
terminated by the respective parties thereto.  The consulting agreements
obligate the 

                                       7
<PAGE>
 
respective consultants to make themselves available to the Company for
consulting and advisory services for an average of three days per month. In
addition to his consulting fee, Dr. Lynch will be entitled to certain option
grants in connection with the Company's success in corporate partnering its
AMPAKINE(R) technology.


Director Compensation

     Each non-employee director (other than the Chairman of the Board or those
who join the Board of Directors to oversee an investment in the Company)
receives $1,500 at each Board of Directors meeting attended and an additional
$750 annual retainer for each committee on which he or she serves.  The Chairman
of the Board receives $2,500 at each Board of Directors meeting attended and an
additional $750 annual retainer for each committee on which he or she serves.
Effective October 5, 1998 the Board of Directors has elected to defer all future
cash payments of director compensation until the Company's financial condition
improves.

     Under the Company's 1996 Stock Incentive Plan, each non-employee director
(other than those who serve on the Board of Directors to oversee an investment
in the Company) is automatically granted options to purchase 15,000 shares of
Common Stock upon commencement of service as a director and additional options
to purchase 6,000 shares of Common Stock on the date of each Annual Meeting of
Stockholders.  Non-employee directors who serve on the Board of Directors to
oversee an investment in the Company receive options to purchase 7,500 shares of
Common Stock upon commencement of service as a director and additional options
to purchase 3,000 shares of Common Stock on the date of each Annual Meeting of
Stockholders.  These nonqualified options have an exercise price equal to 100%
of the fair market value of the Common Stock on the date of grant, have a ten-
year term and vest in equal increments of 33-1/3% on each anniversary date of
the dates of grant, and are otherwise subject to the terms and provisions of the
1996 Stock Incentive Plan.


                              CERTAIN TRANSACTIONS

     The Company's Restated Certificate of Incorporation provides that, pursuant
to Delaware Law, directors of the Company shall not be liable for monetary
damages for breach of the directors' fiduciary duty of care to the Company and
its stockholders.  This provision does not eliminate the duty of care, and in
appropriate circumstances equitable remedies such as injunctions or other forms
of non-monetary relief remain available under Delaware Law.  In addition, each
director will continue to be subject to liability for breach of the director's
duty of loyalty to the Company, for acts or omissions not in good faith or
involving intentional misconduct, for knowing violations of law, for actions
leading to improper personal benefit to the director and for payment of
dividends or approval of stock repurchases or redemptions that are unlawful
under Delaware Law.  The provision also does not affect a director's
responsibility under any other law, such as the federal securities laws.  The
Company has entered into Indemnification Agreements with each of its officers
and directors that obligate the Company to indemnify them as permitted by
applicable law.

     See "Employment and Consulting Agreements" for a description of certain
arrangements and transactions with executive officers and directors.


                             PRINCIPAL STOCKHOLDERS

     The following table sets forth, to the knowledge of the Company, certain
information regarding the beneficial ownership of the Company's Common Stock as
of September 30, 1998, by (i) each person known by the Company to be the
beneficial owner of more than 5% of the outstanding 

                                       8
<PAGE>
 
Common Stock, (ii) each of the directors and nominees, (iii) each of the named
executive officers in the Summary Compensation Table and (iv) all of the
executive officers and directors as a group. Except as indicated in the
footnotes to this table, the Company believes that the persons named in this
table have sole voting and investment power with respect to the shares of Common
Stock indicated.


<TABLE>
<CAPTION>
 
 
Directors,                           Shares              Percent of
Officers, and 5%                  Beneficially           Common Stock
Stockholders                         Owned               Beneficially Owned
- --------------------------------------------------------------------------- 
 
<S>                               <C>                    <C>  
Robert F. Allnutt                    21,750(1)                 *
Charles J. Casamento                 20,000(2)                 *
Carl W. Cotman, Ph.D.               141,125(3)                1.4
Michael G. Grey                      17,625(4)                 *
D. Scott Hagen                       40,651(5)                 *
Harvey S. Sadow, Ph.D.               62,125(6)                 *
Vincent F. Simmon, Ph.D.            204,599(7)                2.0
Davis L. Temple, Jr., Ph.D.          36,750(8)                 *
Quantum Partners LDC (8)            660,000(9)                6.4
Soros Fund Management
888 Seventh Avenue, 33rd Floor
New York, NY 10106
All officers and directors
   as a group (8 persons)           544,625                   5.1
</TABLE>

________________________

*    Less than one percent



(1)  Includes 10,750 shares that may be purchased upon exercise of options
     within 60 days of September 30, 1998.
(2)  Includes 5,000 shares that may be purchased upon exercise of options within
     60 days of September 30, 1998.
(3)  Includes 43,125 shares that may be purchased upon exercise of options
     within 60 days of September 30, 1998.
(4)  Includes 17,625 shares that may be purchased upon exercise of options
     within 60 days of September 30, 1998.
(5)  Includes 40,251 shares that may be purchased upon exercise of options
     within 60 days of September 30, 1998.
(6)  Includes 52,125 shares that may be purchased upon exercise of options
     within 60 days of September 30, 1998.
(7)  Includes 149,999 shares that may be purchased upon exercise of options
     within 60 days of September 30, 1998.
(8)  Includes 36,750 shares that may be purchased upon exercise of options
     within 60 days of September 30, 1998.
(9)  According to a Schedule 13D filed by George Soros (in his capacity as sole
     proprietor of Soros Fund Management) on February 18, 1997, these shares are
     held for the account of Quantum Partners LDC, which has granted investment
     discretion to Soros Fund Management.  Mr. Soros may be deemed to be
     beneficial owner of such shares.

     The Company is not aware of any arrangements that may at a subsequent date
result in a change of control of the Company.

                                       9
<PAGE>
 
                                 PROPOSAL TWO

                 AMENDMENT OF CERTIFICATE OF INCORPORATION TO
                       INCREASE AUTHORIZED COMMON STOCK

     The Board of Directors has directed that there be submitted to the
stockholders of the Company at the meeting a proposed amendment to Article
Fourth of the Company's Restated Certificate of Incorporation to increase the
number of authorized shares of Common Stock of the Company from 20,000,000 to
30,000,000.  Such amendment was unanimously approved by the Company's Board of
Directors on October 5, 1998.  No increase in the number of authorized shares of
Preferred Stock of the Company, currently 5,000,000 shares, is proposed or
anticipated.  As more fully set forth below, the proposed amendment is intended
to improve the Company's flexibility in meeting its future needs for unreserved
Common Stock.  However, and while this is not the intent of the proposal, in
addition to general corporate purposes, the proposed amendment can be used to
make more difficult a change in control of the Company.

     As of the close of business on September 30, 1998, 10,237,126 shares of
Common Stock of the Company were issued and outstanding, and 2,351,925 shares of
Common Stock were committed for issuance pursuant to outstanding stock options
and stock purchase warrants.  As of the same date, an aggregate of 2,244,681
shares of Common Stock were reserved for the conversion of up to an aggregate of
35,000 shares of 9% Cumulative Convertible Preferred Stock, 250 shares of Series
A Convertible Preferred Stock and 150,000 shares of Series B Convertible
Preferred Stock ("Convertible Preferred Stock").

     The Company's reserve of authorized but unissued shares of Common Stock has
been substantially depleted in recent years as a result of the financing
activities through the sale of Common Stock, the granting of stock options under
stock option plans, and the conversion of Convertible Preferred Stock.  The
additional shares of Common Stock for which authorization is sought would be
identical to the shares of Common Stock of the Company authorized prior to
approval of this Proposal.  Holders of Common Stock do not have preemptive
rights to subscribe to additional securities that may be issued by the Company,
which means that current stockholders do not have a prior right to purchase any
new issue of capital stock of the Company in order to maintain their
proportionate ownership thereof.

     If approved, the increased number of authorized shares of Common Stock will
be available for issue from time to time for such purposes and consideration as
the Board of Directors may approve and no further vote of stockholders of the
Company will be required, except as provided under Delaware law or under the
rules of any national securities exchange or market on which shares of Common
Stock of the Company are at the time listed.  The availability of additional
shares for issuance, without the delay and expense of obtaining the approval of
stockholders at a special meeting, will afford the Company greater flexibility
in acting upon proposed transactions.  The increase in the authorized Common
Stock may facilitate certain anti-takeover devices that may be advantageous to
management if management attempts to prevent or delay a change of control.
Employing such devices may adversely impact stockholders who desire a change in
management or who desire to participate in a tender offer or other sale
transaction involving the Company.  By use of anti-takeover devices, the Board
of Directors may thwart a merger or tender offer even though stockholders might
be offered a substantial premium over the then current market price of the
Common Stock.  At the present time, the Company is not aware of any contemplated
mergers, tender offers or other plans by a third party to attempt to effect a
change in control of the Company, and this 

                                      10
<PAGE>
 
Proposal is not being made in response to any such attempts.

     In addition, under certain circumstances the Board of Directors could
create impediments to, or frustrate persons seeking to effect, a takeover or
transfer of control of the Company, by causing such additional authorized shares
to be issued to a holder or holders who might side with the Board in opposing a
takeover bid.  In this connection, the Board could issue shares of Common Stock
to a holder that would thereby have sufficient voting power to assure that
certain types of proposals would not receive the requisite stockholder vote,
including any proposal to remove directors, to accomplish certain business
combinations opposed by the Board, or to alter, amend or repeal provisions in
the Company's Restated Certificate of Incorporation or Bylaws relating to any
such action.  Furthermore, the existence of such shares might have the effect of
discouraging any attempt by a person or entity, through the acquisition of a
substantial number of shares of Common Stock, to acquire control of the Company,
since the issuance of such shares could dilute the Common Stock ownership of
such person or entity.

     The Restated Certificate of Incorporation of the Company authorizes the
issuance of 5,000,000 shares of Preferred Stock, of which 549,100 shares remain
undesignated.  The Board of Directors, within the limitations and restrictions
contained in the Restated Certificate of Incorporation and without further
action by the Company's stockholders, has the authority to issue this
undesignated Preferred Stock from time to time in one or more series and to fix
the number of shares and the relative rights, conversion rights, voting rights,
rights and terms of redemption, liquidation preferences and any other
preferences, special rights and qualifications of any such series.  Any issuance
of Preferred Stock with voting rights could, under certain circumstances, have
the effect of delaying or preventing a change in control of the Company by
increasing the number of outstanding shares entitled to vote and increasing the
number of votes required to approve a change in control of the Company.

     The Company is also governed by Section 203 of the Delaware General
Corporation Law (the "Delaware anti-takeover law"), which provides that certain
"business combinations" between a Delaware corporation whose stock is generally
traded or held of record by more than 2,000 stockholders, such as the Company,
and an "interested stockholder" (generally defined as a stockholder who
beneficially owns 15% or more of a Delaware corporation's voting stock) are
prohibited for a three-year period following the date that such stockholder
became an "interested stockholder," unless certain exceptions apply.  The term
"business combination" is defined generally to include, among other
transactions, mergers, tender offers and transactions which increase an
"interested stockholder's" percentage ownership of stock in a Delaware
corporation.

     As set forth above, such devices may adversely impact stockholders who
desire a change in management and/or the Board of Directors or to participate in
a tender offer or other sale transaction involving a change in control of the
Company.  While it may be deemed to have potential anti-takeover effects, the
proposed amendment to increase the authorized Common Stock is not prompted by
any specific effort or takeover threat currently perceived by the Board of
Directors.  Moreover, the Board of Directors does not currently intend to
propose additional anti-takeover measures in the foreseeable future.

                                      11
<PAGE>
 
     The additional authorized shares of Common Stock will restore the Company's
flexibility to issue Common Stock to a level that the Board of Directors
believes is advisable.  The Company currently has no plans to issue any
additional shares of Common Stock other than the shares that previously have
been reserved for issuance as described above.  However, the additional shares
of Common Stock for which authorization is sought would be available for
issuance by the Company by action of the Board of Directors and could be used
for such purposes as stock dividends, acquisitions, offerings of stock or
additional compensation plans.

Vote Required; Board of Directors' Recommendation

     The affirmative vote of the holders of a majority of the outstanding shares
of Common Stock of the Company is required to authorize the proposed increase in
the authorized number of shares of Common Stock.

     If the amendment is authorized the text of paragraph (A)(1) of Article
Fourth of the Company's Restated Certificate of Incorporation will be as
follows:

            "FOURTH:  (A)(1) - AUTHORIZED CAPITAL.  (a) The total number of
shares of capital stock which the Company has the authority to issue is
35,000,000 consisting of 30,000,000 shares of Common Stock, $0.001 par value per
share (the 'Common Stock'), and 5,000,000 shares of Preferred Stock, $0.001 par
value per share (the 'Preferred Stock')."

          The Board of Directors recommends that stockholders vote FOR the
                                                                   ---    
proposal to amend the Restated Certificate of Incorporation to increase the
authorized number of shares of Common Stock.  Proxies solicited by management
will be voted FOR the proposal unless a vote against the proposal or abstention
              ---                                                              
is specifically indicated.

                                      12
<PAGE>
 
                                 PROPOSAL THREE

              RATIFICATION OF APPOINTMENT OF INDEPENDENT AUDITORS


     The Board of Directors has selected Ernst & Young LLP, independent
auditors, to audit the financial statements of the Company for the fiscal year
ending June 30, 1999.  The Board of Directors recommends that you vote FOR the
                                                                       ---    
ratification of such appointment.  In the event of a negative vote on such
ratification, the Board of Directors will reconsider its selection.  Ernst &
Young LLP's representatives are expected to be present at the meeting with the
opportunity to make a statement if they desire to do so and are expected to be
available to respond to appropriate questions.

     The persons named in the enclosed proxy will vote to appoint Ernst & Young
LLP unless contrary instructions are given in the proxy.  The appointment of
Ernst & Young LLP shall be by the affirmative vote of the holders of a majority
of the shares voting on the proposal in person or by proxy at the meeting.


                             STOCKHOLDER PROPOSALS

     Any stockholder desiring to submit a proposal for action at the 1999 Annual
Meeting of Stockholders and presentation in the Company's proxy statement with
respect to such meeting should arrange for such proposal to be delivered to the
Company's offices, 15241 Barranca Parkway, Irvine, California  92618, addressed
to the Secretary, no later than July 8, 1999 in order to be considered for
inclusion in the Company's proxy statement relating to the meeting.  Matters
pertaining to such proposals, including the number and length thereof,
eligibility of persons entitled to have such proposals included and other
aspects are regulated by the Securities Exchange Act of 1934, Rules and
Regulations of the Securities and Exchange Commission and other laws and
regulations to which interested persons should refer.

     On May 21, 1998 the Securities and Exchange Commission adopted an amendment
to Rule 14a-4, as promulgated under the Securities and Exchange Act of 1934, as
amended.  The amendment to Rule 14a-4(c)(1) governs the Company's use of its
discretionary proxy voting authority with respect to a stockholder proposal
which is not addressed in the Company's proxy statement.  The new amendment
provides that if a proponent of a proposal fails to notify the Company at least
45 days prior to the month and day of mailing of the prior year's proxy
statement, then the Company will be allowed to use its discretionary voting
authority when the proposal is raised at the meeting, without any discussion of
the matter in the proxy statement.

     With respect to the Company's 1999 Annual Meeting of Stockholders, if the
Company is not provided notice of a stockholder proposal, which the stockholder
has not previously sought to include in the Company's proxy statement, by
September 21, 1999, the Company will be allowed to use its voting authority as
described above.

                                      13
<PAGE>
 
                         COMPLIANCE WITH SECTION 16(a)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                                        

     Section 16(a) of the Securities Exchange Act of 1934 requires the Company's
directors and executive officers and persons who own more than ten percent of a
registered class of the Company's equity securities to file with the Securities
and Exchange Commission (the "SEC") initial reports of ownership and reports of
changes in ownership of Common Stock and other equity securities of the Company.
Officers, directors and ten-percent stockholders are required by SEC regulations
to furnish the Company with copies of all Section 16(a) forms they file.  To the
Company's knowledge, based solely on the review of copies of such reports
furnished to the Company and written representations that no other reports were
required, during the fiscal year ended June 30, 1998 all of the Company's
officers, directors and ten-percent stockholders complied with all applicable
Section 16(a) filing requirements.


                         TRANSACTION OF OTHER BUSINESS

     As of the date of this Proxy Statement, the Board of Directors is not aware
of any matters other than those set forth herein and in the Notice of Annual
Meeting of Stockholders that will come before the meeting.  Should any other
matters arise requiring the vote of stockholders, it is intended that proxies
will be voted in respect thereto in accordance with the best judgment of the
person or persons voting the proxies.

     Please return your proxy as soon as possible. Unless a quorum consisting of
a majority of the outstanding shares entitled to vote is represented at the
meeting, no business can be transacted. Therefore, please be sure to date and
sign your proxy exactly as your name appears on your stock certificate and
return it in the enclosed postage prepaid return envelope.  Please act promptly
to ensure that you will be represented at this important meeting.

     THE COMPANY WILL PROVIDE WITHOUT CHARGE, AT THE WRITTEN REQUEST OF ANY
BENEFICIAL OWNER OF SHARES ENTITLED TO VOTE AT THE ANNUAL MEETING OF
STOCKHOLDERS, A COPY (WITHOUT EXHIBITS) OF THE COMPANY'S ANNUAL REPORT ON FORM
10-KSB AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION FOR THE FISCAL YEAR
ENDED JUNE 30, 1998. REQUESTS SHOULD BE MAILED TO THE SECRETARY, CORTEX
PHARMACEUTICALS, INC., 15241 BARRANCA PARKWAY, IRVINE, CALIFORNIA 92618.


                                  By Order of the Board of Directors



                                  /s/ Vincent F. Simmon, Ph.D.
                                  Secretary


November 5, 1998

                                      14
<PAGE>
 
                          CORTEX PHARMACEUTICALS, INC.

                     PROXY SOLICITED BY BOARD OF DIRECTORS


     _______________________ and Vincent F. Simmon, Ph.D., and each or either of
them, with full power of substitution, are hereby appointed proxies to vote the
stock of the undersigned in Cortex Pharmaceuticals, Inc. at the Annual Meeting
of Stockholders on December 15, 1998, and at any postponement and adjournment
thereof, to be held at 15241 Barranca Parkway, Irvine, California  92618, at
9:00 a.m. Pacific Time.

     Management recommends that you vote FOR Proposal 1, FOR Proposal 2 and FOR
     --------------------------------------------------------------------------
Proposal 3.
- ---------- 

     1.  PROPOSAL 1 ELECTION OF DIRECTORS.
         -------------------------------- 

    [_]  FOR all Nominees listed below   [_] WITHHOLD AUTHORITY to
        (except as indicated to the          vote for all Nominees
        contrary below)                      listed below

     Robert F. Allnutt, Charles J. Casamento, Carl W. Cotman, Ph.D., Michael G.
Grey, Vincent F. Simmon, Ph.D. and Davis L. Temple, Jr., Ph.D.


     INSTRUCTION:  To withhold authority to vote for any individual Nominee,
write that Nominee's name in the space provided below.


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


     2.  PROPOSAL 2 AMENDMENT TO RESTATED CERTIFICATE OF INCORPORATION TO
         ----------------------------------------------------------------
INCREASE AUTHORIZED NUMBER OF SHARES OF COMMON STOCK.
- ---------------------------------------------------- 

    [_]  FOR            [_]   AGAINST           [_]      ABSTAIN


     3.  PROPOSAL 3 RATIFICATION OF THE APPOINTMENT OF ERNST & YOUNG LLP AS
         ------------------------------------------------------------------
INDEPENDENT AUDITORS OF THE COMPANY FOR THE FISCAL YEAR ENDING JUNE 30, 1999.
- ---------------------------------------------------------------------------- 


    [_]  FOR            [_]   AGAINST           [_]      ABSTAIN


     In their discretion, the proxies are authorized to vote upon such other
business as may properly come before the meeting or any adjournment thereof,
including procedural and other matters relating to the conduct of the meeting.

                             [Front of Proxy Card]
<PAGE>
 
     THIS PROXY WILL BE VOTED AS DIRECTED.  UNLESS OTHERWISE DIRECTED, THIS
PROXY WILL BE VOTED FOR THE ELECTION OF THE SIX DIRECTOR NOMINEES LISTED ABOVE
AND FOR PROPOSALS 2 AND 3.



                            Please sign exactly as name appears hereon.



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


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



                            Date:  _____________________________, 1998


                            When shares are held by joint tenants, both should
                            sign. When signing as attorney, executor,
                            administrator, trustee or guardian, please give full
                            title as such. If a corporation, please sign in full
                            corporate name by President or other authorized
                            officer. If a partnership, please sign in
                            partnership name by authorized person.



     PLEASE IMMEDIATELY DATE, SIGN AND RETURN THIS CARD IN THE ENCLOSED
ENVELOPE.  THANK YOU FOR YOUR PROMPT ATTENTION TO THIS IMPORTANT MATTER.



                            [Back of Proxy Card]


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