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                                                                    EXHIBIT 10.4


                                                              EDWARD C. MARHANKA

                          TOREADOR ROYALTY CORPORATION

                        INCENTIVE STOCK OPTION AGREEMENT

         THIS AGREEMENT, made as of May 15, 1997, by and between Toreador
Royalty Corporation, a Delaware corporation (the "Company"), and Edward C.
Marhanka ("Optionee") in connection with the grant of an Incentive Option
(hereinafter defined) under the Toreador Royalty Corporation 1990 Stock Option
Plan (the "Plan").

                             W I T N E S S E T H :

         WHEREAS, Optionee is an employee of the Company or an Affiliate
(hereinafter defined) in a key position and the Company desires to encourage
Optionee to own Common Stock (hereinafter defined) and to give Optionee added
incentive to advance the interests of the Company through the Plan and desires
to grant Optionee an Incentive Option (hereinafter defined) to purchase shares
of Common Stock of the Company under terms and conditions established by the
Board (hereinafter defined).

         NOW, THEREFORE, the Company and Optionee hereby agree as follows:

         1.      Definitions.  As used in this Agreement, the following terms
shall have the following meanings, respectively:

                 (a)      "Affiliate" shall have the meaning set forth in
         Section 1.2 of the Plan and shall include any party now or hereafter
         coming within that definition.

                 (b)      "Board" shall mean the Board of Directors of the 
         Company.

                 (c)      "Code" shall mean the Internal Revenue Code of 1986,
         as amended.

                 (d)      "Committee" shall mean the committee appointed
         pursuant to Section 3 of the Plan.

                 (e)      "Common Stock" shall mean the $.15625 par value
         Common Stock of the Company.

                 (f)      "Fair Market Value" shall have the meaning set forth
         in Section 1.8 of the Plan.
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                 (g)      "Incentive Option" shall mean a stock option that is
         intended to be or is denominated as an incentive stock option (within
         the meaning of Section 422 of the Code).

         2.      Grant of Option and Option Period.  The Company hereby grants
to Optionee as of the date of this Agreement (the "Grant Date"), subject to the
provisions of Section 3 hereof and as hereinafter set forth, the option to
purchase 25,000 shares of Common Stock at the price of $2.50 per share (the
"Purchase Price"), at any time or (with respect to partial exercises) from time
to time during a period commencing on the first anniversary of the Grant Date
and ending on May 15, 2007 (the "Option Period"), provided that the number of
shares purchasable hereunder in any period or periods of time during which the
Option is exercised shall be limited as follows:

                 (a)      only 33 1/3% of such shares (if a fractional number,
         then the next lower whole number) are purchasable, in whole at any
         time or in part from time to time, commencing May 15, 1998, if
         Optionee is an employee of the Company or an Affiliate until that
         date;

                 (b)      an additional 33 1/3% of such shares (if a fractional
         number, then the next lower whole number) are purchasable, in whole at
         any time or in part from time to time, commencing May 15, 1999, if
         Optionee is an employee of the Company or an Affiliate until that
         date;

                 (c)      the remainder of such shares are purchasable, in
         whole at any time or in part from time to time, commencing May 15,
         2000, if Optionee is an employee of the Company or an Affiliate until
         that date.

         3.      Termination of Service.  Any provision of Section 2 hereof to
the contrary notwithstanding:

                 (a)      If Optionee ceases to be employed by the Company or
         an Affiliate "for cause" (as defined in Section 6.4(a) of the Plan),
         then that portion, if any, of this Incentive Option that remains
         unexercised, including that portion, if any, that pursuant to this
         Agreement is not yet exercisable, shall automatically terminate and be
         of no further force or effect as of the date Optionee ceases to be
         employed;

                 (b)      If Optionee shall die during the Option Period while
         in the employ of the Company or an Affiliate, this Incentive Option
         may be exercised, to the extent that Optionee was entitled to exercise
         it at the date of Optionee's death, within one year after such death
         (if otherwise within the Option Period), but not thereafter, by the
         executor or administrator of the estate of Optionee or by the person
         or persons




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         who shall have acquired this Incentive Option directly from Optionee
         by bequest or inheritance;

                 (c)      If Optionee ceases to be employed by the Company or
         an Affiliate by reason of disability (as defined in Section 22(e)(3)
         of the Code), this Incentive Option may be exercised, to the extent
         that Optionee was entitled to exercise it at the date of his
         termination, within one year after such termination (if otherwise
         within the Option Period), but not thereafter by Optionee (or
         Optionee's legal representative, if Optionee is legally incompetent);
         and

                 (d)      If Optionee ceases to be employed by the Company or
         an Affiliate for any reason (other than the circumstances specified in
         paragraphs (a), (b) and (c) of this Section 3) within the Option
         Period, this Incentive Option may be exercised, to the extent Optionee
         was able to do so at the date of termination of the employment, within
         three (3) months after such termination (if otherwise within the
         Option Period), but not thereafter.

         4.      Exercise During Employment.  Except as provided in Section 3
hereof, this Incentive Option may not be exercised unless Optionee is at the
time of exercise an employee of the Company or an Affiliate.

         5.      Manner of Exercise.  This Incentive Option may be exercised by
written notice signed by the person entitled to exercise same and delivered to
the Secretary of the Company or sent by United States registered mail addressed
to the Company (for the attention of the Secretary) at its corporate office in
Dallas, Texas.  Such notice shall state the number of shares of Common Stock as
to which the Incentive Option is exercised and shall be accompanied by the full
amount of the purchase price of such shares.  Exercise of this Incentive Option
shall not be effective until the Company has received written notice of
exercise.

         6.      Payment.  The Purchase Price for the Incentive Option shares
may be paid in cash by certified or cashier's check or, with the consent of the
Committee, with shares of Common Stock owned by Optionee which have been held
at least six (6) months prior to the date of exercise or, with the consent of
the Committee, by a combination of cash and such shares.

         7.      Delivery of Shares.  Delivery of the certificates representing
the shares of Common Stock purchased upon exercise of this Incentive Option
shall be made promptly after receipt of notice of exercise and payment.  If the
Company so elects, its obligation to deliver shares of Common Stock upon the
exercise of this Incentive Option shall be conditioned upon its receipt from
the person exercising this Incentive Option of an executed investment letter,
in form and content satisfactory to the Company and its legal counsel,





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evidencing the investment intent of such person and such other matters as the
Company may reasonably require.  If the Company so elects, the certificate or
certificates representing the shares of Common Stock issued upon exercise of
this Incentive Option shall bear a legend in substantially the following form:

         THE SHARES OF STOCK EVIDENCED BY THIS CERTIFICATE HAVE BEEN ISSUED TO
         THE REGISTERED OWNER IN RELIANCE UPON WRITTEN REPRESENTATIONS THAT
         THESE SHARES HAVE BEEN PURCHASED FOR INVESTMENT.  THESE SHARES MAY NOT
         BE SOLD, TRANSFERRED, OR ASSIGNED UNLESS, IN THE OPINION OF THE
         CORPORATION OR ITS LEGAL COUNSEL, SUCH SALE, TRANSFER, OR ASSIGNMENT
         WILL NOT BE IN VIOLATION OF THE SECURITIES ACT OF 1933, AS AMENDED,
         APPLICABLE RULES AND REGULATIONS OF THE SECURITIES AND EXCHANGE
         COMMISSION, AND ANY APPLICABLE STATE SECURITIES LAWS.

       8.      Status of Optionee.  Optionee shall not be deemed to be a
stockholder of the Company with respect to any of the shares of Common Stock
subject to this Incentive Option, except to the extent that such shares shall
have been purchased and transferred to him.  The Company shall not be required
to issue or transfer any certificates for shares of Common Stock purchased upon
exercise of this Incentive Option until all applicable requirements of law have
been complied with and such shares shall have been duly listed on any
securities exchange on which the Common Stock may then be listed.

       9.      Adjustments.  Notwithstanding any other provision hereof, in the
event of any change in the number of outstanding shares of Common Stock
effected without receipt of consideration therefor by the Company, by reason of
a stock dividend, or split, combination, exchange of shares or other
recapitalization, merger, or otherwise, in which the Company is the surviving
corporation, the number and class of shares subject to this Incentive Option
and the exercise price of this Incentive Option shall be automatically adjusted
to accurately and equitably reflect the effect thereupon of such change,
provided that any fractional share resulting from such adjustment may be
eliminated.  In the event of a dispute concerning such adjustment, the decision
of the Committee shall be conclusive.  The number of shares subject to this
Incentive Option shall be automatically reduced by any fraction included
therein which results from any adjustment made pursuant to this Section 9.

       A dissolution or liquidation of the Company; a sale of all or
substantially all of the assets of the Company where it is contemplated that
within a reasonable period of time thereafter the Company will either be
liquidated or converted into a nonoperating company or an extraordinary
dividend will be declared resulting in a partial liquidation of the Company
(but in all cases only with respect to those employees with the Company and its
Affiliates as a result of such sale or assets); a merger or consolidation
(other than a merger





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effecting a reincorporation of the Company in another state or any other merger
or a consolidation in which the shareholders of the surviving corporation and
their proportionate interests therein immediately after the merger or
consolidation are substantially identical to the shareholders of the Company
and their proportionate interests therein immediately prior to the merger or
consolidation) in which the Company is not the surviving corporation (or
survives only as a subsidiary of another corporation in a transaction in which
the shareholders of the parent of the Company and their proportionate interests
therein immediately after the transaction are not substantially identical to
the shareholders of the Company and their proportionate interests therein
immediately prior to the transaction); or a transaction in which another
corporation becomes the owner of 50% or more of the total combined voting power
of all classes of stock of the Company shall cause this Incentive Option to
terminate, but Optionee shall, in any event, have the right, immediately prior
to such dissolution, liquidation, merger, consolidation, or transaction, to
exercise this Incentive Option, to the extent not theretofore exercised,
without regard to the determination as to the periods and installments of
exercisability made pursuant to Section 3 hereof if (and only if) this
Incentive Option has not at that time expired or been terminated.  Such
acceleration of exercisability shall not apply to this Incentive Option if any
surviving or acquiring corporation agrees to assume this Incentive Option in
connection with the merger, consolidation, or transaction.

       10.     Committee Authority.  Any questions concerning the
interpretation of this Agreement and any controversy which may arise under this
Agreement shall be determined by the Committee in its sole discretion.

       11.     Transferability.  This Incentive Option is not transferable
otherwise than by will and the laws of descent and distribution and during the
lifetime of Optionee is exercisable only by Optionee or, if Optionee is legally
incompetent, by Optionee's legal representative.

       12.     Employment.  Nothing in this Agreement confers upon Optionee any
right to continue in the employ of the Company or any Affiliate, nor shall this
Agreement interfere in any manner with the right of the Company or any
Affiliate to terminate the employment of Optionee with or without cause at any
time.

       13.     Incentive Option Subject to Plan.  By execution of this
Agreement, Optionee agrees that this Incentive Option and the shares of Common
Stock to be received upon exercise hereof shall be governed by and subject to
all applicable provisions of the Plan.

       14.     Construction.  This Agreement is governed by, and shall be
construed and enforced in accordance with, the laws of the State of Texas.
Words of any gender used in this Agreement shall be construed to include any
other gender, unless the context requires otherwise.  The headings of the
various sections of this Agreement are intended for convenience of reference
only and shall not be used in construing the terms hereof.





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       IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first above written.

                                        TOREADOR ROYALTY CORPORATION
                                        
                                        
                                        
                                        By: /s/ JOHN MARK MCLAUGHLIN
                                            -----------------------------------
                                            John Mark McLaughlin
                                            Chairman of the Board and President
                                        
                                        
                                                                               
                                        /s/ EDWARD C. MARHANKA
                                        ---------------------------------------
                                        Edward C. Marhanka, Optionee






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