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                                                                    EXHIBIT 10.1


                                                            FINAL EXECUTION COPY

                                   AGREEMENT


         This AGREEMENT, dated June 25, 1998 (the "Agreement"), by and among
Mr.  G. Thomas Graves, III and Mr. William I. Lee, individuals whose business
address is 4809 Cole Avenue, Suite 107, Dallas, Texas 75205, Lee Global Energy
Fund, L.P., a Texas limited partnership ("Lee Global"), Gralee Capital
Corporation, a Texas corporation, ("Gralee Capital"), and Gralee Partners,
L.P., a Texas limited partnership ("Gralee Partners" and, together with Mr.
Graves, Mr. Lee, Lee Global and Gralee Capital, collectively referred to as the
"Gralee Persons"); Mr. Peter Lawrence Falb and Mr. Edward Nathan Dane,
individuals whose business address is 33 Broad Street, Boston, Massachusetts
02109, Firethorn I Limited Partnership, a Massachusetts limited partnership
("Firethorn"), The Hilary Bell Falb 1983 Trust (the "HBF Trust"), the Alison
Forslund Falb 1985 Trust (the "AFF Trust"), the Forslund Irrevocable Trust (the
"Forslund Trust"), and Dane, Falb, Stone & Co., Inc., a Massachusetts
corporation ("Dane Falb" and, together with Mr. Falb, Mr. Dane, the HBF Trust,
the AFF Trust and Firethorn, collectively referred to as the "Dane Falb
Persons"); Toreador Royalty Corporation, a Delaware corporation (the
"Company"); and the other persons identified on Exhibit A, (together with the
Company, collectively referred to as the "Company Related Parties").  The
Gralee Persons, the Dane Falb Persons and the Company Related Parties are
sometimes collectively referred to herein as the "Parties."

                              W I T N E S S E T H:

         WHEREAS, the Gralee Persons and the Dane Falb Persons have indicated
to the Company's Board of Directors as constituted on the date hereof (the
"Current Board") that they desire one or more of their respective designees to
be nominated for election to the Board of Directors of the Company (the
"Board") at the 1998 annual meeting of stockholders of the Company at which the
election of directors is to be considered (the "1998 Annual Meeting");

         WHEREAS, the Gralee Persons and the Dane Falb Persons have also
indicated to the Current Board their intention to solicit proxies for the
election of their respective designees and in opposition to the slate of
nominees of the Current Board (the "Proxy Contest");

         WHEREAS, each of the Gralee Persons and the Dane Falb Persons has
determined that its and the Company's best interests would be served by (i) not
engaging in the Proxy Contest, and (ii) the receipt of the other rights and
benefits set forth herein;

         WHEREAS, the Company has determined that the best interests of the
Company and its stockholders would be served by (i) not engaging in the Proxy
Contest and avoiding any further proxy contest with any Gralee Person or Dane
Falb Person until December 31, 2000, and (ii) the receipt of other rights and
benefits set forth herein;
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         WHEREAS, the Gralee Persons, the Dane Falb Persons and certain other
stockholders of the Company have entered into a Stockholder Voting Agreement
regarding nominations to the Board (the "Stockholder Voting Agreement"); and

         WHEREAS, the Board has heretofore adopted the resolutions attached
hereto as Exhibit B (the "Resolutions");

         NOW, THEREFORE, in consideration of the foregoing and the mutual
agreements set forth herein the Parties hereby agree as follows:

         1.      Definitions of Certain Agreement Terms.  For purposes of this
Agreement, the terms hereinafter set forth shall have the following definitions
unless otherwise specifically stated:

         "Common Stock" means the common stock, par value $.15625 per share, of
the Company.

         "Company Securities" means any securities issued by the Company,
including the Common Stock and any other debt or equity securities of the
Company that are outstanding as of the date hereof or may hereafter be issued.

         "Person" means any individual, corporation, association, general or
limited partnership, limited liability company, limited liability partnership,
joint venture, trust, estate, other entity or organization or group.

         2.      Date of 1998 Annual Meeting.  The Company will hold its 1998
Annual Meeting on July 23, 1998.  The Company agrees that it will not postpone
the annual meeting, or adjourn the annual meeting, except to the extent
necessary to finalize the results of the meeting.

         3.      Press Release.  Promptly after execution and delivery of this
Agreement, the Company shall issue the press release in the form of Exhibit C
attached hereto.  No Party to this Agreement nor any of their respective
affiliates, associates or representatives shall issue any other press release
or other publicly available document that is inconsistent with, or is otherwise
contrary to, the statements in such press release.  Each of the Parties agrees
that until December 31, 2000, neither such Party nor such Party's affiliates
shall make any statement or take any action (other than a sale of Company
Securities) that is critical or disparaging of the other Parties or the
management of the Company.

         4.      SEC Filings.  All Company filings with the Securities and
Exchange Commission will be submitted to each member of the Board elected at
the 1998 Annual Meeting, the 1999 annual meeting at which the election of
directors is to be considered, and the 2000 annual meeting of stockholders at
which the election of directors is to be considered, prior to the filing
thereof by the Company.

         5.      Actions prior to 1998 Annual Meeting.  Prior to the 1998
Annual Meeting, the Company Related Parties agree that such parties will not
take any action to (i) amend the



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Company's Certificate of Incorporation, as amended, or Bylaws, as amended, or
(ii) amend, change, alter or repeal the Resolutions.

         6.      Representations and Warranties of the Gralee Persons.  The
Gralee Persons jointly and severally represent and warrant to the Company
Related Parties as follows:

                 (a)      Each Gralee Person has the power and authority to
execute, deliver and carry out the terms and provisions of this Agreement and
to consummate the transactions contemplated hereby, and has taken all necessary
action to authorize the execution, delivery and performance of this Agreement.

                 (b)      This Agreement has been duly and validly authorized,
executed and delivered by each Gralee Person, and constitutes a valid and
binding obligation of each Gralee Person, enforceable in accordance with its
terms, subject to applicable bankruptcy, reorganization, insolvency or other
laws affecting the enforcement of creditors' rights generally.

         7.      Representations and Warranties of the Dane Falb Persons.  The
Dane Falb Persons jointly and severally represent and warrant to the Company
Related Parties as follows:

                 (a)      Each Dane Falb Person has the power and authority to
execute, deliver and carry out the terms and provisions of this Agreement and
to consummate the transactions contemplated hereby, and has taken all necessary
action to authorize the execution, delivery and performance of this Agreement.

                 (b)      This Agreement has been duly and validly authorized,
executed and delivered by each Dane Falb Person, and constitutes a valid and
binding obligation of each Dane Falb Person, enforceable in accordance with its
terms, subject to applicable bankruptcy, reorganization, insolvency or other
laws affecting the enforcement of creditors' rights generally.

         8.      Representations and Warranties of the Company.  The Company
Related Parties hereby represent and warrant to the Gralee Persons and the Dane
Falb Persons as follows:

                 (a)      The Company has the corporate power and authority to
execute, deliver and carry out the terms and provisions of this Agreement and
to consummate the transactions contemplated hereby, and has taken all necessary
action to authorize the execution, delivery and performance of this Agreement.

                 (b)      This Agreement has been duly and validly authorized,
executed and delivered by the Company and constitutes a valid and binding
agreement of the Company, enforceable in accordance with its terms, subject to
applicable bankruptcy, reorganization, insolvency or other laws affecting the
enforcement of creditors' rights generally.





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         9.      Release of Claims.

                 (a)      Each of the Parties (a "Releasing Party"), on behalf
of itself and all of its affiliates, successors and assigns, jointly and
severally releases and discharges each of the other Parties, together with its
present and former affiliates, officers, directors, employees, agents,
attorneys, successors and assigns (each, a "Released Person"), from any and all
claims, losses, demands, liabilities, obligations, indemnities, charges and
causes of action (collectively, "Claims") of any and all nature whatsoever
whether based on tort, contract, statute, equitable theory of recovery, or
otherwise, whether now known, unknown, unforeseen, or unsuspected, which the
Releasing Party may now or in the future have jointly or severally against the
Released Persons, individually or in combination with others, from the
beginning of time until the effective date of this Agreement and which arise
out of any Released Person's activities to the date hereof with respect to, or
are in any way connected with, the Company, including without limitation the
issuance, acquisition, ownership, holding, or voting of any Company Securities,
the management or conduct of the Company's affairs by any Released Person
acting as or entitled to nominate a member of the Board.

                 (b)      With respect to the releases set forth above, each
person or entity granting or receiving such a release (i) agrees that such
releases do not preclude any Party hereto from seeking to enforce any
undertaking or promise contained in the Settlement Documents (as defined below)
or from seeking redress for the breaches of any representation or warranty
contained in the Settlement Documents; (ii) agrees not to directly or
indirectly encourage or pursue with or before any federal, state or other
governmental agency, authority or court any claim or complaint against any of
the Released Persons, including but not limited to any such claim or complaint
relating to matters covered by the Settlement Documents (other than the
enforcement of any undertaking or promise contained therein); and (iii) agrees
not to challenge, and shall use its best efforts to cause each of its
affiliates, associates and representatives not to challenge, the validity of
any provisions of the Settlement Documents.

                 (c)      Except as may be otherwise required by law, the
Gralee Persons and the Dane Falb Persons will not encourage or cooperate with
plaintiffs in any subsequently initiated derivative, class action or
stockholder litigation related to the Company Related Parties.  In the event
that any part of this Agreement is temporarily, preliminarily or permanently
enjoined or restrained by a court of competent jurisdiction, the Parties hereto
shall use their commercially reasonable efforts to cause any such injunction or
restraining order to be vacated or dissolved or otherwise declared or
determined to be of no further force or effect.

         10.     Insurance Coverage.  For six years after the date of this
Agreement, the Company shall be required to maintain or obtain officers' and
directors' liability insurance covering the persons who are as of the date of
this Agreement covered by the Company's officers and directors liability
insurance policy in such persons' capacities as officers or directors of the
Company with respect to matters existing or occurring at or prior to the date
of this Agreement on terms not less favorable than those in effect on the date
hereof in terms of coverage and amounts; provided, however, that if the
aggregate annual premiums for such insurance at any time during such period
shall exceed 200% of the per annum rate of premium currently paid by the
Company for such insurance on the date of this Agreement, the Company shall
provide the maximum coverage that shall then be available at an annual premium
equal to 200% of such rate.





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         11.     Miscellaneous.

                 (a)      No Duress, etc..  The Parties hereto agree that this
Agreement is entered into without duress, in good faith and for sufficient
consideration, and that it is fair, just and reasonable to all Parties.

                 (b)      Full Knowledge; Independent Advice, etc..  All
Parties have received or have had made available to them all financial and
other information they or their counsel considered necessary to an informed
judgment concerning this Agreement.  Each Party has received independent legal
advice, has conducted such investigation as he or his counsel thought
appropriate, and has consulted with such other independent advisors as each of
them and their counsel deemed appropriate, regarding this Agreement and their
rights and asserted rights in connection therewith.  None of the Parties is
relying upon any representations or statements made by any other Party, or such
other Party's employees, agents, representatives or attorneys, regarding this
Agreement or its preparation except to the extent such representations are
expressly set forth herein.

                 (c)      Reasonable Efforts.  All Parties hereto agree to
exercise all commercially reasonable efforts and to take all commercially
reasonable steps necessary to effectuate the settlement set forth in this
Agreement.

                 (d)      Successors and Assigns.  All the terms and provisions
of this Agreement shall inure to the benefit of and shall be enforceable by the
Parties hereto and their respective heirs, successors and assigns, and upon any
corporation or other entity into or with which any Party hereto may merge,
combine or consolidate (provided that the Party is the survivor in such merger,
combination or consolidation); provided, however, that no Party may assign its
rights under this Agreement without the other Parties' written consent.

                 (e)      Survival of Representations.  All representations,
warranties and agreements made by the Gralee Persons, the Dane Falb Persons and
the Company Related Parties in this Agreement or pursuant hereto shall survive
the date hereof.

                 (f)      Entire Agreement; Amendments.  This Agreement,
including the documents attached hereto as Exhibits to be executed and
delivered concurrently with this Agreement, the Stockholder Voting Agreement,
and such additional instruments as may be concurrently executed and delivered
pursuant to this Agreement (collectively, the "Settlement Documents"),
constitutes the entire understanding of the Parties with respect to its subject
matter.  There are no restrictions, agreements, promises, representations,
warranties, covenants or undertakings other than those expressly set forth in
the Settlement Documents.  This Agreement may be amended only by a written
instrument duly executed by the Parties or their respective successors or
assigns.

                 (g)      Headings.  The section headings contained in this
Agreement are for reference purposes only and shall not effect in any way the
meaning or interpretation of this Agreement.





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                 (h)      Notices.  All notices, requests, claims, demands and
other communications hereunder shall be in writing and shall be given (and
shall be deemed to have been duly given if so given) by hand delivery,
facsimile or by mail (registered or certified, postage prepaid, return receipt
requested) to the respective Parties as follows:

                 If to the Company Related Parties:

                          Toreador Royalty Corporation
                          8117 Preston Road
                          Suite 530
                          Dallas, Texas 75225
                          Fax No: (214) 369-3183

                 with a copy to:

                          Thompson & Knight, P.C.
                          1700 Pacific Avenue
                          Suite 3300
                          Dallas, Texas 75201
                          Attention:  Mr. Joe Dannenmaier
                          Fax No: (214) 969-1751

                 If to the Gralee Persons:

                          Gralee Capital Corp.
                          4809 Cole Avenue
                          Suite 107
                          Dallas, Texas 75205
                          Attention:  Mr. G. Thomas Graves III
                          Fax No: (214) 521-8834

                 with a copy to:

                          Haynes & Boone, LLP
                          901 Main Street
                          Suite 3100
                          Dallas, Texas 75202
                          Attention:  Ms. Janice V. Sharry
                          Fax No: (214) 651-5940





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<PAGE>   7
                 If to the Dane Falb Persons:

                          Dane, Falb, Stone & Co., Inc.
                          33 Broad Street
                          Boston, Massachusetts 02109
                          Attention: Mr. Peter Falb
                          Fax No: (617) 742-2304

                 with a copy to:

                          Richards, Layton & Finger
                          920 King Street
                          Wilmington, Delaware  19801
                          Attn: Mr. Jesse Finkelstein
                          Fax No.: (302) 658-6548

                 and:

                          Choate, Hall & Stewart
                          Exchange Place
                          53 State Street
                          Boston, MA 02109
                          Attn: Ms. Carla Herwitz
                          Fax No.: (617) 248-4000

or to such other address as the person to whom notice is given may have
previously furnished to the others in writing in the manner set forth above.

                 (i)      Governing Law.  This Agreement shall be governed by
and construed and enforced in accordance with the laws of the State of
Delaware, without reference to the conflict of laws principles thereof.

                 (j)      Waiver.  Any waiver by any Party of a breach of any
provision of this Agreement shall not operate as or be construed to be a waiver
of any other breach of such provision or of any breach of any other provision
of this Agreement.  The failure of a Party to insist upon strict adherence to
any term of this Agreement on one or more occasions shall not be considered a
waiver or deprive that Party of the right thereafter to insist upon strict
adherence to that term or any other term of this Agreement.

                 (k)      Specific Performance.  Each of the Parties
acknowledges and agrees that irreparable harm would occur if any provision of
this Agreement were not performed in accordance with the terms thereof, or were
otherwise breached, and that such harm could not be remedied by an award of
damages.  Accordingly, the Parties hereto agree that any non-breaching Party
shall be entitled to an injunction to prevent breaches of this Agreement and to
enforce specifically the terms and provisions hereof.





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                 (l)      Counterparts.  This Agreement may be executed in
counterparts, each of which shall be an original, but each of which together
shall constitute one and the same Agreement.





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         IN WITNESS WHEREOF, and intending to be legally bound hereby, each of
the undersigned Parties has executed or caused this Agreement to be executed on
the date first above written.

                                  LEE GLOBAL ENERGY FUND, L.P.

                                  By:   Gralee Partners, L.P., its general
                                        partner

                                        By: Gralee Capital Corp., its general
                                            partner

                                            By: /s/ G.T. Graves, III    
                                               ---------------------------------
                                            Name:   G.T. Graves, III    
                                                 -------------------------------
                                            Title:  President
                                                  ------------------------------
                                            

                                  GRALEE CAPITAL CORPORATION


                                  By:    /s/ G.T. Graves, III                  
                                     -------------------------------------------
                                     Name:   G.T. Graves, III                  
                                          --------------------------------------
                                     Title:  President                         
                                           -------------------------------------

                                  GRALEE PARTNERS, L.P.

                                  By:   Gralee Capital Corp., its general
                                        partner


                                        By:     /s/ G.T. Graves, III        
                                           -------------------------------------
                                            Name:   G.T. Graves, III      
                                                 -------------------------------
                                            Title:  President 
                                                  ------------------------------



                                  /s/ G. Thomas Graves, III                     
                                  ----------------------------------------------
                                  G. Thomas Graves, III


                                  /s/ Peter Lawrence Falb                       
                                  ----------------------------------------------
                                  Peter Lawrence Falb


                                  /s/ Edward Nathan Dane                        
                                  ----------------------------------------------
                                  Edward Nathan Dane





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                                  FIRETHORN I LIMITED PARTNERSHIP

                                  By:   Firethorn II Limited Partnership, its
                                        general partner

                                  By:   Eaglerock Corporation, its general
                                        partner


                                        By:  /s/ Peter L. Falb
                                           -------------------------------------
                                            Name:   Peter L. Falb 
                                                 -------------------------------
                                            Title:  Treasurer
                                                  ------------------------------


                                  THE HILARY BELL FALB 1983 TRUST


                                  By:   /s/ Karen F. Falb, Trustee              
                                        ----------------------------------------
                                            Karen F. Falb, Trustee


                                  THE ALISON FORSLUND FALB 1985 TRUST


                                  By:   /s/ Karen F. Falb, Trustee              
                                        ----------------------------------------
                                            Karen F. Falb, Trustee



                                  DANE, FALB, STONE & CO., INC.



                                  By:    /s/ Peter L. Falb
                                     -------------------------------------------
                                     Name:   Peter L. Falb
                                          --------------------------------------
                                     Title:  Principal
                                           -------------------------------------


                                  TOREADOR ROYALTY CORPORATION



                                  By:    /s/ John Mark McLaughlin
                                     -------------------------------------------
                                     Name:   John Mark Mclaughlin
                                          --------------------------------------
                                     Title:  Chairman
                                           -------------------------------------





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                                  /s/ John Mark McLaughlin                      
                                  ----------------------------------------------
                                  John Mark McLaughlin


                                  /s/ John V. Ballard                           
                                  ----------------------------------------------
                                  John V. Ballard


                                  /s/ J. W. Bullion                             
                                  ----------------------------------------------
                                  J. W. Bullion


                                  /s/ Thomas P. Kellogg, Jr.                    
                                  ----------------------------------------------
                                  Thomas P. Kellogg, Jr.


                                  /s/ Peter R. Vig                              
                                  ----------------------------------------------
                                  Peter R. Vig


                                  /s/ Jack L. Woods                             
                                  ----------------------------------------------
                                  Jack L. Woods





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                                  THE FORSLUND IRREVOCABLE TRUST


                                  By:   /s/ Karen F. Falb, Trustee          
                                        ------------------------------------
                                            Karen F. Falb, Trustee






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