CORTEX PHARMACEUTICALS INC/DE/
DEF 14A, 1999-10-28
PHARMACEUTICAL PREPARATIONS
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<PAGE>

                                 SCHEDULE 14A
===============================================================================

          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:

[_]  Preliminary Proxy Statement         [_]  Confidential, for use of the
                                              Commission Only (as permitted by
                                              Rule 14a-6(e)(2))

[X]  Definitive Proxy Statement

[_]  Definitive Additional Materials

[_]  Soliciting Material Pursuant to Section 240.14a-11(c) or Section 240.14a-12

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

                                      N/A
- --------------------------------------------------------------------------------
   (Name of Person(s) Filing Proxy Statement, if other than the Registrant)

Payment of Filing Fee (Check the appropriate box):

[X]  No fee required

[_]  Fee computed on table below per Exchange Act Rules 14a-6(i)(4) 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 with 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.

<PAGE>

                         CORTEX PHARMACEUTICALS, INC.
                            15241 Barranca Parkway
                           Irvine, California  92618

                   NOTICE OF ANNUAL MEETING OF STOCKHOLDERS

                               December 17, 1999


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, 15231 Barranca Parkway, Irvine, California, on Friday, December 17,
1999 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)  To ratify the appointment of Ernst & Young LLP as independent auditors
of the Company for the fiscal year ending June 30, 2000 (Proposal 2); and

     (3)  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, 1999,
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



                                 Vincent F. Simmon, Ph.D.
                                 Secretary

Irvine, California
November 5, 1999
<PAGE>

                         CORTEX PHARMACEUTICALS, INC.
                            15241 Barranca Parkway
                           Irvine, California  92618
                             --------------------

                                PROXY STATEMENT
                        ANNUAL MEETING OF STOCKHOLDERS
                         To Be Held December 17, 1999
                                   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 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, 1999. 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, 1999, will be entitled to notice of, and to vote at, the meeting.
As of the record date, there were 15,528,182 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, 64, has been a director since December 1995 and Chairman
of the Board since February 1999. 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 Governmental Relations of Communications Satellite
Corporation from May 1984 until May 1985. Prior to 1985, 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.
He also serves as a member of the Boards of Directors of the Partnership for
Caring and of the National Medals of Science and Technology. 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, 54, 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. in Pharmacy and an M.B.A. from
Fordham University and is a licensed pharmacist.

                                       2
<PAGE>

     Carl W. Cotman, Ph.D., 59, 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, 46, has been a director of the Company since September
1994.  Since January 1999, Mr. Grey has been President and Chief Executive
Officer of Trega Biosciences, Inc., a drug discovery company pursuing the
identification and early-stage development of novel, small-molecule drug
therapies.  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., and was responsible for the worldwide
licensing activities of Glaxo.  Since July 1999, Mr. Grey has also served as a
member of the Board of Directors of Epimmune Inc., a developer of vaccines to
treat and prevent infectious diseases and cancer.  Mr. Grey holds a B.Sc. in
Chemistry from the University of Notingham.

     Vincent F. Simmon, Ph.D., 56, 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 to 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. in Biology and Chemistry from
Amherst College, a M.S. from the University of Toledo in Plant Physiology and a
Ph.D. in Molecular Biology from Brown University.  Dr. Simmon was a post-
doctoral fellow from 1971 to 1973 at Stanford University.

                                       3
<PAGE>

     Davis Temple, Jr., Ph.D., 56, has been a director of and consultant to the
Company since March 1994 and served as co-member of the Office of Chief
Executive Officer of the Company from October 1995 to May 1996.  In April 1997,
Dr. Temple was appointed as Chief Executive Officer of Cognetix, a privately
held biopharmaceutical drug discovery and development company.  Dr. Temple has
served as the Chairman of Cognetix since January 1999.  From November 1995 until
April 1998, 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,
of 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. in
Pharmacy and a Ph.D. in Medicinal Chemistry and Pharmacology from the University
of Mississippi.  Dr. Temple completed post-doctorate research at Louisiana State
University.

Executive Officer

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

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., 56, 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 again from December 1994 to December 1995.  Dr.
Lynch has been a Professor in the Department of Psychology 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 four (4) meetings during fiscal 1999 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 (1) meeting during
fiscal 1999 and is comprised of Mr. Allnutt and Mr. Casamento.

                                       4
<PAGE>

Attendance at Meetings

     During the fiscal year ended June 30, 1999, the Board of Directors held a
total of twelve (12) 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.

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, 1999, to the Company's Chief Executive Officer.

<TABLE>
<CAPTION>
                                             Summary Compensation Table
                                                                                     Long Term
                                                 Annual Compensation            Compensation Awards
                                                 -------------------          -----------------------

                                                                           Securities
                                                                           Underlying
Name and                                                     Other Annual  Options/   All Other
Principal Position            Year    Salary    Bonus (2)    Compensation   SARs(#)   Compensation($)
- ------------------            ----    ------    ---------    -------------  -------   ---------------
<S>                            <C>     <C>        <C>         <C>          <C>            <C>
Vincent F. Simmon, Ph.D.(1)    1999  $ 211,370  $ 100,000     $    --      330,000 (4)    $   --
President, Chief               1998    203,178        --           --           --            --
Executive Officer,             1997    200,000    53,138       35,307 (3)       --            --
Acting Chief
Financial Officer
and Secretary
- ----------------------------
</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)  According to Dr. Simmon's employment agreement, he is eligible to receive a
     bonus of between 15% to 50% of his annual base salary. Dr. Simmon
     voluntarily postponed any bonus for the year ended June 30, 1998. The bonus
     for the year ended June 30, 1999 includes an amount to adjust for the bonus
     not paid in fiscal 1998.  Of the bonus amount indicated for the year ended
     June 30, 1999, $20,000 was deferred and paid in fiscal 2000.
(3)  Represents relocation reimbursements.
(4)  Includes stock options to purchase 180,000 shares of the Company's Common
     Stock that were repriced in December 1998 from an exercise price of $5.625
     per share to $0.375 per share, which represented the fair market value of
     the Company's Common Stock at the time of repricing.

                                       5
<PAGE>

Option Matters

          Option Grants.  The following table sets forth certain information
concerning grants of stock options to the Company's executive officer named in
the Summary Compensation Table during the fiscal year ended June 30, 1999.

<TABLE>
<CAPTION>
                 Option Grants in Last Fiscal Year

                          Number of     % of Total
                          Securities    Options
                          Underlying    Granted to
                          Options       Employees in     Exercise    Expiration
Name                      Granted(#)    Fiscal Year (1)  Price($/Sh)  Date
- ----                      ----------    ---------------  -----------  ----
<S>                       <C>                 <C>          <C>        <C>
Vincent F. Simmon, Ph.D.  150,000             21%          $0.469     02/05/09
                          180,000(2)          25%          $0.375     12/22/08
- -----------------------
</TABLE>

 (1) Includes options repriced on December 23, 1998.
 (2) Represents options originally granted to Dr. Simmon in May 1996, in
     connection with his employment.  On December 23, 1998, these options were
     repriced from an exercise price of $5.625 per share to $0.375 per share,
     representing the fair market value of the Company's common stock at the
     time of repricing.

     Option Exercises.  The following table sets forth certain information
concerning the exercise of options by the Company's executive officer during the
fiscal year ended June 30, 1999, 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, 1999.  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 $1.00,
the closing price of Common Stock on June 30, 1999, as reported by the OTC
Bulletin Board.

                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.   0                 $         0     60,000        270,000         $  37,500      $   154,650

- ------------------------
</TABLE>

     Option Repricing. During the year ended June 30, 1999, the Company restated
the exercise price of stock options to purchase 180,000 shares of the Company's
common stock previously granted to its executive officer, Vincent F. Simmon,
Ph.D. To recognize the contributions of Dr. Simmon, the Company's Compensation
Committee restated the exercise price of such stock options from an exercise
price of $5.625 per share to $0.375 per share, representing the fair market
value of the Company's common stock as of the date of the repricing.

                                       6
<PAGE>

Employment and Consulting Agreements

     Vincent F. Simmon joined the Company as President and Chief Executive
Officer in May 1996.  His employment agreement currently calls for a base salary
of $220,000 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.  In December 1998, the exercise price of these
options was restated to $0.375 per share.

     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 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 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.  The Board of Directors
elected to defer all cash payments of director compensation for Board of
Directors meetings held from October 1998 through January 1999.

     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.

                                       7
<PAGE>

                              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.

                                       8
<PAGE>

                             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, 1999, by (i) each person known by the Company to be the
beneficial owner of more than 5% of the outstanding Common Stock, (ii) each of
the Company's directors and nominees, (iii) the named executive officer in the
Summary Compensation Table and (iv) all of the Company's 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 (1)             Owned (2)      Beneficially Owned (2)
       -----------------          ------------    ------------------------
  <S>                             <C>             <C>
  Robert F. Allnutt                  25,125(3)                *
  Charles J. Casamento               12,000(4)                *
  Carl W. Cotman, Ph.D.             153,375(5)                *
  Michael G. Grey                    25,375(6)                *
  Vincent F. Simmon, Ph.D.          119,500(7)                *
  Davis L. Temple, Jr., Ph.D.        47,875(8)                *
  All officers and directors
     as a group (6 persons)         383,250(9)              2.4%

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

</TABLE>

 *  Less than one percent

 (1)  Except as otherwise indicated, the address of such beneficial owner is at
      the Company's principal executive offices, 15241 Barranca Parkway, Irvine,
      California  92618.
 (2)  Applicable percentage of ownership at September 30, 1999 is based upon
      15,528,182 shares of Common Stock outstanding.  Beneficial ownership is
      determined in accordance with the rules of the Securities and Exchange
      Commission and includes voting and investment power with respect to shares
      shown as beneficially owned.  Shares of Common Stock subject to options or
      warrants currently exercisable or exercisable within 60 days of September
      30, 1999 are deemed outstanding for computing the shares and percentage
      ownership of the person holding such options or warrants, but are not
      deemed outstanding for computing the percentage ownership of any other
      person or entity.
 (3)  Includes 19,125 shares that may be purchased upon exercise of options
      within 60 days of September 30, 1999.
 (4)  Includes 12,000 shares that may be purchased upon exercise of options
      within 60 days of September 30, 1999.
 (5)  Includes 55,375 shares that may be purchased upon exercise of options
      within 60 days of September 30, 1999.
 (6)  Includes 25,375 shares that may be purchased upon exercise of options
      within 60 days of September 30, 1999.
 (7)  Includes 60,000 shares that may be purchased upon exercise of options
      within 60 days of September 30, 1999.
 (8)  Includes 47,875 shares that may be purchased upon exercise of options
      within 60 days of September 30, 1999.
 (9)  Includes 219,750 shares that may be purchased upon exercise of options
      within 60 days of September 30, 1999.

     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

              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, 2000.  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 2000 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, 2000 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 2000 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, 2000, the Company will be allowed to use its voting authority as
described above.

                                       10
<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, 1999, 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, 1999. REQUESTS SHOULD BE MAILED TO THE SECRETARY, CORTEX
PHARMACEUTICALS, INC., 15241 BARRANCA PARKWAY, IRVINE, CALIFORNIA  92618.

                                  By Order of the Board of Directors



                                  Vincent F. Simmon, Ph.D.
                                  Secretary

November 5, 1999

                                       11
<PAGE>

                         CORTEX PHARMACEUTICALS, INC.

                     PROXY SOLICITED BY BOARD OF DIRECTORS

     Robert F. Allnutt 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 17, 1999, and at any postponement and adjournment
thereof, to be held at 15231 Barranca Parkway, Irvine, California  92618, at
9:00 a.m. Pacific Time.

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

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 RATIFICATION OF THE APPOINTMENT OF ERNST & YOUNG LLP AS
    ------------------------------------------------------------------
    INDEPENDENT AUDITORS OF THE COMPANY FOR THE FISCAL YEAR ENDING JUNE 30,
    -----------------------------------------------------------------------
    2000.
    -----

    [_]  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 PROPOSAL 2.


                            Please sign exactly as name appears hereon.

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

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

                            Date:  _____________________, 1999

                            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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