FRONTIER OIL CORP /NEW/
DEF 14A, 1999-03-26
PETROLEUM REFINING
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                              SCHEDULE 14A
                INFORMATION REQUIRED IN PROXY STATEMENT

                        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:
 [ ] Preliminary proxy statement
 [ ] Confidential, for use of the Commission only (as permitted by
     Rule 14a-b(e)(2)
 [x] Definitive proxy statement
 [ ] Definitive additional materials
 [ ] Soliciting material pursuant to Rule 14a-11(c) or Rule 14a-12

                     FRONTIER OIL CORPORATION
- ------------------------------------------------------------------------------
                                                                 
         (Name of Registrant as Specified In Its Charter)

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

Payment of filing fee (Check the appropriate box):
 [x] No fee required.
 [ ] $500 per each party to the controversy pursuant to Exchange Act Rule
     14a-6(I)(3).
 [ ] 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:(1)

                                                                 
- ------------------------------------------------------------------------------
 (4) Proposed maximum aggregate value of transaction:

                                                                 
- ------------------------------------------------------------------------------
 [ ] 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.

 (1)    Amount previously paid:

                                                                 
- ------------------------------------------------------------------------------
 (2)    Form, schedule or registration statement no.:

                                                                 
- ------------------------------------------------------------------------------
 (3)    Filing party:

                                                                 
- ------------------------------------------------------------------------------
 (4)    Date filed:
                                                                 
- ----------
(1) Set forth the amount on which the filing fee is calculated and state how it
    was determined.

<PAGE>
                                     
                              March 26, 1999


To Our Shareholders:

     On behalf of the Board of Directors, I cordially invite all shareholders to
attend the Annual Meeting of Frontier Oil Corporation to be held on Thursday,
April 29, 1999 at 9:00 a.m. in the Company's corporate offices located at 10000
Memorial Drive, Suite 600, Houston, Texas. Proxy materials, which include a
Notice of the Meeting, Proxy Statement and proxy card, are enclosed with this
letter. The Company's 1998 Annual Report to shareholders, which is not a part of
the proxy materials, is also enclosed and provides additional information
regarding the financial results of the Company in 1998.

     Even if you plan to attend the meeting, you are requested to sign, date and
return the proxy card in the enclosed envelope. If you attend the meeting after
having returned the enclosed proxy card, you may revoke your proxy, if you wish,
and vote in person. If you would like to attend the meeting and your shares are
not registered in your own name, please ask the broker, trust, bank or other
nominee that holds the shares to provide you with evidence of your share
ownership.

     Thank you for your support.


                              Sincerely,



                              James R. Gibbs
                              President and Chief Executive Officer






10000 Memorial Drive, Suite 600   Houston, Texas 77024-3411   (713) 688-9600  
                            fax (713) 688-0616
                                     
<PAGE>



                      10000 MEMORIAL DRIVE, SUITE 600
                         HOUSTON, TEXAS 77024-3411
                                                            

                 NOTICE OF ANNUAL MEETING OF SHAREHOLDERS

                              APRIL 29, 1999
                                                            

To Our Shareholders:

  The 1999 Annual Meeting of Shareholders of Frontier Oil Corporation (the
"Company") will be held in its corporate offices at 10000 Memorial Drive, Suite
600, Houston, Texas at 9:00 a.m. on Thursday, April 29, 1999, for the following
purposes:

     1. To elect six directors (constituting the entire Board of Directors) to
        serve until the next Annual Meeting of Shareholders or until their
        respective successors have been elected or appointed.

     2. To ratify the Frontier Oil Corporation 1999 Stock Plan.

     3. To ratify and approve the appointment of Arthur Andersen LLP,
        independent certified public accountants, as the Company's auditors for
        the year ending December 31, 1999.

     4. To act upon any and all matters incident to the foregoing and to
        transact such other business as may properly be brought before the
        meeting or any postponement or adjournment thereof.

   THE BOARD OF DIRECTORS RECOMMENDS THAT YOU VOTE FOR EACH OF THE FIRST THREE
PROPOSALS SET FORTH ABOVE. THE ACCOMPANYING PROXY STATEMENT CONTAINS INFORMATION
RELATING TO EACH OF SUCH PROPOSALS. The holders of record of the Company's
common stock at the close of business on March 19, 1999 are entitled to notice
of and to vote at the meeting with respect to all proposals. We urge you to sign
and date the enclosed proxy and return it promptly by mail in the enclosed
envelope, whether or not you plan to attend the meeting in person. No postage is
required if mailed in the United States. If you do attend the meeting in person,
you may withdraw your proxy and vote personally on all matters brought before
the meeting.



                                      By Order of the Board of Directors,


  
                                      Julie H. Edwards
                                      Secretary

Houston, Texas
March 26, 1999

<PAGE>

                         FRONTIER OIL CORPORATION

                      10000 MEMORIAL DRIVE, SUITE 600

                         HOUSTON, TEXAS 77024-3411

                                                             
            
                              PROXY STATEMENT
                                                            

                 SOLICITATION AND REVOCABILITY OF PROXIES

   THIS PROXY STATEMENT IS FURNISHED BY THE BOARD OF DIRECTORS OF FRONTIER OIL
CORPORATION (THE "COMPANY") IN CONNECTION WITH THE SOLICITATION OF PROXIES FOR
USE AT THE ANNUAL MEETING OF SHAREHOLDERS TO BE HELD APRIL 29, 1999, AND AT ANY
POSTPONEMENT OR ADJOURNMENT THEREOF. The shares represented by the form of proxy
enclosed herewith will be voted in accordance with the specifications noted
thereon. If no choice is specified, said shares will be voted in favor of the
proposals set forth in the notice attached hereto. The form of proxy also
confers discretionary authority with respect to amendments or variations to
matters identified in the notice of meeting and any other matters which may
properly come before the meeting. This Proxy Statement and the enclosed proxy
form are first being sent to shareholders on or about March 26, 1999.

   A shareholder who has given a proxy may revoke it as to any motion on which a
vote has not already been taken by signing a proxy bearing a later date or by a
written notice delivered to the Secretary of the Company in care of Harris Trust
and Savings Bank, 311 West Monroe, Chicago, Illinois 60606 ("Harris") or at the
offices of the Company, 10000 Memorial Drive, Suite 600, Houston, Texas
77024-3411, at any time up to the meeting or any postponement or adjournment
thereof, or by delivering it to the Chairman of the meeting on such date.

   The cost of solicitation of these proxies will be paid by the Company,
including reimbursement paid to brokerage firms and other custodians, nominees
and fiduciaries for reasonable costs incurred in forwarding the proxy material
to and solicitation of proxies from the beneficial record owners of shares. In
addition to such solicitation and the solicitation made hereby, certain
directors, officers and employees of the Company may solicit proxies by fax,
telex, telephone and personal interview.

                             VOTING SECURITIES

   All shareholders of record as of the close of business on March 19, 1999 are
entitled to notice of and to vote at the meeting. Provided that a complete and
executed form of proxy shall have been delivered to Harris prior to the meeting,
any person may attend and vote that number of shares for which he holds a proxy.
On March 19, 1999, the Company had 27,440,724 shares of common stock, without
par value ("Common Stock"), outstanding excluding Common Stock held by the
Company. The Common Stock is the only class of voting securities of the Company.
The presence in person or by proxy of the holders of a majority of the issued
and outstanding Common Stock, excluding Common Stock held by the Company, is
necessary to constitute a quorum at this meeting. In the absence of a quorum at
the meeting, the meeting may be postponed or adjourned from time to time without
notice other than announcement at the meeting until a quorum shall be formed.

<PAGE>

   Directors shall be elected by a plurality of the votes cast by shareholders
entitled to vote in the election at a meeting at which a quorum is present.
Cumulative voting for the election of directors is not permitted.  In conformity
with Wyoming law and the bylaws of the Company, action regarding the
ratification of the appointment of auditors will be approved if the votes cast
in favor exceed the votes cast opposing such proposal. Abstentions are counted
as "shares present" at the meeting for purposes of determining the presence of a
quorum while broker non-votes (which result when a broker holding shares for a
beneficial owner has not received timely voting instructions on certain matters
from such beneficial owner) are not considered "shares present" with respect to
any matter. Accordingly, abstentions will have no effect on the outcome of the
election of directors but with respect to any other proposal will operate to
prevent the approval of such proposal to the same extent as a vote against such
proposal.


                               ANNUAL REPORT

   The annual report to shareholders, including consolidated financial
statements, accompanies this Proxy Statement. Such annual report does not form
any part of the proxy solicitation materials.

                                    - 2 -

<PAGE>


                          PRINCIPAL SHAREHOLDERS

   The following table sets forth, as of March 19, 1999, the beneficial
ownership of the Company's Common Stock, with respect to each person known by
the Company to be the beneficial owner of more than five percent of the
Company's outstanding voting securities, excluding Common Stock held by the
Company:

<TABLE>
<CAPTION>

                                                AMOUNT AND NATURE
                                                  OF BENEFICIAL       PERCENTAGE OF SHARES
      NAME AND ADDRESS                              OWNERSHIP          OF COMMON STOCK (1)
- ----------------------------------------------  -----------------     --------------------
<S>                                             <C>                   <C>

Ingalls & Snyder LLC                                5,745,158 (2)              20.9
 61 Broadway
 New York, NY 10006

Kornitzer Capital Management, Inc.                  2,395,000 (3)               8.7
 P.O. Box 918
 Shawnee Mission, KS 66201

Great Plains Trust Company                          1,639,200 (3)               6.0
 4705 Mission Road
 Westwood, KS 66205

The Guardian Life Insurance Company of America      2,478,700 (4)               9.0
 201 Park Avenue South
 New York, NY 10003

FMR Corp.                                           2,220,900 (5)               8.1
 82 Devonshire Street
 Boston, MA 02109

</TABLE>

(1) Represents percentage of 27,440,724 outstanding shares of the Company as of
    March 19, 1999.

(2) Ingalls & Snyder LLC ("Ingalls & Snyder") filed with the Commission a
    Schedule 13G, dated September 6, 1995, and amendments thereto dated December
    8, 1995, January 17 and June 10, 1996, January 29 and July 28, 1997,
    February 9, 1998 and February 5, 1999.  Based on the most recent amendment,
    Ingalls & Snyder had sole voting power with respect to 375,660 of the above
    shares, sole dispositive power with respect to 375,660 of the above shares
    and shared dispositive power with respect to 5,369,498 of the above shares
    of Common Stock.

(3) Kornitzer Capital Management, Inc. ("KCM") filed with the Commission a
    Schedule 13G, dated March 29, 1996, and amendments thereto, dated February
    10, 1997, February 17, 1998 (filed jointly with Great Plains Trust Company
    ("Great Plains")) and two amendments dated February 27, 1999 (one of which
    was filed jointly with Great Plains).  Based on the most recent amendments,
    (i) KCM had shared voting power and shared dispositive power with respect to
    2,395,000 shares of Common Stock, and (ii) Great Plains had shared voting
    power and shared dispositive power with respect to 1,639,200 shares of
    Common Stock.
 
(4) The Guardian Life Insurance Company of America ("Guardian Life")  and
    certain related entities disclosed below jointly filed with the Commission a
    Schedule 13G, dated February 4, 1996, and amendments thereto dated February
    11, 1998 and February 11, 1999.  Based on the most recent amendment, (i)
    Guardian Life had sole

                                    - 3 -

<PAGE>

    voting and dispositive power with respect to 1,112,400 shares of Common
    Stock and shared voting and dispositive power with respect to 419,700 shares
    of Common Stock, (ii) The Guardian Investor Services Corporation ("GISC"), a
    wholly owned subsidiary of Guardian Life, had sole voting and dispositive
    power with respect to no shares of Common Stock and shared voting and
    dispositive power with respect to 946,600 shares of Common Stock, (iii) The
    Guardian Park Avenue Fund, a mutual fund sponsored by Guardian Life and
    managed by GISC, had sole voting and dispositive power with respect to no
    shares of Common Stock and shared voting and dispositive power with respect
    to 495,300 shares of Common Stock, (iv) The Guardian Stock Fund, Inc., a
    mutual fund sponsored by Guardian Life and managed by GISC, had sole voting
    and dispositive power with respect to no shares of Common Stock and shared
    voting and dispositive power with respect to 451,300 shares of Common Stock,
    (v) The Guardian Employees' Incentive Savings Plan, an employee benefit plan
    offered to the employees of Guardian Life, had sole voting and dispositive
    power with respect to no shares of Common Stock and shared voting and
    dispositive power with respect to 314,000 shares of Common Stock and (vi)
    The Guardian Life Insurance Company of American Master Pension Trust, a
    pension fund for the employees of Guardian Life, had sole voting and
    dispositive power with respect to no shares of common stock and shared
    voting and dispositive power with respect to 105,700 shares of Common Stock.
    Based on such amendment, Guardian Life and such related entities
    beneficially owned, in the aggregate without duplication, 2,478,700 shares
    of Common Stock.

(5) FMR Corp. has filed a Schedule 13G dated February 1, 1999 with the
    Commission.  Based on such filing, Fidelity Management & Research Company
    ("Fidelity"), 82 Devonshire Street, Boston, Massachusetts 02109, a
    wholly-owned subsidiary of FMR Corp. and an investment adviser registered
    under Section 203 of the Investment Advisers Act of 1940, is the beneficial
    owner of 1,845,400 shares or 6.7% of the Common Stock outstanding of
    Frontier Oil Corporation ("the Company") as a result of acting as investment
    adviser to various investment companies registered under Section 8 of the
    Investment Company Act of 1940.

    Edward C. Johnson 3d, FMR Corp., through its control of Fidelity, and the
    funds each has sole power to dispose of 1,845,400 shares owned by the Funds.

    Neither FMR Corp. nor Edward C. Johnson 3d, Chairman of FMR Corp., has the
    sole power to vote or direct the voting of the shares owned directly by the
    Fidelity Funds, which power resides with the Funds' Boards of Trustees.
    Fidelity carries out the voting of the shares under written guidelines
    established by the Funds' Boards of Trustees.

    Fidelity Management Trust Company, 82 Devonshire Street, Boston,
    Massachusetts 02109, a wholly-owned subsidiary of FMR Corp. and a bank as
    defined in Section 3(a)(6) of the Securities Exchange Act of 1934, is the
    beneficial owner of 375,500 shares or 1.4% of the Common Stock outstanding
    of the Company as a result  of its serving as investment manager of the
    institutional account(s).

    Edward C. Johnson 3d and FMR Corp., through its control of Fidelity
    Management Trust Company, each has sole dispositive power over 375,500
    shares and sole power to vote or to direct the voting of 375,500 shares of
    Common Stock owned by the institutional account(s) as reported above.

    Members of the Edward C. Johnson 3d family and trusts for the benefit are
    the predominant owners of Class B Shares of common stock of FMR Corp.,
    representing approximately 49% of the voting power of FMR Corp.  Mr. Johnson
    3d owns 12.0% and Abigail Johnson owns 24.5% of the aggregate outstanding
    voting stock of FMR Corp.  Mr. Johnson 3d is Chairman of FMR Corp. and
    Abigail P. Johnson is a Director of FMR Corp.  The Johnson family group and
    all other Class B shareholders have entered into a shareholders' voting
    agreement under which all Class B shares will be voted in accordance with
    the majority vote of Class B shares. Accordingly, through their ownership of
    voting common stock and the execution of the shareholders' voting agreement,
    members of the Johnson family may be deemed, under the Investment Company
    Act of 1940, to form a controlling group with respect to FMR Corp.

                                    - 4 -

<PAGE>

          COMMON STOCK OWNED BY DIRECTORS AND EXECUTIVE OFFICERS

   The following table sets forth, as of March 19, 1999, the amount of Common
Stock beneficially owned by: (i) each director of the Company, (ii) the Chief
Executive Officer and the four most highly compensated officers other than the
Chief Executive Officer; and (iii) all directors and executive officers as a
group:

<TABLE>
<CAPTION>

                                                               AMOUNT AND NATURE
                                                                 OF BENEFICIAL      PERCENTAGE OF SHARES
NAME                                                               OWNERSHIP         OF COMMON STOCK (1)
- ------------------------------------------------------------   -----------------    --------------------
<S>                                                            <C>                  <C>

James R. Gibbs (2) . . . . . . . . . . . . . . . . . . . . .       587,370 (3)             2.1
Douglas Y. Bech (2). . . . . . . . . . . . . . . . . . . . .        12,000                  *
Paul B. Loyd, Jr. (2). . . . . . . . . . . . . . . . . . . .         2,000                  *
James S. Palmer(2) . . . . . . . . . . . . . . . . . . . . .        22,622                  *
Derek A. Price (2) . . . . . . . . . . . . . . . . . . . . .         7,000                  *
Carl W. Schafer (2). . . . . . . . . . . . . . . . . . . . .         7,000                  *
S. Clark Johnson . . . . . . . . . . . . . . . . . . . . . .       175,500 (4)              *
Julie H. Edwards . . . . . . . . . . . . . . . . . . . . . .       153,900 (5)              *
J. Currie Bechtol. . . . . . . . . . . . . . . . . . . . . .             0                  *
Jon D. Galvin. . . . . . . . . . . . . . . . . . . . . . . .        56,440 (6)              *
Directors and executive officers as a group (11 persons) . .     1,058,532                 3.9

</TABLE>

* Less than 1%

(1) Represents percentage of outstanding shares plus shares issuable upon
    exercise of all stock options owned by the individual listed that are
    currently exercisable or that will become exercisable within 60 days of the
    date for which beneficial ownership is provided in the table, assuming stock
    options owned by all other shareholders are not exercised.  As of March 19,
    1999, 27,440,724 shares of Common Stock were outstanding.

(2) Director.

(3) Includes 512,160 shares with respect to which Mr. Gibbs has the right to
    acquire beneficial ownership under one of the Company's stock option plans
    within 60 days of the date for which beneficial ownership is provided in the
    table. Of the 587,370 shares that Mr. Gibbs is deemed to beneficially own,
    Mr. Gibbs has sole voting and sole dispositive power with respect to 75,210
    shares.

(4) Includes 125,500 shares with respect to which Mr. Johnson has the right to
    acquire beneficial ownership under one of the Company's stock option plans
    within 60 days of the date for which beneficial ownership is provided in the
    table. Of the 175,500 shares that Mr. Johnson is deemed to beneficially own,
    Mr. Johnson has sole voting power and sole dispositive power with respect to
    50,000 shares.

(5) Includes 141,500 shares with respect to which Ms. Edwards has the right to
    acquire beneficial ownership under one of the Company's stock option plans
    within 60 days of the date for which beneficial ownership is provided in the
    table. Of the 153,900 shares that Ms. Edwards is deemed to beneficially own,
    Ms. Edwards has sole voting power and sole dispositive power with respect to
    12,400 shares.

(6) Includes 56,440 shares with respect to which Mr. Galvin has the right to
    acquire beneficial ownership under one of the Company's stock option plans
    within 60 days of the date for which beneficial ownership is provided in the
    table.

                                    - 5 -

<PAGE>

                                PROPOSAL 1:

                           ELECTION OF DIRECTORS

   A Board of Directors is to be elected, with each director to hold office
until the next Annual Meeting of Shareholders and until his successor shall be
elected or appointed. The persons whose names are set forth as proxies in the
enclosed form of proxy will vote all shares over which they have control "FOR"
the election of the Board of Directors' nominees, unless otherwise directed.
Although the Board of Directors of the Company does not contemplate that any of
the nominees will be unable to serve, if such a situation should arise prior to
the meeting, the appointed proxies will use their discretionary authority
pursuant to the proxy and vote in accordance with their best judgment.

NOMINEES

   All of the persons listed below are members of the present Board of Directors
and have consented in writing to be named in this Proxy Statement and to serve
as a director, if elected.

   Mr. James R. Gibbs (54) joined the Company in February 1982 and has been
President and Chief Operating Officer since January 1987. He assumed the
additional position of Chief Executive Officer on April 1, 1992.  Mr. Gibbs is a
member of the Board of Directors of Smith International, Inc., an oil field
service company; an advisory director of Frost National Bank, N.A.; and a
director of Veritas DGC Inc., a seismic service company. Mr. Gibbs was elected a
director of the Company in 1985.

   Mr. Douglas Y. Bech (53) has been Chairman and Chief Executive Officer of
Raintree Resorts International, Inc. since August 1997. From October 1994 to
October 1997, Mr. Bech was a partner in the law firm of Akin, Gump, Strauss,
Hauer & Feld, L.L.P. of Houston, Texas. Since August 1994, he has also been a
managing director of Raintree Capital Company, L.L.C., a merchant banking firm.
From May 1993 to July 1994, Mr. Bech was a partner of Gardere & Wynne, L.L.P. of
Houston, Texas.  From 1977 until May 1993, Mr. Bech was a partner of Andrews &
Kurth L.L.P.  Mr. Bech is a member of the Board of Directors of Pride Refining,
Inc., the general partner of Pride Companies, L.P., a products pipeline and
crude gathering company; and eFax.com, Inc., an internet document communications
company. He was appointed a director of the Company in 1993.

   Mr. G. Clyde Buck (61) has been a Managing Director of the investment banking
firm Harris Webb & Garrison, Inc. since 1998.  Prior to that time, he was a
Managing Director of Rauscher Pierce Refsnes, Inc., also an investment banking
firm, for 15 years.  Mr. Buck is a member of the Board of Directors of Smith
International, Inc., an oil field service company.  Mr. Buck is being nominated
to the Board of Directors of the Company for the first time to fill a vacancy.

   Mr. Paul B. Loyd, Jr. (52) has been Chairman of R&B Falcon Corporation since
December 1997. Mr. Loyd was Chairman and Chief Executive Officer of Reading &
Bates Corporation, an offshore contract drilling company, from June 1991 until
December 1997 and was a director of Reading & Bates from April 1991 until
December 1997. Mr. Loyd  has been President of Loyd & Associates, Inc., a
financial consulting firm, since 1989. Mr. Loyd was Chief Executive Officer and
a director of Chiles-Alexander International, Inc. from 1987 to 1989, President
and a director of Griffin-Alexander Drilling Company from 1984 to 1987, and
prior to that, a director and Chief Financial Officer of Houston Offshore
International, all of which are companies in the offshore drilling industry. Mr.
Loyd is a member of the Board of Directors of Carrizo Oil & Gas, Inc. He was
appointed a director of the Company in 1994.

   Mr. Derek A. Price (66) is a trustee of The J.W. McConnell Family Foundation,
a charitable foundation.  Prior to April 1991, Mr. Price was Chairman of the
Board of Directors and Chief Executive Officer of Starlaw Holdings Limited, a
private investment company with holdings principally in the areas of financial
services, real estate and manufacturing. Mr. Price was elected a director of the
Company in 1987.

                                    - 6 -

<PAGE>

   Mr. Carl W. Schafer (63) has been the President of the Atlantic Foundation, a
charitable foundation which mainly supports oceanographic research, since 1990.
From 1987 until 1990, Mr. Schafer was a principal of the investment management
firm of Rockefeller & Co., Inc. Mr. Schafer presently serves on the Board of
Directors of Roadway Express, Inc., a transportation company; the PaineWebber
and Guardian Groups of Mutual Funds, registered investment companies; Electronic
Clearing House, Inc., an electronic financial transactions processing company;
Evans Systems, Inc., a fuel distribution, convenience store and diversified
company; and Nutraceutix Inc., a biotechnology company. Mr. Schafer was elected
a director of the Company in 1984.


THE BOARD OF DIRECTORS AND ITS COMMITTEES

   The Board of Directors met four times and held three telephonic meetings in
1998, during which each incumbent director of the Company, other than Mr. Loyd,
attended 75 percent or more of the aggregate number of meetings of the Board of
Directors and meetings held by committees of the Board on which he served. The
Board of Directors has standing audit, compensation, safety and environmental,
executive and nominating committees that are composed of directors of the
Company.

   Audit Committee: The Audit Committee is comprised of three outside directors,
currently Messrs. Loyd, Price and Schafer. The Audit Committee's functions
include recommendations concerning the engagement of independent public
accountants, reviewing with the independent public accountants the plan and
results of the audit engagement, approving professional services provided by the
independent public accountants, reviewing the independence of the independent
public accountants, considering the range of audit and non-audit fees and
reviewing the adequacy of the Company's internal accounting controls. The Audit
Committee met twice during 1998.

   Compensation Committee: The Compensation Committee is comprised of three
outside directors, currently Messrs. Bech, Loyd and Schafer. The Compensation
Committee's functions include the approval of officers' salaries and
administration of all of the Company's employee benefit plans. The Compensation
Committee met twice during 1998.

   Safety and Environmental Committee:  The Safety and Environmental Committee
is comprised of three members of the Board of Directors, currently Messrs.
Palmer, Gibbs and Price. The Safety and Environmental Committee's functions
include the adoption and review of the Company's safety, health and
environmental policies and programs. The Safety and Environmental Committee met
once during 1998.

   Executive Committee: The Executive Committee is comprised of Mr. Gibbs and
two outside directors, currently Messrs. Palmer and Bech. The Executive
Committee functions in the place of the Board of Directors between regular
meetings of the Board and has all the power and authority of the Board of
Directors, except for certain matters that may not be delegated under the
Company's bylaws. The Executive Committee did not meet during 1998.

   Nominating Committee: The Nominating Committee is comprised of three members
of the Board of Directors, currently Messrs. Gibbs, Palmer and Schafer. The
purpose of the committee is to review possible candidates for the Board of
Directors and recommend nomination of appropriate candidates by the Board. The
Nominating Committee did not meet during 1998.

   Pursuant to the Company's bylaws, nominations for candidates for election to
the Board of Directors may be made by any shareholder entitled to vote at a
meeting of shareholders called for the election of directors. Nominations made
by a shareholder must be made by giving notice of such in writing to the
Secretary of the Company before the later to occur of (i) 60 days prior to the
date of the meeting of shareholders called for the election of directors or (ii)
ten days after the Board first publishes the date of such meeting. Such notice
shall include all information concerning each nominee as would be required to be
included in a proxy statement soliciting proxies for the election of such
nominee under the Securities Exchange Act of 1934, as amended (the "1934 Act").
Such notice shall also include a

                                    - 7 -

<PAGE>

signed consent of each nominee to hold office until the next Annual Meeting of
Shareholders or until his successor shall be elected or appointed.

COMPENSATION OF DIRECTORS

   Directors' fees are presently $1,666.67 per month and $1,500.00 for each
Board meeting attended in person, plus $1,250.00 for any committee meeting
attended.  Additionally, committee chairmen receive a fee of $2,000 per year and
outside directors are eligible to participate in the Company's Directors' Stock
Grant Plan which is described on page 19.

   No member of the Board of Directors was paid any remuneration in 1998 for his
service as a director of the Company other than pursuant to the standard
compensation arrangement for directors. Directors who are officers of the
Company do not receive any compensation for their services as a director. The
Company reimburses its directors for travel expenses incurred in attending Board
meetings. Mr. Palmer joined the Board of Directors of the Company in 1975 and
plans to serve through the date of the 1999 Annual Meeting.  In addition to the
six directors elected by shareholders, Mr. James S. Palmer will serve as
Director Emeritus at the request of the Board. During 1998, Mr. William
Scheerer, II served as Director Emeritus. He had served as a director of the
Company from 1975 through 1994.  As compensation for his services as Director
Emeritus, Mr. Scheerer was paid $1,000 for each board meeting attended in person
plus reimbursement for related travel expenses. Mr. Scheerer retired in November
1998.

                                    - 8 -

<PAGE>

                                PROPOSAL 2:
                                     
                    RATIFICATION OF THE 1999 STOCK PLAN

   The Board recommends the approval of the adoption of the Frontier Oil
Corporation 1999 Stock Plan (the "Plan"), which authorizes the grant of various
stock and stock-related awards ("Awards").  The Plan was adopted by the Board on
February 25, 1999, contingent upon its approval by the shareholders.  The Board
believes the Company's success and long-term progress are dependent upon
attracting and retaining officers, employees, directors and consultants of the
Company and its subsidiaries and affiliates.  The Plan gives the Compensation
Committee the maximum flexibility to use various forms of incentive awards as
part of the Company's overall compensation program. The Company's current equity
incentive plan (the 1968 Stock Option Plan) is limited in the types of equity
awards available for grants.  As of March 19, 1999, there were 91,290 shares of
Common Stock available for grants of awards under the Company's existing option
plans.

   The full text of the Plan is set forth in Exhibit A to this Proxy Statement.
The essential features of the Plan are summarized below, but such summary is
qualified in its entirety by reference to the full text of the Plan.  All
capitalized terms not defined herein shall have the meaning as defined in the
Plan.

PURPOSE OF THE PLAN

   The Plan is intended to encourage employees, directors and consultants of the
Company, its subsidiaries and affiliated entities to acquire or increase their
equity interest in the Company.  Additionally, the Plan is intended to provide a
means whereby employees, directors and consultants may develop a sense of
proprietorship and personal involvement in the development and financial success
of the Company and to encourage them to remain with and devote their best
efforts to the business of the Company, thereby advancing the interests of the
Company and its shareholders.  The Plan is also contemplated to enhanced the
ability of the Company, its subsidiaries and affiliated entities to attract and
retain the services of individuals who can contribute to the progress, growth
and profitability of the Company.

ADMINISTRATION OF THE PLAN

   The Plan is administered by the Compensation Committee of the Company's Board
of Directors, which consists solely of non-employee directors within the meaning
of Rule 16b-3 of the Exchange Act.  The powers of the Compensation Committee may
be delegated to the Chief Executive Officer of the Company, subject to certain
limitations.  The Compensation Committee, or the Chief Executive Officer if the
power is so delegated, will select the participants who will receive Awards,
determine the type and terms of Awards to be granted and interpret and
administer the Plan.

   Shares Available for Awards.  Subject to adjustment as described below, two
million (2,000,000) shares of Common Stock may be awarded under the Plan.

   Adjustments.  The Compensation Committee may provide for adjustment of Awards
under the Plan if it determines such adjustment is required to prevent dilution
or enlargement of the rights of participants in the Plan that would otherwise
result from a stock dividend, stock split, reverse stock split, combination of
shares, recapitalization, merger, consolidation, reorganization, split-up,
spin-off or other similar corporate transaction.

   Eligibility for Participation.  Any Employee, Director, or Consultant shall
be eligible to be designated a Participant.

                                    - 9 -

<PAGE>

TYPES OF AWARDS

   The Plan permits the granting of any or all of the following types of Awards:
options, restricted stock, performance awards, bonus shares, phantom shares,
cash awards, and other stock-based awards.

   Options.  Stock Options granted under the Plan are subject to such terms and
conditions as may be established by the Compensation Committee, which may
include conditioning the exercisability of an option on the achievement of one
or more performance goals, except that in all events: (i) no stock options may
be granted after the termination of the Plan; and (ii) the option exercise price
cannot be less than the market value per share of the Common Stock at the date
of grant.  The Compensation Committee shall determine the time or times at which
an Option may be exercised in whole or in part, and the method or methods by
which, and the form or forms (which may include, without limitation, cash, check
acceptable to the Company, Shares already-owned for more than six months,
outstanding Awards, Shares that would otherwise be acquired upon exercise of the
Option, a "cashless-broker" exercise (through procedures approved by the
Company), other securities or other property, loans, notes approved by the
Compensation Committee, or any combination thereof, having a Fair Market Value
on the exercise date equal to the relevant exercise price) in which payment of
the exercise price with respect thereto may be made or deemed to have been made.

   Stock options may be granted as incentive stock options ("ISOs") under
Section 422 of the Internal Revenue Code of 1986, as amended (the "Code").
However, ISOs can only be granted to participants who are employees of the
Company or a subsidiary of the Company, within the meaning of Section 424 of the
Code.  In addition, to the extent the aggregate Fair Market Value of the Shares
(determined as of the date of grant) of an Option to the extent exercisable for
the first time during any calendar year (under all plans of the Company and its
parent and subsidiary corporations) exceeds $100,000, such Option Shares in
excess of $100,000 shall not be incentive stock options.

   Restricted Stock.  The Compensation Committee may also make grants of
restricted stock, which are shares of Common Stock that may not be disposed of
by the participant until the restrictions specified in the Award expire. The
restrictions may include the achievement of specified performance goals.
Dividends paid on Restricted Stock may be paid directly to participants, or may
be credited to a bookkeeping cash account, or may be reinvested in additional
shares of Common Stock subject to similar restrictions, all as determined by the
Compensation Committee in its discretion.  Except as otherwise determined by the
Compensation Committee or the terms of the Award, upon termination of a
participant's employment for any reason during the restricted period, all
restricted stock will be forfeited by the participant and re-acquired by the
Company.  Restricted Stock is subject to the same transfer limitations as other
Awards, as outlined below.

   Performance Awards.  Performance Awards may consist of payments in cash,
shares of Common Stock or a combination thereof, payable upon the achievement of
specified performance goals.  The Compensation Committee shall determine the
performance goals to be achieved during any performance period and the length of
any performance period as well as whether the Award will be paid in cash or
Shares or both, and whether paid in a lump sum or in installments.

   Bonus Shares.  The Compensation Committee may deliver unrestricted shares of
Common Stock to eligible persons as additional compensation for the person's
services to the Company and its affiliates or in lieu of cash bonuses payable to
a participant.

   Phantom Shares.  The Compensation Committee may grant Awards of phantom
shares of Common Stock, which may be payable in cash, shares of Common Stock or
a combination thereof, in consideration of the fulfillment of such conditions as
the Compensation Committee may specify.  Each Phantom Share Award shall
constitute an agreement by the Company to issue or transfer a specified number
of Shares or pay an amount of cash equal to a specified number of Shares, or a
combination thereof to the Participant in the future, subject to the fulfillment
during the Restricted Period of such conditions, including performance
objectives, if any, as the Compensation Committee may specify at the date of
grant.  During the Restricted Period, the Participant shall not have any right
to transfer any rights under the subject Award, shall not have any rights of
ownership in the Phantom Shares and shall not have any right to vote such
shares.  Any Phantom Share Award may provide that any or all dividends or other
distributions paid on Shares during the Restricted Period be

                                    - 10 -

<PAGE>

credited in a cash bookkeeping account (without interest) or that equivalent
additional Phantom Shares be awarded, which account or shares may be subject to
the same restrictions as the underlying Award or such other restrictions as the
Compensation Committee may determine.

   Cash Awards.  The Compensation Committee shall have the authority to
determine the Participants to whom Cash Awards shall be granted, the amount, and
the terms or conditions, if any, as additional compensation for the
Participant's services to the Company or its Affiliates.  A Cash Award may be
granted (simultaneously or subsequently) separately or in tandem with another
Award and may entitle a Participant to receive a specified amount of cash from
the Company upon such other Award becoming taxable to the Participant, which
cash amount may be based on a formula relating to the anticipated taxable income
associated with such other Award and the payment of the Cash Award.

   Other Stock-Based Awards.  The Compensation Committee may also grant to
Participants an Other Stock-Based Award, which shall consist of a right which is
an Award denominated or payable in, valued in whole or in part by reference to,
or otherwise based on or related to, Shares as is deemed by the Compensation
Committee to be consistent with the purposes of the Plan.  Subject to the terms
of the Plan, the Compensation Committee shall determine the terms and conditions
of any such Other Stock-Based Award.

GENERAL PROVISIONS

   Limits on Transferability of Awards.  Except as provided below, each Award,
and each right under any Award, shall be exercisable only by the Participant
during the Participant's lifetime, or by the person to whom the Participant's
rights shall pass by will or the laws of descent and distribution.
Additionally, except as provided below, no Award and no right under any such
Award may be assigned, alienated, pledged, attached, sold or otherwise
transferred or encumbered by a Participant otherwise than by will or by the laws
of descent and distribution (or, in the case of Restricted Stock, to the
Company) and any such purported assignment, alienation, pledge, attachment,
sale, transfer or encumbrance shall be void and unenforceable against the
Company or any Affiliate.

   Notwithstanding anything in the Plan to the contrary, to the extent
specifically provided by the Compensation Committee with respect to a grant, an
Option (other than an incentive stock option) may be transferred to immediate
family members or related family trusts, limited partnerships or similar
entities on such terms and conditions as the Compensation Committee may
establish.

   Amendment and Termination.  Except to the extent prohibited by applicable law
and unless otherwise expressly provided in an Award Agreement or in the Plan:

   Amendments to the Plan.  Except as required by applicable law or the rules of
   the principal securities market on which the shares are traded and subject to
   Amendments to Awards below, the Board or the Compensation Committee may
   amend, alter, suspend, discontinue, or terminate the Plan without the consent
   of any stockholder, Participant, other holder or beneficiary of an Award, or
   other Person.

   Amendments to Awards.  The Compensation Committee may waive any conditions or
   rights under, amend any terms of, or alter any Award theretofore granted,
   provided no change, other than pursuant to Amendments of Awards Upon the
   Occurrence of Certain Unusual or Nonrecurring Events below, in any Award
   shall reduce the benefit to Participant without the consent of such
   Participant.

   Adjustment of Awards Upon the Occurrence of Certain Unusual or Nonrecurring
   Events.  The Compensation Committee is hereby authorized to make adjustments
   in the terms and conditions of, and the criteria included in, Awards in
   recognition of unusual or nonrecurring events (including, without limitation,
   the events described in Section 4(c) of the Plan) affecting the Company, any
   Affiliate, or the financial statements of the Company or any Affiliate, or of
   changes in applicable laws, regulations, or accounting principles, whenever
   the Compensation Committee determines that such adjustments are appropriate
   in order to prevent dilution or enlargement of the benefits

                                    - 11 -

<PAGE>

   or potential benefits intended to be made available under the Plan.

   Change in Control.   Notwithstanding any other  provision of the Plan to the
contrary, in the event of a Change in Control of the Company all outstanding
Awards automatically shall become fully vested immediately prior to such Change
in Control (or such earlier time as set by the Compensation Committee), all
restrictions, if any, with respect to such Awards shall lapse, all performance
criteria, if any, with respect to such Awards shall be deemed to have been met
in full (at the highest level), and unless the Company survives as an
independent publicly traded company, all Options outstanding at the time of the
event or transaction shall terminate, except to the extent provision is made in
writing in connection with such event or transaction for the continuation of the
Plan and/or the assumption of the Options theretofore granted, or for the
substitution for such Options of new options covering the stock of a successor
entity, or the parent or subsidiary thereof, with appropriate adjustments as to
the number and kinds of shares and exercise prices, in which event the Plan and
Options theretofore granted shall continue in the manner and under the terms so
provided.

   Withholding.  The Company or any Affiliate is authorized to withhold from any
Award, from any payment due or transfer made under any Award or under the Plan
or from any compensation or other amount owing to a participant the amount (in
cash, Shares, other securities, Shares that would otherwise be issued pursuant
to such Award, other Awards or other property) of any applicable taxes payable
in respect of an Award, its exercise, the lapse of restrictions thereon, or any
payment or transfer under an Award or under the Plan and to take such other
action as may be necessary in the opinion of the Company to satisfy all
obligations for the payment of such taxes.  In addition, the Compensation
Committee may provide, in an Award Agreement, that the participant may direct
the Company to satisfy such Participant's tax obligation through the
"constructive" tender of already-owned Shares or the withholding of Share
otherwise to be acquired upon the exercise or payment of such Award.

   Term of Awards and of the Plan.  While the term of each Award will be
determined by the Compensation Committee, in no event may the term of any Award
exceed a period of 10 years from the date of its grant.  Unless sooner
terminated, the Plan will terminate on April 29, 2009, after which time no
additional Awards may be made under it; however, all Awards then outstanding
will continue pursuant to their terms.

FEDERAL INCOME TAX CONSEQUENCES.  

   The following is a brief summary of the federal income tax consequences of
certain transactions under the Plan based on federal income tax laws in effect
on January 1, 1999.  This summary is not intended to be exhaustive and does not
describe state or local tax consequences.  Additional or different federal
income tax consequences to the employee or the Company may result depending upon
other consideration not described below.

   Options.  In general, an optionee will not recognize any taxable income at
the time a non-qualified stock option (an option not qualified under Section 422
of the Code) ("NQO") is granted. Upon the exercise of a NQO, an optionee will
generally recognize ordinary income in an amount equal to the difference between
the option price paid for the shares and the fair market value of the shares if
they are nonrestricted on the date of exercise.  Upon the sale of shares
acquired pursuant to the exercise of a NQO, an optionee will generally treat any
appreciation (or depreciation) in the value of the shares after the date of
exercise as either short term or long term capital gain (or loss) depending on
how long the shares have been held.

   No income generally will be recognized by an optionee upon the grant or
exercise of an ISO, although the excess of the fair market value on the date of
exercise over the option price is included in alternative minimum taxable income
for alternative minimum tax purposes.  However, if the optionee exercises the
ISO and disposes of the shares of Common Stock in the same year and the amount
realized is less than the fair market value on the date of exercise, only the
difference between the amount realized and the adjusted basis of the stock will
be included in alternative minimum taxable income.  If shares of Common Stock
are issued to an optionee pursuant to the exercise of an ISO and no disposition
of the shares is made by the optionee within two years after the date of grant
or within one year after the transfer of the shares to the optionee (the
"Holding Periods"), then, upon the sale of the shares, any amount realized in
excess of the option price will

                                    - 12 -

<PAGE>

be taxed to the optionee as long term capital gain and any loss sustained will
be a long term capital loss.

   If shares of Common Stock acquired upon the exercise of an ISO are disposed
of prior to the expiration of either Holding Period described above, the
optionee generally will recognize ordinary income in the year of disposition in
an amount equal to any excess of the fair market value of the shares at the time
of exercise (or, if less, the amount realized on the disposition of the shares
in a sale or exchange) over the option price paid for the shares.  Any further
gain (or loss) realized by the optionee generally will be taxed as short term or
long term capital gain (or loss) depending on the holding period.

   Restricted Stock.  A recipient of restricted stock generally will be subject
to tax at ordinary income rates on the fair market value of the restricted stock
reduced by any amount paid by the recipient at such time as the shares are no
longer subject to a risk of forfeiture or restrictions on transfer for purposes
of Section 83 of the Code.  Further, any dividends received with respect to
restricted stock that are subject at that time to a risk of forfeiture or
restrictions on transfer generally will be treated as compensation that is
taxable as ordinary income to the recipient.  However, a recipient who so elects
under Section 83(b) of the Code within 30 days of the date of transfer of shares
will have taxable ordinary income on the date of transfer of the shares equal to
the excess of the fair market value of the shares (determined without regard to
the risk of forfeiture or restrictions on transfer) over any purchase price paid
for the shares and any dividend received while the shares are subject to a
substantial risk of forfeiture or restrictions will be treated as dividend
income to the recipient.

   Phantom Shares or Performance Awards.  No income generally will be recognized
upon the grant of phantom shares or performance awards.  Upon payment in respect
of phantom shares or earned performance awards, the recipient generally will be
required to include as taxable ordinary income in the year of receipt an amount
equal to the amount of cash received and the fair market value of any
nonrestricted shares of Common Stock received less any amount paid for such
award at the time of payment or transfer pursuant to the fulfillment of the
specified conditions or the achievement of the performance goals.

   Bonus Shares.  The recipient of bonus shares generally will be subject to tax
at ordinary income rates on the fair market value of nonrestricted shares of
Common Stock on the date that such shares are transferred to the recipient,
reduced by any amount paid by the recipient, and the capital gain or loss
holding period for such shares will also commence on that date.

   Cash Awards.  No income will be recognized upon the grant of a cash award.
The recipient of a cash award will be subject to tax at ordinary income rates on
the cash received pursuant to the Award.

   Other Stock-Based Awards.  Generally, Other Stock-Based Awards will be
subject to tax in the same manner as described above for a similar stock award.

   To the extent that a participant recognizes ordinary income in the
circumstances described above, the Company or subsidiary for which the
participant performs services will be entitled to a corresponding deduction for
federal income tax purposes provided that, among other things, the income (i)
meets the test of reasonableness and is an ordinary and necessary business
expense, (ii) is properly and timely reported to the Internal Revenue Service by
the Company, (iii) is not an "excess parachute payment" within the meaning of
Section 280G of the Code and (iv) the $1.0 million limitation of Section 162(m)
of the Code is not exceeded.

                                    - 13 -

<PAGE>

                                PROPOSAL 3:

                  RATIFICATION OF APPOINTMENT OF AUDITORS

   The Board of Directors recommends the ratification of the appointment of
Arthur Andersen LLP as independent auditors for the Company for the year ending
December 31, 1999. This firm has served in such capacity since 1974 and is
familiar with the Company's affairs and financial procedures. Their appointment
as auditors for the year ended December 31, 1998 was approved by the
shareholders at the last Annual Meeting on April 27, 1998.

   Representatives of Arthur Andersen LLP are expected to be present at the
Annual Meeting and will have an opportunity to make a statement if they desire
to do so and to respond to appropriate questions from those attending the
meeting.


                              OTHER BUSINESS

   The Board of Directors of the Company knows of no matters expected to be
presented at the Annual Meeting other than those described above; however, if
other matters are properly presented to the meeting for action, it is intended
that the persons named in the accompanying form of proxy, and acting thereunder,
will vote in accordance with their best judgment on such matters.


                       EXECUTIVE AND OTHER OFFICERS

Set forth below are the executive officers of the Company as of year end 1998
along with the age as of March 19, 1999 and office held by each officer.

   Mr. James R. Gibbs (54) is President and Chief Executive Officer. Information
about Mr. Gibbs is included on page six with the information on nominees for the
Board.

   Ms. Julie H. Edwards (40) is Senior Vice President-Finance & Chief Financial
Officer . She joined the Company in March 1991 as Vice President-Secretary &
Treasurer and  was promoted to her current position in August 1994. From 1985 to
February 1991, she was employed by Smith Barney, Harris Upham & Co. Inc. in the
Corporate Finance Department.  Prior to 1985, she was employed by Amerada Hess
Corporation and American Ultramar, Ltd., which are oil companies, as a
geologist. Ms. Edwards is a member of the Board of Directors of Evans Systems,
Inc., a fuel distribution, convenience store and diversified company.

   Mr. S. Clark Johnson (53) is Senior Vice President-Refining Operations and
serves as president of the refining subsidiaries of the Company.  He has over 25
years of experience in refining and marketing.   Prior to joining the Company,
Mr. Johnson served as Senior Vice President-Marketing, Supply & Terminals at
Kerr-McGee Refining Corporation since 1990.  In 1989, Mr. Johnson served as
President of Coastal Mart, Inc., a retail subsidiary of Coastal Corporation.
Previously, Mr. Johnson was with Tenneco Oil Company for 20 years where he held
numerous positions, including Vice President-Retail Marketing from 1987 to 1988.
Mr. Johnson is a member of the Board of Directors of Pride Refining, Inc., the
general partner of Pride Companies, L.P., a products pipeline and crude oil
gathering company.

   Mr. J. Currie Bechtol (57) has been Vice President-General Counsel of the
Company since January 1998.  Prior to joining the Company, Mr. Bechtol has been
in private legal practice for 28 years, most recently as a partner of Hutcheson
& Grundy L.L.P. from 1984 until joining the Company.

                                    - 14 -

<PAGE>

   Mr. Jon D. Galvin (45) is Vice President-Controller of the Company. He was
appointed to this position in September 1997. Mr. Galvin has been the Chief
Financial Officer of the Company's Frontier refining subsidiaries since February
1992.  Previously, he had spent 15 years with Arthur Andersen, ultimately as
Audit Principal.

   Mr. Gerald B. Faudel (49) is Vice President-Safety and Environmental Affairs
and has held that position with the Company since November 1993. He holds a
similar position with the refining subsidiaries. From October 1991 through
November 1993, Mr. Faudel was Director of Safety, Environmental and External
Affairs of the refining subsidiaries of the Company. Mr. Faudel was employed by
Frontier Oil Corporation from October 1989 through October 1991 as Director of
Safety, Environmental and External Affairs. Prior to October 1989, Mr. Faudel
was employed with Tosco Corporation's Avon Refinery as Manager of Hazardous
Waste and Wastewater Program.


      REPORT OF THE COMPENSATION COMMITTEE OF THE BOARD OF DIRECTORS

   All members of the Compensation Committee are independent, non-employee
directors. The Committee regularly reviews and, with any changes it believes
appropriate, approves the Company's executive compensation program. An
independent compensation consultant employed by KPMG Peat Marwick and formerly
employed by Towers Perrin has been retained by the Committee and has advised the
Committee on all compensation matters since 1988. The Company's executive
compensation program is structured to help the Company achieve its business
objectives by:

   -  setting levels of compensation designed to attract and retain key
      executives;

   -  providing incentive compensation that varies directly with both Company
      performance and individual contribution to that performance; and

   -  linking compensation to financial targets which affect short and long term
      share price performance.

COMPENSATION PROGRAM COMPONENTS

   The particular elements of the compensation program for executive officers
are further explained below.

   Base Salary. Base pay levels are largely determined through comparisons with
a peer group of companies of similar size, activity and complexity to the
Company as determined by KPMG Peat Marwick and which companies are included in
the Peer Group Index in the graph on page 20. The relative stock price
performance of the Company compared to the peer group is one factor used in
determining compensation. In addition, salaries are based on the Company's
recent performance and on individual performance contributions within a
competitive salary range for each position that is established through job
evaluation and market comparisons. Base pay levels for the executive officers
are generally in the middle of a competitive range of salaries.

   Annual Incentive Compensation. The Company's officers and certain other
employees are eligible to participate in an annual incentive compensation plan
with awards based primarily on the attainment of certain earnings and cash flow
goals established by the Company's annual budget, which is approved by the Board
of Directors. The objective of this incentive plan is to deliver competitive
levels of compensation for the attainment of financial targets that the
Committee believes are important determinants of share price over time.

   In 1995 and 1996, no awards were made due to net losses for the years. In
1997, the Company both exceeded its budget earnings and cash flow and was
profitable. Accordingly, awards were made to all employees in early 1998 based
on 1997 results. In 1998, the Company was again profitable, achieving record
earnings from continuing operations.  However, the results failed to meet
budget. Accordingly, awards were proportionally reduced and were made to all
employees in early 1999 based on 1998 results.

   Stock Option Program. The Committee strongly believes that by providing those
persons who have substantial

                                    - 15 -

<PAGE>

responsibility for the management and growth of the Company with an opportunity
to increase their ownership of the Company stock, the best interests of the
shareholders and executives will be closely aligned. Therefore, executives and
managers are eligible to receive stock options from time to time at the
discretion of the Compensation Committee, giving them the right to purchase
shares of Common Stock at a specified price in the future. The number of stock
options granted to executive officers is based on such officer's ability to
influence the Company's performance as determined by the Compensation Committee.

CEO COMPENSATION

   In accordance with the discussion above of the Company's philosophy for
executive compensation, a significant portion of the compensation for the Chief
Executive Officer is based upon the Company's performance. Mr. Gibbs, who has
served as Chief Executive Officer since April 1992 joined the Company in 1982
and has served in a number of executive positions. Up to one half of Mr. Gibbs'
total cash compensation is tied to the performance of the Company. In 1995, his
salary was increased slightly in recognition of the strong operational
performance of 1994 and additional tasks of winding down the U.S. oil and gas
operations.  He received no increase in 1996 or 1997 nor bonus in 1995 or 1996
due to the Company's net losses in 1995 and 1996. He received meaningful bonus
awards in early 1998 based on 1997 results and in early 1999 based on 1998
results.  As is reflected in the Summary Compensation Table, Mr. Gibbs also
participated in the Company's savings plans.

                                 Compensation Committee Members:

                                         Douglas Y. Bech
                                        Paul B. Loyd, Jr.
                                         Carl W. Schafer

                                    - 16 -

<PAGE>

               EXECUTIVE COMPENSATION AND OTHER INFORMATION

EXECUTIVE COMPENSATION

   The following table sets forth information regarding compensation earned by
the Company's Chief Executive Officer and the four most highly compensated
officers other than the Chief Executive Officer  for services rendered in all
capacities to the Company and its subsidiaries in the years 1996 through 1998.

                        SUMMARY COMPENSATION TABLE

<TABLE>
<CAPTION>

                                                                          LONG TERM COMPENSATION
                                                                          ----------------------------------
                                              ANNUAL COMPENSATION                   AWARDS           PAYOUTS
                                         -------------------------------  ------------------------  --------
                                                                 OTHER                  SECURITIES
                                                                 ANNUAL    RESTRICTED   UNDERLYING
                                                                COMPEN-      STOCK       OPTIONS/     LTIP       ALL OTHER
   NAME AND                                SALARY     BONUS      SATION      AWARDS        SARS     PAYOUTS   COMPENSATION (1)
PRINCIPAL POSITION                YEAR       ($)       ($)         ($)        ($)          (#)        ($)           ($)
- -------------------------------  ------  ---------  ---------  ---------  ------------  ----------  --------  ----------------
<S>                              <C>     <C>        <C>        <C>        <C>           <C>         <C>       <C>

James R. Gibbs                   1998     445,000    232,000          0             0           0         0        110,891 (2)
 President and Chief             1997     415,000    415,000          0             0     242,800         0         64,820
 Executive Officer               1996     415,000          0          0             0     125,000         0         54,389

S. Clark Johnson                 1998     280,000    112,000          0             0           0         0         60,456 (3)
 Senior Vice President-          1997     265,000    185,500          0             0      28,000         0         40,541
 Refining Operations             1996     255,000          0          0             0      68,000         0         32,025

Julie H. Edwards                 1998     227,000     91,000          0             0           0         0         34,647 (4)
 Senior Vice President-Finance   1997     210,000    147,000          0             0      23,000         0         23,866
 & Chief Financial Officer       1996     195,000          0          0             0      94,000         0         20,635

J. Currie Bechtol                1998     150,000     42,000          0             0           0         0         17,952 (5)
 Vice President-General          1997           0          0          0             0           0         0              0
    Counsel                      1996           0          0          0             0           0         0              0

Jon D. Galvin                    1998     175,000     49,000          0             0           0         0         32,781 (6)
 Vice President-Controller       1997     163,264     79,000          0             0      37,200         0         18,019
                                 1996     157,743          0          0             0      38,800         0         17,500

</TABLE>

 
(1) Includes amounts contributed under the Company's retirement/savings plans,
    deferred compensation plan and premiums paid by the Company for individual
    life insurance. Detail is given in the following notes.

(2) Mr. Gibbs' Other Compensation includes $17,548 of Company contribution to
    his retirement/savings plan account, $86,052 of Company contribution to his
    retirement/savings plan account through a deferred compensation program and
    $7,291 of life insurance premiums paid by the Company.

                                    - 17 -

<PAGE>

(3) Mr. Johnson's Other Compensation includes $17,548 of Company contribution to
    his retirement/savings plan account, $38,712 of Company contribution to his
    retirement/savings plan account through a deferred compensation program and
    $4,196 of life insurance premiums paid by the Company.

(4) Ms. Edwards' Other Compensation includes $17,548 of Company contribution to
    her retirement/savings plan account, $14,892 of Company contribution to her
    retirement/savings plan account through a deferred compensation program and
    $2,207 of life insurance premiums paid by the Company.

(5) Mr. Bechtol's Other Compensation includes $12,948 of Company contribution to
    his retirement/savings plan account, $2,052 of Company contribution to his
    retirement/savings plan account through a deferred compensation program and
    $2,952 of life insurance premiums paid by the Company.

(6) Mr. Galvin's Other Compensation includes $17,548 of Company contribution to
    his retirement/savings plan account, $13,332 of Company contribution to his
    retirement/savings plan account through a deferred compensation program and
    $1,901 of life insurance premiums paid by the Company.


STOCK OPTIONS

   The Company currently maintains three stock option plans in which employees
are eligible to participate, pursuant to which options to purchase shares of
Common Stock are outstanding or available for future grants. The purpose of the
stock option plans is to advance the best interest of the Company by providing
those persons who have substantial responsibility for the management and growth
of the Company with additional incentive by increasing their proprietary
interest in the success of the Company. No option grants were made during 1998.
As of March 19, 1999, there were 91,290 shares of Common Stock available for
grants under the Company's existing stock option plans.
                                     
                                    - 18 -

<PAGE>

                    AGGREGATE OPTION EXERCISES IN 1998
                  AND OPTION VALUES AT DECEMBER 31, 1998

<TABLE>
<CAPTION>

                       SHARES                   NUMBER OF SECURITIES         VALUE OF UNEXERCISED
                     ACQUIRED ON   VALUE       UNDERLYING UNEXERCISED      IN-THE-MONEY OPTIONS AT
                      EXERCISE    REALIZED    OPTIONS AT DEC. 31, 1998         DEC. 31, 1998($)
NAME                     (#)        ($)      EXERCISABLE/UNEXERCISABLE  EXERCISABLE/UNEXERCISABLE (1)
- -------------------  -----------  ---------  -------------------------  -----------------------------
<S>                  <C>          <C>        <C>                        <C>

James R. Gibbs . .       40,000     37,500         512,160/39,840               639,900/62,250
S. Clark Johnson .            0          0         150,500/15,000               160,254/23,438
Julie H. Edwards .       29,000     74,750         141,500/15,000               188,311/23,438
J. Currie Bechtol.            0          0                      0                            0
Jon D. Galvin. . .            0          0           56,440/7,560                97,888/11,813

</TABLE>

(1) Computed based on the difference between aggregate fair market value and
    aggregate exercise price.  The fair market value of the Company's Common
    Stock on December 31, 1998 as $4.9375 based on the closing sale price on
    December 31, 1998.
   
DIRECTORS' STOCK GRANT PLAN

   In 1995, the Board of Directors established a stock grant plan for
non-employee directors.  The purpose of the stock grant plan is to advance the
best interest of the Company by increasing the non-employee directors'
proprietary interest in the success of the Company.  Further, the stock grant
plan allows for additional compensation to the non- employee directors without
incurring cash expenses to the Company.

   Under the Directors' Stock Grant Plan, automatic grants of a fixed number of
shares (currently 500 shares per non-employee director) are made on certain
predetermined dates (currently approximately every 15 months) out of the
Treasury shares owned by the Company in 1995. In 1995, 1996, 1997 and again in
early 1999, each of five non- employee directors received 500 shares of common
stock. As of March 19, 1999, 50,000 shares of common stock are in the Company's
Treasury which are available for grant under this plan.

EMPLOYMENT AGREEMENTS

   In April 1998, the Company entered into employment agreements with Mr. Gibbs,
Ms. Edwards, Mr.  Johnson, Mr. Bechtol, Mr. Galvin and Mr. Faudel. These
agreements provide that in the event of a change of control of the Company, the
executive will remain in his or her position as of the date of the agreement
with commensurate duties for a period of three years from the change of control.
Each agreement provides that the executive officer will receive at least the
same level of base compensation and other benefits as were being received by
such executive officer immediately prior to the change of control. In addition,
the agreements each provide for payment of annual performance bonuses determined
by percentages of the base salary (65% for Mr. Gibbs, 50% for Ms. Edwards and
Mr. Johnson and 35% for Messrs. Bechtol, Galvin and Faudel) in effect during the
three year term.  In the event of termination of the executive officer for any
reason other than cause during the three year term of employment, the Company is
required to continue to pay the executive officer the stated compensation,
including the value of unexercised in-the-money stock options, either
periodically or in a lump sum, as provided by the terms of the agreements.

                                    - 19 -

<PAGE>

CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

Burnet, Duckworth & Palmer, a law firm of which Mr. Palmer is a partner, is
retained by the Company as its counsel for certain Canadian legal matters.

                                     
                                     
             COMPARISON OF 5 YEAR CUMULATIVE TOTAL RETURN OF 
          THE COMPANY, PEER GROUP INDICES AND BROAD MARKET INDEX
                                     
                                     
<TABLE>
<CAPTION>
                                     REFINING PEER
               FRONTIER OIL CO.         GROUP             S & P 500
               ---------------       --------------     ------------
<S>            <C>                   <C>                <C>
1993                   100                  100               100
1994                122.58                95.40             98.46
1995                 83.87                99.80            132.05
1996                 80.65               118.13            158.80
1997                204.84               161.55            208.05
1998                127.42               115.38            263.53

</TABLE>
                                     
                                     
                                     
Assumes $100 invested December 31, 1993 in (i) the Company's Common Stock, (ii)
a peer group of independent refining companies (the "Refining Peer Group") which
includes Ashland Inc., Crown Central Petroleum, Giant Industries, Holly
Corporation, Sun Company and Tosco Corporation, and (iii) the S & P 500 Index.

                                    - 20 -

<PAGE>

        COMPENSATION COMMITTEE INTERLOCKS AND INSIDER PARTICIPATION

   Members of the Compensation Committee are Messrs. Bech, Loyd and Schafer. No
member of the Compensation Committee of the Board of Directors of the Company
was, during 1998, an officer or employee of the Company or any of its
subsidiaries, or was formerly an officer of the Company or any of its
subsidiaries or had any relationships requiring disclosure by the Company.

   During 1998 no executive officer of the Company served as (i) a member of the
Compensation Committee (or other board committee performing equivalent
functions) of another entity, one of whose executive officers served on the
Compensation Committee of the Board of Directors, (ii) a director of another
entity, one of whose executive officers served on the Compensation Committee of
the Company, or (iii) a member of the compensation committee (or other board
committee performing equivalent functions) of another entity, one of whose
executive officers served as a director of the Company.

                       SECTION 16 FILINGS DISCLOSURE

   Section 16(a) of the 1934 Act 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 Commission and the New York Stock
Exchange initial reports of ownership and reports of changes in ownership of
Common Stock of the Company. Officers, directors and greater than ten-percent
shareholders are required by Commission regulations to furnish the Company with
copies of all Section 16(a) forms they file.

   To the Company's knowledge, based solely on review of the Company's copies of
such reports furnished to the Company and written representations that no other
reports were required, during the fiscal year ended December 31, 1998, all
Section 16(a) filing requirements applicable to its officers, directors and
greater than ten-percent beneficial owners were complied with except for a Form
4 with respect to the purchase of shares in January 1998 by Mr. Johnson and a
Form 4 with respect to the conversion of a debenture into common shares in March
1998 by Mr. Palmer.

                           SHAREHOLDER PROPOSALS

   Proposals of shareholders intended to be included in the Proxy Statement
relating to the Company's 2000 Annual Meeting of Shareholders (the "2000 Annual
Meeting") pursuant to Rule 14a-8 under the 1934 Act ("Rule 14a-8") must be
received by the Company no later than November 26, 1999 and must otherwise
comply with the requirements of Ruly 14a-8.

   Proposals of shareholders submitted for considerations at the Company's 2000
Annual Meeting (outside of the Rule 14a-8 process), in accordance with the
Company's bylaws, must be received by the Company by the later of 60 days before
the 2000 Annual Meeting or 10 days after notice of such meeting is first
published.  If such timely notice of a proposal is not given, the proposal may
not be brought before the 2000 Annual Meeting.

                                    - 21 -

<PAGE>

                               MISCELLANEOUS

   All information contained in this Proxy Statement relating to the
occupations, affiliations and securities holdings of directors and officers of
the Company and their relationship and transactions with the Company is based
upon information received from directors and officers.  All information relating
to any beneficial owners of more than 5% of the Company's Common Stock is based
upon information contained in reports filed by such owner with the Commission.


                                       By Order of the Board of Directors,

                                              JULIE H. EDWARDS
                                       Senior Vice President-Finance & 
                                           Chief Financial Officer
                                                  Secretary
                                                 
March 26, 1999
Houston, Texas

                                    - 22 -

<PAGE>

                                 EXHIBIT A


                         FRONTIER OIL CORPORATION
                              1999 STOCK PLAN


  SECTION 1.   Purpose of the Plan.

  The Frontier Oil Corporation 1999 Stock Plan (the "Plan") is intended to
promote the interests of Frontier Oil Corporation, a Wyoming corporation (the
"Company"), by encouraging officers, employees, directors and consultants of the
Company and its Affiliates to acquire or increase their equity interest in the
Company and to provide a means whereby they may develop a sense of
proprietorship and personal involvement in the development and financial success
of the Company, and to encourage them to remain with and devote their best
efforts to the business of the Company thereby advancing the interests of the
Company and its shareholders. The Plan is also contemplated to enhance the
ability of the Company and its Affiliates to attract and retain the services of
individuals who are essential for the growth and profitability of the Company.

  SECTION 2.   Definitions.

  As used in the Plan, the following terms shall have the meanings set forth
below:

  "Affiliate" shall mean (i) any entity that, directly or through one or more
intermediaries, is controlled by the Company, (ii) any entity in which the
Company has a significant equity interest, as determined by the Committee, and
(iii) any "parent corporation" of the Company (as defined in Section 424(e) of
the Code) and any "subsidiary corporation" of any such parent (as defined in
Section 424(f) of the Code) thereof.

  "Award" shall mean any Option, Restricted Stock, Performance Award, Phantom
Shares, Bonus Shares, Other Stock-Based Award or Cash Award.

  "Award Agreement" shall mean any written agreement, contract, or other
instrument or document evidencing any Award, which may, but need not, be
executed or acknowledged by a Participant.

  "Board" shall mean the Board of Directors of the Company.

  "Bonus Shares" shall mean an award of Shares granted pursuant to Section 6(d)
of the Plan.

  "Cash Award" shall mean an award payable in cash granted pursuant to Section
6(f) of the Plan.

  "Change in Control" shall mean a change in control of a nature that would be
required to be disclosed in a proxy statement, governed by the rules of the
Securities and Exchange Commission  as in effect on the date of this Agreement;
provided that without limitation, such a change in control shall be deemed to
have occurred upon the occurrence of any one of the following:

  (a) the consummation of any transaction (including without limitation, any
  merger, consolidation, tender offer, or exchange offer) the result of which is
  that any individual or "person" (as such term is used in Sections 13(d)(3) and
  14(d)(2), of the Securities Exchange Act of 1934 - the "Exchange Act") is or
  becomes the "beneficial owner" (as such term is defined in Rule 13d-3 and Rule
  13d-5 under the Exchange Act), directly or indirectly, of securities of the
  Company representing 25% or more of the combined voting power of the Company's
  then outstanding securities,

                                    - A1 -

<PAGE>

  (b) the first day during any period of 24 consecutive months, commencing
  before or after the date of this Agreement that the individuals, who at the
  beginning of such 24 month period were directors of the Company for whom the
  Executive shall have voted, cease for any reason to constitute at least a
  majority of the Board of Directors of the Company,

  (c) the sale, lease, transfer, conveyance or other disposition (including by
  merger or consolidation) in one or a series of related transactions, of all or
  substantially all of the assets of the Company and its Subsidiaries, taken as
  a whole,

  (d) the adoption of a plan relating to the liquidation or dissolution of the
  Company, or

  (e) the date the Company files a report or proxy statement with the SEC
  stating that a change in control has or may occur pursuant to any then
  existing contract or termination.

  "Code" shall mean the Internal Revenue Code of 1986, as amended from time to
time, and the rules and regulations thereunder.

  "Committee" shall mean the Compensation Committee of the Board.

  "Consultant" shall mean any individual, other than a Director or an Employee,
who renders consulting services to the Company or an Affiliate for a fee.

  "Director" shall mean a "non-employee director" of the Company, as defined in
Rule 16b-3.

  "Employee" shall mean any employee of the Company or an Affiliate or any
person who has been extended an offer of employment by the Company or an
Affiliate.

  "Exchange Act" shall mean the Securities Exchange Act of 1934, as amended.

  "Fair Market Value" shall mean, with respect to Shares, the closing sales
price of a Share on the applicable date (or if there is no trading in the Shares
on such date, on the next preceding date on which there was trading) as reported
in The Wall Street Journal (or other reporting service approved by the
Committee).  In the event the Shares are not publicly traded at the time a
determination of its fair market value is required to be made hereunder, the
determination of fair market value shall be made in good faith by the Committee.

  "Option" shall mean an option granted under Section 6(a) of the Plan. Options
granted under the Plan shall constitute "incentive stock options" for purposes
of Section 422 of the Code or nonqualified stock option.

  "Other Stock-Based Award" shall mean an award granted pursuant to Section 6(g)
of the Plan that is not otherwise specifically provided for, the value of which
is based in whole or in part upon the value of a Share.

  "Participant" shall mean any Director, Employee or Consultant granted an Award
under the Plan.

  "Performance Award" shall mean any right granted under Section 6(c) of the
Plan.

  "Person" shall mean individual, corporation, partnership, association,
joint-stock company, trust, unincorporated organization, government or political
subdivision thereof or other entity.

  "Phantom Shares" shall mean an Award of the right to receive Shares issued at
the end of a Restricted Period which is granted pursuant to Section 6(e) of the
Plan.

                                    - A2 -

<PAGE>

  "Restricted Period" shall mean the period established by the Committee with
respect to an Award during which the Award either remains subject to forfeiture
or is not exercisable by the Participant.

  "Restricted Stock" shall mean any Share, prior to the lapse of restrictions
thereon, granted under Sections 6(b) of the Plan.

  "Rule 16b-3" shall mean Rule 16b-3 promulgated by the SEC under the Exchange
Act, or any successor rule or regulation thereto as in effect from time to time.

  "SEC" shall mean the Securities and Exchange Commission, or any successor
thereto.

  "Shares" or "Common Shares" or "Common Stock" shall mean the common stock of
the Company, no par value, and such other securities or property as may become
the subject of Awards under the Plan.

  SECTION 3.  Administration.

  The Plan shall be administered by the Committee.  A majority of the Committee
shall constitute a quorum, and the acts of the members of the Committee who are
present at any meeting thereof at which a quorum is present, or acts unanimously
approved by the members of the Committee in writing, shall be the acts of the
Committee.   Subject to the following, the Committee, in its sole discretion,
may delegate any or all of its powers and duties under the Plan, including the
power to grant Awards under the Plan, to the Chief Executive Officer of the
Company, subject to such limitations on such delegated powers and duties as the
Committee may impose. Upon any such delegation all references in the Plan to the
"Committee", other than in Section 7, shall be deemed to include the Chief
Executive Officer; provided, however, that such delegation shall not limit the
Chief Executive Officer's right to receive Awards under the Plan.
Notwithstanding the foregoing, the Chief Executive Officer may not grant Awards
to, or take any action with respect to any Award previously granted to, a person
who is an officer or a member of the Board.  Subject to the terms of the Plan
and applicable law, and in addition to other express powers and authorizations
conferred on the Committee by the Plan, the Committee shall have full power and
authority to: (i) designate Participants; (ii) determine the type or types of
Awards to be granted to a Participant; (iii) determine the number of Shares to
be covered by, or with respect to which payments, rights, or other matters are
to be calculated in connection with, Awards; (iv) determine the terms and
conditions of any Award; (v) determine whether, to what extent, and under what
circumstances Awards may be settled or exercised in cash, Shares, other
securities, other Awards or other property, or canceled, forfeited, or suspended
and the method or methods by which Awards may be settled, exercised, canceled,
forfeited, or suspended; (vi) determine whether, to what extent, and under what
circumstances cash, Shares, other securities, other Awards, other property, and
other amounts payable with respect to an Award shall be deferred either
automatically or at the election of the holder thereof or of the Committee;
(vii) interpret and administer the Plan and any instrument or agreement relating
to an Award made under the Plan; (viii) establish, amend, suspend, or waive such
rules and regulations and appoint such agents as it shall deem appropriate for
the proper administration of the Plan; and (ix) make any other determination and
take any other action that the Committee deems necessary or desirable for the
administration of the Plan.  Unless otherwise expressly provided in the Plan,
all designations, determinations, interpretations, and other decisions under or
with respect to the Plan or any Award shall be within the sole discretion of the
Committee, may be made at any time and shall be final, conclusive, and binding
upon all Persons, including the Company, any Affiliate, any Participant, any
holder or beneficiary of any Award, any stockholder and any Employee.

  SECTION 4.  Shares Available for Awards.

  (a)  Shares Available.  Subject to adjustment as provided in Section 4(c), the
number of Shares with respect to which Awards may be granted under the Plan
shall be 2.0 million.  If any Award is exercised, paid, forfeited, terminated or
canceled without the delivery of Shares or other consideration, then the Shares
covered by such Award, to the extent of such payment, exercise, forfeiture,
termination or cancellation, shall again be Shares with respect to

                                    - A3 -

<PAGE>

which Awards may be granted. 


  (b)  Sources of Shares Deliverable Under Awards.  Any Shares delivered
pursuant to an Award may consist, in whole or in part, of authorized and
unissued Shares or of treasury Shares.

  (c)  Adjustments.  In the event that the Committee determines that any
dividend or other distribution (whether in the form of cash, Shares, other
securities, or other property), recapitalization, stock split, reverse stock
split, reorganization, merger, consolidation, split-up, spin-off, combination,
repurchase, or exchange of Shares or other securities of the Company, issuance
of warrants or other rights to purchase Shares or other securities of the
Company, or other similar corporate transaction or event affects the Shares such
that an adjustment is determined by the Committee to be appropriate in order to
prevent dilution or enlargement of the benefits or potential benefits intended
to be made available under the Plan, then the Committee shall, in such manner as
it may deem equitable, adjust any or all of (i) the number and type of Shares
(or other securities or property) with respect to which Awards may be granted,
(ii) the number and type of Shares (or other securities or property) subject to
outstanding Awards, and (iii) the grant or exercise price with respect to any
Award or, if deemed appropriate, make provision for a cash payment to the holder
of an outstanding Award.

  SECTION 5.   Eligibility.

  Any Employee, Director or Consultant shall be eligible to be designated a
Participant.

  SECTION 6.   Awards.

  (a)  Options.  Subject to the provisions of the Plan, the Committee shall have
the authority to determine the Participants to whom Options shall be granted,
the number of Shares to be covered by each Option, the purchase price therefor
and the conditions and limitations applicable to the exercise of the Option,
including the following terms and conditions and such additional terms and
conditions, as the Committee shall determine, that are not inconsistent with the
provisions of the Plan.

       (i)   Exercise Price.  The purchase price per Share purchasable under an
  Option shall be determined by the Committee at the time the Option is granted,
  but shall not be less than the Fair Market Value per Share on such grant date.

       (ii)  Time and Method of Exercise.  The Committee shall determine the
  time or times at which an Option may be exercised in whole or in part, and the
  method or methods by which, and the form or forms (which may include, without
  limitation, cash, check acceptable to the Company, Shares already-owned for
  more than six months, outstanding Awards, Shares that would otherwise be
  acquired upon exercise of the Option, a "cashless- broker" exercise (through
  procedures approved by the Company), other securities or other property,
  loans, notes approved by the Committee, or any combination thereof, having a
  Fair Market Value on the exercise date equal to the relevant exercise price)
  in which payment of the exercise price with respect thereto may be made or
  deemed to have been made.

       (iii) Incentive Stock Options.  The terms of any Option granted under the
  Plan intended to be an incentive stock option shall comply in all respects
  with the provisions of Section 422 of the Code, or any successor provision,
  and any regulations promulgated thereunder.  Incentive stock options may be
  granted only to employees of the Company and its parent corporation and
  subsidiary corporations, within the meaning of Section 424 of the Code. To the
  extent the aggregate Fair Market Value of the Shares (determined as of the
  date of grant) of an Option to the extent exercisable for the first time
  during any calendar year (under all plans of the Company and its parent and
  subsidiary corporations) exceeds $100,000, such Option Shares in excess of
  $100,000 shall not be incentive stock options.

                                    - A4 -

<PAGE>

  (b)  Restricted Stock.  Subject to the provisions of the Plan, the Committee
shall have the authority to determine the Participants to whom Restricted Stock
shall be granted, the number of Shares of Restricted Stock to be granted to each
such Participant, the duration of the Restricted Period during which, and the
conditions, including performance criteria, if any, under which, the Restricted
Stock may be forfeited to the Company, and the other terms and conditions of
such Awards.

       (i)   Dividends.  Dividends paid on Restricted Stock may be paid directly
  to the Participant, may be subject to risk of forfeiture and/or transfer
  restrictions during any period established by the Committee or sequestered and
  held in a bookkeeping cash account (with or without interest) or reinvested on
  an immediate or deferred basis in additional shares of Common Stock, which
  credit or shares may be subject to the same restrictions as the underlying
  Award or such other restrictions, all as determined by the Committee in its
  discretion.

       (ii)  Registration.  Any Restricted Stock may be evidenced in such manner
  as the Committee shall deem appropriate, including, without limitation,
  book-entry registration or issuance of a stock certificate or certificates. In
  the event any stock certificate is issued in respect of Restricted Stock
  granted under the Plan, such certificate shall be registered in the name of
  the Participant and shall bear an appropriate legend referring to the terms,
  conditions, and restrictions applicable to such Restricted Stock.

       (iii) Forfeiture and Restrictions Lapse. Except as otherwise determined
  by the Committee or the terms of the Award that granted the Restricted Stock,
  upon termination of a Participant's employment (as determined under criteria
  established by the Committee) for any reason during the applicable Restricted
  Period, all Restricted Stock shall be forfeited by the Participant and
  re-acquired by the Company. Unrestricted Shares, evidenced in such manner as
  the Committee shall deem appropriate, shall be issued to the holder of
  Restricted Stock promptly after the applicable restrictions have lapsed or
  otherwise been satisfied.

       (iv)  Transfer Restrictions.  During the Restricted Period, Restricted
  Stock will be subject to the limitations on transfer as provided in Section
  6(h)(iii).

  (c)  Performance Awards.  The Committee shall have the authority to determine
the Participants who shall receive a Performance Award, which shall be
denominated as a cash amount at the time of grant and confer on the Participant
the right to receive payment of such Award, in whole or in part, upon the
achievement of such performance goals during such performance periods as the
Committee shall establish with respect to the Award.

       (i)   Terms and Conditions.  Subject to the terms of the Plan and any
  applicable Award Agreement, the Committee shall determine the performance
  goals to be achieved during any performance period, the length of any
  performance period, the amount of any Performance Award and the amount of any
  payment or transfer to be made pursuant to any Performance Award.

       (ii)  Payment of Performance Awards. Performance Awards may be paid (in
  cash and/or in Shares, in the sole discretion of the Committee) in a lump sum
  or in installments following the close of the performance period, in
  accordance with procedures established by the Committee with respect to such
  Award.

  (d)  Bonus Shares.  The Committee shall have the authority, in its discretion,
to grant Bonus Shares to Participants.  Each Bonus Share shall constitute a
transfer of an unrestricted Share to the Participant, without other payment
therefor, as additional compensation for the Participant's services to the
Company.

  (e)  Phantom Shares.  The Committee shall have the authority to grant Awards
of Phantom Shares to Participants upon such terms and conditions as the
Committee may determine.

       (i)   Terms and Conditions.  Each Phantom Share Award shall constitute an
  agreement by the Company to issue or transfer a specified number of Shares or
  pay an amount of cash equal to a specified number of Shares,

                                    - A5 -

<PAGE>

  or a combination thereof to the Participant in the future, subject to the
  fulfillment during the Restricted Period of such conditions, including
  performance objectives, if any, as the Committee may specify at the date of
  grant. During the Restricted Period, the Participant shall not have any right
  to transfer any rights under the subject Award, shall not have any rights of
  ownership in the Phantom Shares and shall not have any right to vote such
  shares.

       (ii)  Dividends.  Any Phantom Share award may provide that any or all
  dividends or other distributions paid on Shares during the Restricted Period
  be credited in a cash bookkeeping account (without interest) or that
  equivalent additional Phantom Shares be awarded, which account or shares may
  be subject to the same restrictions as the underlying Award or such other
  restrictions as the Committee may determine.

  (f)  Cash Awards.  The Committee shall have the authority to determine the
Participants to whom Cash Awards shall be granted, the amount, and the terms or
conditions, if any, as additional compensation for the Participant's services to
the Company or its Affiliates.  A Cash Award may be granted (simultaneously or
subsequently) separately or in tandem with another Award and may entitle a
Participant to receive a specified amount of cash from the Company upon such
other Award becoming taxable to the Participant, which cash amount may be based
on a formula relating to the anticipated taxable income associated with such
other Award and the payment of the Cash Award.

  (g)  Other Stock-Based Awards.  The Committee may also grant to Participants
an Other Stock-Based Award, which shall consist of a right which is an Award
denominated or payable in, valued in whole or in part by reference to, or
otherwise based on or related to, Shares as is deemed by the Committee to be
consistent with the purposes of the Plan.  Subject to the terms of the Plan, the
Committee shall determine the terms and conditions of any such Other Stock-Based
Award.

  (h)  General.

       (i)   Awards May Be Granted Separately or Together.  Awards may, in the
  discretion of the Committee, be granted either alone or in addition to, in
  tandem with, or in substitution for any other Award granted under the Plan or
  any award granted under any other plan of the Company or any Affiliate.
  Awards granted in addition to or in tandem with other Awards or awards granted
  under any other plan of the Company or any Affiliate may be granted either at
  the same time as or at a different time from the grant of such other Awards or
  awards.

       (ii)  Forms of Payment by Company Under Awards.  Subject to the terms of
  the Plan and of any applicable Award Agreement, payments or transfers to be
  made by the Company or an Affiliate upon the grant, exercise or payment of an
  Award may be made in such form or forms as the Committee shall determine,
  including, without limitation, cash, Shares, other securities, other Awards or
  other property, or any combination thereof, and may be made in a single
  payment or transfer, in installments, or on a deferred basis, in each case in
  accordance with rules and procedures established by the Committee.  Such rules
  and procedures may include, without limitation, provisions for the payment or
  crediting of reasonable interest on installment or deferred payments.

       (iii) Limits on Transfer of Awards.

         (A) Except as provided in (C) below, each Award, and each right under
       any Award, shall be exercisable only by the Participant during the
       Participant's lifetime, or by the person to whom the Participant's rights
       shall pass by will or the laws of descent and distribution.

         (B) Except as provided in (C) below, no Award and no right under any
       such Award may be assigned, alienated, pledged, attached, sold or
       otherwise transferred or encumbered by a Participant otherwise than by
       will or by the laws of descent and distribution (or, in the case of
       Restricted Stock, to the Company) and any such purported assignment,
       alienation, pledge, attachment, sale, transfer or encumbrance shall be

                                    - A6 -

<PAGE>

       void and unenforceable against the Company or any Affiliate.

         (C) Notwithstanding anything in the Plan to the contrary, to the extent
       specifically provided by the Committee with respect to a grant, an Option
       (other than an incentive stock option) may be transferred to immediate
       family members or related family trusts, limited partnerships or similar
       entities on such terms and conditions as the Committee may establish.

       (iv)  Term of Awards.  The term of each Award shall be for such period as
  may be determined by the Committee; provided, that in no event shall the term
  of any Award exceed a period of 10 years from the date of its grant.

       (v)   Share Certificates.  All certificates for Shares or other
  securities of the Company or any Affiliate delivered under the Plan pursuant
  to any Award or the exercise thereof shall be subject to such stop transfer
  orders and other restrictions as the Committee may deem advisable under the
  Plan or the rules, regulations, and other requirements of the SEC, any stock
  exchange upon which such Shares or other securities are then listed, and any
  applicable federal or state laws, and the Committee may cause a legend or
  legends to be put on any such certificates to make appropriate reference to
  such restrictions.

       (vi)  Consideration for Grants.  Awards may be granted for no cash
  consideration or for such consideration as the Committee determines including,
  without limitation, such minimal cash consideration as may be required by
  applicable law.

       (vii) Delivery of Shares or other Securities and Payment by Participant
  of Consideration.  No Shares or other securities shall be delivered pursuant
  to any Award until payment in full of any amount required to be paid pursuant
  to the Plan or the applicable Award Agreement (including, without limitation,
  any exercise price, tax payment or tax withholding) is received by the
  Company.  Such payment may be made by such method or methods and in such form
  or forms as the Committee shall determine, including, without limitation,
  cash, Shares, other securities, other Awards or other property, withholding of
  Shares, cashless exercise with simultaneous sale, or any combination thereof;
  provided that the combined value, as determined by the Committee, of all cash
  and cash equivalents and the Fair Market Value of any such Shares or other
  property so tendered to the Company, as of the date of such tender, is at
  least equal to the full amount required to be paid pursuant to the Plan or the
  applicable Award Agreement to the Company.

  SECTION 7.   Amendment and Termination.

  Except to the extent prohibited by applicable law and unless otherwise
expressly provided in an Award Agreement or in the Plan:

       (i)   Amendments to the Plan.  Except as required by applicable law or
  the rules of the principal securities market on which the shares are traded
  and subject to Section 7(ii) below, the Board or the Committee may amend,
  alter, suspend, discontinue, or terminate the Plan without the consent of any
  stockholder, Participant, other holder or beneficiary of an Award, or other
  Person.

       (ii)  Amendments to Awards. The Committee may waive any conditions or
  rights under, amend any terms of, or alter any Award theretofore granted,
  provided no change, other than pursuant to Section 7(iii), in any Award shall
  reduce the benefit to Participant without the consent of such Participant.

       (iii) Adjustment of Awards Upon the Occurrence of Certain Unusual or
  Nonrecurring Events.  The Committee is hereby authorized to make adjustments
  in the terms and conditions of, and the criteria included in, Awards in
  recognition of unusual or nonrecurring events (including, without limitation,
  the events described in Section 4(c) of the Plan) affecting the Company, any
  Affiliate, or the financial statements of the Company or any

                                    - A7 -

<PAGE>

  Affiliate, or of changes in applicable laws, regulations, or accounting
  principles, whenever the Committee determines that such adjustments are
  appropriate in order to prevent dilution or enlargement of the benefits or
  potential benefits intended to be made available under the Plan.

  SECTION 8.   Change in Control.

  Notwithstanding any other  provision of this Plan to the contrary, in the
event of a Change in Control of the Company all outstanding Awards automatically
shall become fully vested immediately prior to such Change in Control (or such
earlier time as set by the Committee), all restrictions, if any, with respect to
such Awards shall lapse, all performance criteria, if any, with respect to such
Awards shall be deemed to have been met in full (at the highest level), and
unless the Company survives as an independent publicly traded company, all
Options outstanding at the time of the event or transaction shall terminate,
except to the extent provision is made in writing in connection with such event
or transaction for the continuation of the Plan and/or the assumption of the
Options theretofore granted, or for the substitution for such Options of new
options covering the stock of a successor entity, or the parent or subsidiary
thereof, with appropriate adjustments as to the number and kinds of shares and
exercise prices, in which event the Plan and Options theretofore granted shall
continue in the manner and under the terms so provided.

  SECTION 9.   General Provisions.

  (a)  No Rights to Awards.  No Director, Employee, Consultant or other Person
shall have any claim to be granted any Award, and there is no obligation for
uniformity of treatment of Employees, Consultants, or holders or beneficiaries
of Awards.  The terms and conditions of Awards need not be the same with respect
to each recipient.

  (b)  Withholding.  The Company or any Affiliate is authorized to withhold from
any Award, from any payment due or transfer made under any Award or under the
Plan or from any compensation or other amount owing to a Participant the amount
(in cash, Shares, other securities, Shares that would otherwise be issued
pursuant to such Award, other Awards or other property) of any applicable taxes
payable in respect of an Award, its exercise, the lapse of restrictions thereon,
or any payment or transfer under an Award or under the Plan and to take such
other action as may be necessary in the opinion of the Company to satisfy all
obligations for the payment of such taxes.  In addition, the Committee may
provide, in an Award Agreement, that the Participant may direct the Company to
satisfy such Participant's tax obligation through the "constructive" tender of
already-owned Shares or the withholding of Shares otherwise to be acquired upon
the exercise or payment of such Award.

  (c)  No Right to Employment.  The grant of an Award shall not be construed as
giving a Participant the right to be retained in the employ of the Company or
any Affiliate.  Further, the Company or an Affiliate may at any time dismiss a
Participant from employment, free from any liability or any claim under the
Plan, unless otherwise expressly provided in the Plan or in any Award Agreement.

  (d)  Governing Law.  The validity, construction, and effect of the Plan and
any rules and regulations relating to the Plan shall be determined in accordance
with the laws of the State of Wyoming and applicable federal law.

  (e)  Severability.  If any provision of the Plan or any Award is or becomes or
is deemed to be invalid, illegal, or unenforceable in any jurisdiction or as to
any Person or Award, or would disqualify the Plan or any Award under any law
deemed applicable by the Committee, such provision shall be construed or deemed
amended to conform to the applicable laws, or if it cannot be construed or
deemed amended without, in the determination of the Committee, materially
altering the intent of the Plan or the Award, such provision shall be stricken
as to such jurisdiction, Person or Award and the remainder of the Plan and any
such Award shall remain in full force and effect.

  (f)  Other Laws.  The Committee may refuse to issue or transfer any Shares or
other consideration under an Award if, acting in its sole discretion, it
determines that the issuance of transfer or such Shares or such other
consideration might violate any applicable law or regulation or entitle the
Company to recover the same under Section

                                    - A8 -

<PAGE>

16(b) of the Exchange Act, and any payment tendered to the Company by a
Participant, other holder or beneficiary in connection with the exercise of such
Award shall be promptly refunded to the relevant Participant, holder or
beneficiary.

  (g)  No Trust or Fund Created.  Neither the Plan nor the Award shall create or
be construed to create a trust or separate fund of any kind or a fiduciary
relationship between the Company or any Affiliate and a Participant or any other
Person.  To the extent that any Person acquires a right to receive payments from
the Company or any Affiliate pursuant to an Award, such right shall be no
greater than the right of any general unsecured creditor of the Company or any
Affiliate.

  (h)  No Fractional Shares.  No fractional Shares shall be issued or delivered
pursuant to the Plan or any Award, and the Committee shall determine whether
cash, other securities, or other property shall be paid or transferred in lieu
of any fractional Shares or whether such fractional Shares or any rights thereto
shall be canceled, terminated, or otherwise eliminated.

  (i)  Headings.  Headings are given to the Sections and subsections of the Plan
solely as a convenience to facilitate reference.  Such headings shall not be
deemed in any way material or relevant to the construction or interpretation of
the Plan or any provision thereof.

  (j)  Parachute Tax Gross-Up.  If it shall be finally determined that the
grant, payment or acceleration of vesting or payment, whether in cash or stock,
of any Award made to a Participant under the Plan is subject to the excise tax
imposed by Section 4999 of the Code, the Company shall pay such person an amount
of cash (the "Additional Amount") such that the net amount received by such
person after paying all applicable taxes (and any interest and penalties imposed
with respect thereto) on such Additional Amount shall be equal to the amount
that such person would have received if Section 4999 were not applicable.

  SECTION 10.   Effective Date of the Plan.

  The Plan shall be effective as of April 29, 1999.

  SECTION 11.   Term of the Plan.

  No Award shall be granted under the Plan after the 10th anniversary of the
date the Plan is adopted by the Board. However, unless otherwise expressly
provided in the Plan or in an applicable Award Agreement, any Award granted
prior to such termination, and the authority of the Board or the Committee to
amend, alter, adjust, suspend, discontinue, or terminate any such Award or to
waive any conditions or rights under such Award, shall extend beyond such
termination date.

                                    - A9 -

<PAGE>

                                                                           PROXY
 
                           FRONTIER OIL CORPORATION
 
               THIS PROXY IS SOLICITED BY THE BOARD OF DIRECTORS
 
  The undersigned hereby appoint(s) JAMES R. GIBBS and JULIE H. EDWARDS, or
either of them, lawful attorneys and proxies of the undersigned with full power
of substitution, for and in the name, place and stead of the undersigned to
attend the Annual Meeting of Shareholders of Frontier Oil Corporation to be held
in the Company's corporate offices located at 10000 Memorial Drive, Suite 600,
Houston, Texas, on Monday, April 29, 1999 at 9:00 a.m., Houston time, and any
adjournment(s) thereof, with all powers the undersigned would possess if
personally present and to vote the number of votes the undersigned would be
entitled to vote if personally present.
 
                     Please Date and Sign on Reverse Side.
<PAGE>
 
                           FRONTIER OIL CORPORATION
     PLEASE MARK VOTE IN OVAL IN THE FOLLOWING MANNER USING DARK INK ONLY. / /
 
                                                                       FOR ALL 
1. WITH RESPECT TO THE ELECTION OF DIRECTORS--   FOR     WITHHELD      EXCEPT  
   Nominees: James R. Gibbs; G. Clyde Buck;      / /        / /          / /
   Douglas Y. Bech; Paul B. Loyd, Jr.;
   Derek A. Price; and Carl W. Schafer.

2. Proposal to ratify the 1999 Stock Plan.       FOR      AGAINST      ABSTAIN
                                                 / /        / /          / /

3. Proposal to ratify the appointment of         FOR      AGAINST      ABSTAIN
   Arthur Andersen LLP as auditors for           / /        / /          / /   
   the year ending December 31, 1999.



- ---------------------
 Nominee Exception
 
In their discretion, said attorneys and proxies are authorized to vote upon
such other business as may properly come before the meeting.
 
This Proxy when properly executed will be voted in accordance with the instruc-
tions given hereof, but IF NO INSTRUCTIONS ARE GIVEN, THIS PROXY WILL BE VOTED
FOR THE ELECTION OF THE NOMINEES OF THE BOARD OF DIRECTORS AND FOR THE PROPOSALS
SET FORTH IN (2) AND (3).

Dated: _________________________________________________________, 1999

Signature(s) ___________________________________________________________________

________________________________________________________________________________
(Please sign as your name appears hereon. When signing as attorney, executor,
administrator, trustee or guardian, please give your full title. If the appoin-
tor is a corporation, this instrument must be under the corporate seal or under
the hand of an officer or attorney so authorized.)

    Shareholders are Urged to Complete, Sign and Return this Proxy Promptly.





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