UNOCAL CORP
SC 13D, 1999-12-23
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>

                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549
                                ______________

                                 SCHEDULE 13D

                   Under the Securities Exchange Act of 1934

                            TITAN EXPLORATION, INC.
- --------------------------------------------------------------------------------
                               (Name of Issuer)

                                 Common Stock
- --------------------------------------------------------------------------------
                        (Title of Class of Securities)

                                   888289105
- --------------------------------------------------------------------------------
                                (CUSIP Number)

                           Dennis P. R. Codon, Esq.
            Vice President, Chief Legal Officer and General Counsel
                              UNOCAL CORPORATION
                       2141 Rosecrans Avenue, Suite 4000
                         El Segundo, California 90245
                                (310) 726-7600
- --------------------------------------------------------------------------------
                 (Name, Address and Telephone Number of Person
               Authorized to Receive Notices and Communications)

                               December 13, 1999
- --------------------------------------------------------------------------------
                     (Date of Event which Requires Filing
                              of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(b)(3) or (4), check the following box: [_]

                       (Continued on following page(s))
                               Page 1 of 6 Pages
<PAGE>

- --------------------------------------------------------------------------------
1.   NAME OF REPORTING PERSON
     S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

     Unocal Corporation., I.R.S. No.: 95-3825062

- --------------------------------------------------------------------------------
2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                   (a) [_]
                                                                         (b) [X]
     N/A
- --------------------------------------------------------------------------------
3    SEC USE ONLY

- --------------------------------------------------------------------------------
4    SOURCE OF FUNDS*

     00
- --------------------------------------------------------------------------------
5    CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS
     2(d) OR 2(e)                                                            [_]

- --------------------------------------------------------------------------------
6    CITIZENSHIP OR PLACE OF ORGANIZATION
     Delaware

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

NUMBER OF           7       SOLE VOTING POWER
SHARES                      -0-
BENEFICIALLY        -----------------------------------------------------------
OWNED               8       SHARED VOTING POWER
BY EACH                     4,389,690 shares of Common Stock
REPORTING           -----------------------------------------------------------
PERSON              9       SOLE DISPOSITIVE POWER
WITH:                       -0-
                    -----------------------------------------------------------
                    10       SHARED DISPOSITIVE POWER
                             -0-
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     Same as 7 above.
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
                                                                             [_]
     N/A
- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     10.9% of Titan Exploration Inc.'s outstanding Common Stock.
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     CO
- --------------------------------------------------------------------------------

<PAGE>

- --------------------------------------------------------------------------------
1.   NAME OF REPORTING PERSON
     S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

     Union Oil Company of California, I.R.S. No.: 95-1315450

- --------------------------------------------------------------------------------
2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                   (a) [_]
                                                                         (b) [X]
     N/A
- --------------------------------------------------------------------------------
3    SEC USE ONLY

- --------------------------------------------------------------------------------
4    SOURCE OF FUNDS*

     00
- --------------------------------------------------------------------------------
5    CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS
     2(d) OR 2(e)                                                            [X]

- --------------------------------------------------------------------------------
6    CITIZENSHIP OR PLACE OF ORGANIZATION
     Delaware

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

NUMBER OF           7       SOLE VOTING POWER
SHARES                      -0-
BENEFICIALLY        -----------------------------------------------------------
OWNED               8       SHARED VOTING POWER
BY EACH                     4,389,690 shares of Common Stock
REPORTING           -----------------------------------------------------------
PERSON              9       SOLE DISPOSITIVE POWER
WITH:                       -0-
                    -----------------------------------------------------------
                    10       SHARED DISPOSITIVE POWER
                             -0-
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     Same as 7 above.
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
                                                                             [_]
     N/A
- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     10.9% of Titan Exploration Inc.'s outstanding Common Stock.
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     CO
- --------------------------------------------------------------------------------

                               Page 3 of 6 Pages
<PAGE>

Item 1.  Security and Issuer:
- -------  -------------------

     This statement relates to the Common Stock, par value $0.01 per share (the
"Company Common Stock"), of Titan Exploration, Inc., a Delaware corporation (the
"Company"), whose principal executive offices are located at 500 West Texas,
Suite 500, Midland, Texas 79701.  This statement is being filed because Union
Oil Company of California, a wholly-owned subsidiary of Unocal Corporation, has
entered into a Voting Agreement dated December 13, 1999 (the "Voting Agreement")
with respect to certain shares of Company Common Stock in connection with the
Merger (as defined below).

Item 2.  Identity and Background:
- -------  -----------------------

     This statement is being filed jointly by Unocal Corporation, a Delaware
corporation ("Unocal"), and Union Oil Company of California, a California
corporation ("Union Oil").  Unocal conducts substantially all of its operations
through Union Oil and subsidiaries of Union Oil.  Unocal is one of the world's
largest independent oil and gas exploration and production companies, with major
oil and gas exploration and production activities in Asia and the United States
Gulf of Mexico.  Unocal is also a leading producer of geothermal energy; a
provider of electrical power; and a manufacturer and marketer of nitrogen-based
fertilizers, petroleum coke, graphites and specialty minerals. Other activities
include project development, ownership in proprietary and common carrier
pipelines and the marketing and trading of hydrocarbon commodities.

     Unocal's and Union Oil's principal executive offices are located at 2141
Rosecrans Avenue, Suite 4000, El Segundo, California 90245 and their telephone
number at that address is (310) 726-7600. Schedule I attached hereto sets forth
certain additional information with respect to each director and each executive
officer of Unocal and Union Oil.  The filing of this statement on Schedule 13D
shall not be construed as an admission that Unocal, Union Oil or any person
listed on Schedule I hereto is, for the purposes of Section 13(d) or 13(g) of
the Securities Exchange Act of 1934, the beneficial owner of any securities
covered by this statement.

     During the past five years, Union Oil has been convicted of a number of
misdemeanor criminal violations.  These cases usually involved minor violations
of state or local environmental laws.  However, two of these misdemeanor
convictions were significant.  In 1994, Union Oil plead no contest to a number
of misdemeanor violations of California statutes which prohibit the discharge of
petroleum into the environment.  The case was filed in Municipal Court for the
County of San Luis Obispo, California.  Fines and civil penalties in excess of
$1,000,000 were paid to resolve the violations.  On July 19, 1995, Union Oil
plead no contest to a number of misdemeanor violations of California state laws
which prohibit the unlawful discharge of airborne contaminants into the
environment.  The case was filed in Municipal Court for the County of Contra
Costa, California.  A fine of $951,000 was paid to resolve the violations.  In
addition, civil penalties in the amount of $2,050,000 were paid in a companion
civil case.

     Except as provided above, during the past five years, neither Unocal nor
Union Oil nor any of the persons referred to in Schedule I has been convicted in
a criminal proceeding (excluding traffic violations and similar misdemeanors).

     To the best knowledge of each of Unocal and Union Oil, neither Union Oil
nor Unocal nor any of the persons referred to in Schedule I has been the subject
of a civil judgment, decree or final order enjoining future violations of, or
prohibiting or mandating activities subject to, federal or state securities laws
or finding any violation with respect to such laws, during the last five years.

                               Page 3 of 6 Pages
<PAGE>

     All persons named in Schedule I are citizens of the United States.

Item 3.  Source and Amount of Funds or Other Consideration:
- -------  -------------------------------------------------

     On December 13, 1999, Union Oil and Jack D. Hightower, Chief Executive
Officer and President of the Company ("Hightower") entered into the Voting
Agreement simultaneously with the execution by Union Oil, the Company, Titan
Resources Holdings, Inc., a wholly-owned subsidiary of Union Oil (renamed Pure
Energy Resources, Inc. and referred to herein as "Pure"), and TRH, Inc., a
wholly-owned subsidiary of Pure ("Merger Sub") of an Agreement and Plan of
Merger (the "Merger Agreement") providing for the Merger of Merger Sub with and
into the Company, as more fully described in Item 4.  Hightower entered into the
Voting Agreement in order to induce Union Oil to enter into the Merger Agreement
and related agreements, and no separate consideration in cash or property was
paid by Union Oil to Hightower in consideration of the Voting Agreement.

Item 4.  Purpose of Transaction:
- -------  ----------------------

     This filing refers to a Voting Agreement dated December 13, 1999 (the
"Voting Agreement") between Union Oil and Hightower, pursuant to which, among
other things, Hightower has agreed, subject to certain exceptions, to vote the
4,389,690 shares of Company Common Stock of which he is the record owner in
favor of the Merger (as defined below) at a meeting of stockholders of the
Company (the "Special Meeting") that will be called for the purpose of voting on
the Merger and related matters and to vote all of such shares of Company Common
Stock against any proposed business combination that may interfere with or be
inconsistent with the Merger.  In addition, Hightower has agreed that he will
not sell, transfer or otherwise dispose of any of the shares of Company Common
Stock covered by the Voting Agreement to any person prior to the termination of
the Merger Agreement, unless such person agrees in writing to be bound by the
terms of the Voting Agreement.  The foregoing summary of the Voting Agreement is
qualified in its entirety by reference to a copy of the Voting Agreement
included as Exhibit A to this Schedule 13D and incorporated herein in its
entirety by reference.

     The Merger Agreement provides that, on the Closing Date immediately
following the Closing (as such terms are defined in the Merger Agreement),
Merger Sub will merge with and into the Company, and the Company will become a
wholly owned subsidiary of Pure (such events constituting the "Merger").  Once
the Merger is consummated, Merger Sub will cease to exist as a corporation and
all of the business, assets, liabilities and obligations of Merger Sub will be
merged into the Company with the Company remaining as the surviving corporation
(the "Surviving Corporation") and a wholly-owned subsidiary of Pure.  Following
the Merger, the directors and officers of the Surviving Corporation will be the
persons listed in Schedule 1.6 of the Merger Agreement, which has been filed as
Exhibit B to this Schedule 13D.  As a result of the Merger, each outstanding
share of the Company Common Stock, other than shares owned by the Company or any
wholly owned subsidiary of the Company, will be converted into the right to
receive .4302314 of a share (the "Exchange Ratio") of Common Stock, par value
$0.01 per share, of Pure ("Pure Common Stock"). At the effective time of the
Merger, each outstanding option to purchase Company Common Stock under the
Company's stock option plans (each a "Company Common Stock Option") will be
assumed by Pure (each an "Assumed Option") and will become an option to purchase
that number of shares of Pure Common Stock equal (subject to rounding) to the
number of shares of Company Common Stock that was subject to such option
immediately prior to the Merger, multiplied by the Exchange Ratio.  The exercise
price of each Assumed Option will be equal to the quotient determined by
dividing the exercise price per share of Company Common Stock at which such
Company Common Stock Option was exercisable immediately prior to the effective
time of the Merger by the Exchange Ratio, rounded up to the nearest whole cent.

                               Page 4 of 6 Pages
<PAGE>

     On the Closing Date Union Oil will transfer to Pure substantially all of
its oil and gas exploration and production assets in the Permian Basin and San
Juan Basin areas of Texas, New Mexico and Colorado in return for Pure Common
Stock.  Upon consummation of the Merger immediately following the Closing, Union
Oil will own 32,709,067 shares of Pure Common Stock, representing approximately
65% of the outstanding Pure Common Stock, and the former stockholders of the
Company will own the remaining shares representing approximately 35% of the
outstanding Pure Common Stock.

     Simultaneously with the execution of the Merger Agreement, Union Oil, Pure
and the Company entered into a Business Opportunities Agreement pursuant to
which, among other things, Pure and the Company agreed that, following the
Merger, Pure and its subsidiaries will not, without the consent of Union Oil,
engage in any businesses other than the oil and gas exploration and production
business and will not pursue any business opportunity that involves any direct
or indirect ownership interest in properties located outside designated areas of
Arkansas, Colorado, Kansas, New Mexico, Oklahoma and onshore Texas, including
the Permian Basin and San Juan Basin.  Pursuant to the Merger Agreement, the
Company agreed that it will not take any action prior to the Closing that would
be prohibited by the Business Opportunities Agreement following the Closing.

     The foregoing summaries of the Merger Agreement and the Business
Opportunities Agreement are qualified in their entirety by reference to copies
of the Merger Agreement and the Business Opportunities Agreement included as
Exhibits C and D to this Schedule 13D and incorporated herein in their entirety
by reference.

Item 5.  Interest in Securities of the Issuer:
- -------  ------------------------------------

     Pursuant to the Merger Agreement, the Company represented to Union Oil that
as of December 13, 1999, there were 40,189,843 outstanding shares of Company
Common Stock.  As a result of executing the Voting Agreement, Unocal and Union
Oil may be deemed to beneficially own and have shared voting power with respect
to the 4,389,690 shares of Company Common Stock covered thereby, which, based on
such representation, constitutes approximately 10.9% of the total issued and
outstanding shares of Company Common Stock as of December 13, 1999.

     Other than the transactions described herein, none of Unocal, Union Oil or
to the knowledge of Unocal or Union Oil, any person listed on Schedule I has
effected any transactions in shares of Company Common Stock during the preceding
sixty days.

Item 6.  Contracts, Arrangements, Understandings or Relationships With Respect
- -------  ---------------------------------------------------------------------
          to Securities of the Issuer:
          ---------------------------

     Other than the foregoing, the Merger Agreement, the Voting Agreement and
the Business Opportunities Agreement, to the best knowledge of Unocal and Union
Oil, there are no contracts, arrangements, understandings or relationships
(legal or otherwise) among the persons named in Item 2 and between such persons
and any person with respect to any securities of the Company, including but not
limited to transfer or voting of any of the securities, finder's fees, joint
ventures, loan or option arrangement, puts or calls, guarantees of profits,
division of profits or loss, or the giving or withholding of proxies.

Item 7.  Material to be Filed as Exhibits:
- -------  --------------------------------

          Exhibit 2.1: Voting Agreement between Union Oil and Jack D. Hightower
dated December 13, 1999.

                               Page 5 of 6 Pages
<PAGE>

          Exhibit 2.2:  Directors and Officers of the Surviving Corporation
following the Merger (Schedule 1.6 to Agreement and Plan of Merger).

          Exhibit 2.3:  Agreement and Plan of Merger among Union Oil, the
Company, Pure, and Merger Sub dated December 13, 1999 (with exhibits and
schedules omitted).

          Exhibit 2.4:  Business Opportunities Agreement among Union Oil, the
Company, Merger Sub and Pure dated December 13, 1999.

          Exhibit 99.1: Joint Filing Agreement.

     After reasonable inquiry and to the best knowledge and belief of the
undersigned, the undersigned certify that the information set forth in this
statement is true, complete and correct.

Date:  December 23, 1999            UNOCAL CORPORATION


                                    By: /s/Joseph A. Householder
                                       -----------------------------------
                                      Name:   Joseph A. Householder
                                      Title:  Vice President, Corporate
                                              Development, and Assistant
                                              Chief Financial Officer


                                    UNION OIL COMPANY OF CALIFORNIA


                                    By: /s/ Joseph A. Householder
                                       -----------------------------------
                                      Name:   Joseph A. Householder
                                      Title:  Vice President, Corporate
                                              Development, and Assistant
                                              Chief Financial Officer

                               Page 6 of 6 Pages
<PAGE>

                                                                      Schedule I

                       DIRECTORS AND EXECUTIVE OFFICERS
                              UNOCAL CORPORATION

<TABLE>
<CAPTION>
Name and Business Address*          Citizenship        Position and Occupation
<S>                                 <C>                <C>
Roger C. Beach                      U.S.A.             Director, Chairman of the Board of Directors
                                                       and Chief Executive Officer, Unocal
                                                       Corporation

John F. Imle, Jr.                   U.S.A.             Director, Vice Chairman of the Board of
                                                       Directors, Unocal Corporation

John W. Amerman                     U.S.A.             Director, Unocal Corporation, Former Chairman
2101 Rosecrans Ave., Suite 6280                        of the Board and Chief Executive Officer,
El Segundo, CA 90245                                   Mattel, Inc.

John W. Creighton, Jr.              U.S.A.             Director, Unocal Corporation, Former
Madrona Investment Group                               President and Chief Executive Officer,
1000 Second Avenue, Suite 3700                         Weyerhaeuser Company
Seattle, WA 98104

James W. Crownover                  U.S.A.             Director, Unocal Corporation, Former
C/O McKinsey & Company, Inc.                           Director, McKinsey & Company, Inc.
909 Fannin, Suite 3675
Houston, Texas 77010

Frank C. Herringer                  U.S.A.             Director, Unocal Corporation, Chairman and
Transamerica Corporation                               Chief Executive Officer, Transamerica
600 Montgomery Street                                  Corporation
San Francisco, CA 94111

Donald B. Rice                      U.S.A.             Director, Unocal Corporation, President and
UroGenesys, Inc.                                       Chief Executive Officer, UroGenesys, Inc.
1701 Colorado Avenue
Santa Monica, CA 90404

Kevin W. Sharer                     U.S.A.             Director, Unocal Corporation, President and
Amgen Inc.                                             Chief Operating Officer, Amgen Inc.
One Amgen Center
Thousand Oaks, CA 91320-1789
</TABLE>
<PAGE>

<TABLE>
<S>                                 <C>                <C>
Marina v.N. Whitman                 U.S.A.             Director, Unocal Corporation, Professor of
Institute of Public Policy Studies                     Business Administration and Public Policy,
University of Michigan                                 University of Michigan
411 Lorch Hall
Ann Arbor, MI 48109-1220

Joe D. Cecil                        U.S.A.             Vice President and Comptroller, Unocal
                                                       Corporation

Dennis P.R. Codon                   U.S.A.             Vice President, Chief Legal Officer and
                                                       General Counsel, Unocal Corporation

Joseph A. Householder               U.S.A.             Vice President, Corporate Development, and
                                                       Assistant Chief Financial Officer, Unocal
                                                       Corporation

Timothy H. Ling                     U.S.A.             Executive Vice President, North American
                                                       Energy Operations, and Chief Financial
                                                       Officer, Unocal Corporation

L.E. (Ed) Scott                     U.S.A.             Group Vice President, Diversified Business
376 South Valencia Avenue                              Group, Unocal Corporation
Brea, CA 92823

Charles R. Williamson               U.S.A.             Executive Vice President, International
                                                       Energy Operations, Unocal Corporation

William T. Wilson                   U.S.A.             Vice President, Commodity Trading and Risk
14141 Southwest Freeway                                Management, Unocal Corporation
Sugar Land TX 77478
</TABLE>

*Unless otherwise indicated, the business address of these individuals is c/o
Unocal Corporation at the address shown on the cover of this Schedule 13D.
<PAGE>

                       DIRECTORS AND EXECUTIVE OFFICERS
                        UNION OIL COMPANY OF CALIFORNIA

<TABLE>
<CAPTION>
Name and Business Address*          Citizenship        Position and Occupation
<S>                                 <C>                <C>
Roger C. Beach                      U.S.A.             Director, Chairman of the Board of Directors
                                                       and Chief Executive Officer, Union Oil
                                                       Company of California

John F. Imle, Jr.                   U.S.A.             Director, Vice Chairman of the Board of
                                                       Directors, Union Oil Company of California

Timothy H. Ling                     U.S.A.             Director, Executive Vice President, North
                                                       American Energy Operations, and Chief
                                                       Financial Officer, Union Oil Company of
                                                       California

Charles R. Williamson               U.S.A.             Director, Executive Vice President,
                                                       International Energy Operations, Union Oil
                                                       Company of California

Joe D. Cecil                        U.S.A.             Vice President and Comptroller, Union Oil
                                                       Company of California

Dennis P.R. Codon                   U.S.A.             Vice President, Chief Legal Officer and
                                                       General Counsel, Union Oil Company of
                                                       California

Joseph A. Householder               U.S.A.             Vice President, Corporate Development, and
                                                       Assistant Chief Financial Officer, Union Oil
                                                       Company of California

L.E. (Ed) Scott                     U.S.A.             Group Vice President, Diversified Business
376 South Valencia Avenue                              Group, Union Oil Company of California
Brea, CA 92833

William T. Wilson                   U.S.A.             Vice President, Commodity Trading and Risk
14141 Southwest Freeway                                Management, Union Oil Company of California
Sugar Land TX 77478
</TABLE>

*Unless otherwise indicated, the business address of these individuals is c/o
Unocal Corporation at the address shown on the cover of this Schedule 13D.

<PAGE>

                                                                    EXHIBIT 2.1

                        TITAN RESOURCES HOLDINGS, INC.

                         Stockholders Voting Agreement
                         -----------------------------

     This STOCKHOLDERS VOTING AGREEMENT, dated December 13, 1999 (the
"Agreement"), is made and entered into by and among Titan Resources Holdings,
Inc., a Delaware corporation (the "Company"), Union Oil Company of California, a
California corporation ("Union Oil"), and Mr. Jack D. Hightower, an individual
who resides in Midland County, Midland, Texas  ("CEO").

                             W I T N E S S E T H:

     WHEREAS, the Company, Union Oil, TRH, Inc., a Delaware corporation and
wholly-owned subsidiary of the Company ("Sub"), and Titan Exploration, Inc., a
Delaware corporation ("Titan"), propose to enter into an Agreement and Plan of
Merger concurrently with the execution hereof  (the "Merger Agreement"),
pursuant to which Sub shall be merged with and into Titan, which shall become a
wholly-owned subsidiary of the Company (the "Merger"); and

     WHEREAS, as a condition to the agreement of the parties to the Merger
Agreement to enter into the Merger Agreement, the Company, Union Oil and CEO
have agreed to enter into this Agreement to provide for certain agreements
relating to the composition of the Board of Directors of the Company following
the Effective Time of the Merger (as defined in the Merger Agreement, the
"Effective Time").

     NOW, THEREFORE, in consideration of the foregoing and the mutual agreements
set forth herein the parties to this Agreement 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:

     "Board" means the Board of Directors of the Company.

     "Bylaws" means the Bylaws of the Company as hereinafter amended or
     supplemented.

     "Capital Stock" means the Common Stock and any other capital stock of the
     Company.

     "Common Stock" means the common stock, par value $.01 per share, of the
     Company.

     "Exchange Act" means the Securities Exchange Act of 1934, as amended.
<PAGE>

     "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.

     "SEC" means the United States Securities and Exchange Commission.

     "Securities Act" means the Securities Act of 1933, as amended.

     "Union Oil Affiliate" means any natural person who is a partner, officer,
director or employee of, or is (directly or indirectly) the owner of 10% or more
of any class of equity securities of, Union Oil, Unocal Corporation, a Delaware
corporation, or any of its subsidiaries (other than the Company or any of its
subsidiaries).

     "Union Oil Ownership Percentage" means the percentage obtained by
multiplying 100 by an amount equal to (i) the number of shares of Common Stock
beneficially owned by Union Oil and its affiliates divided by (ii) the number of
shares of Common Stock issued and outstanding.

     The terms "participant," "proxy" and "solicitation" shall be used as
defined in Regulation 14A under the Exchange Act.  The terms "beneficial
ownership" and "group" shall be used as defined in Regulation 13D-G under the
Exchange Act.  The terms "affiliate" and "associate" shall be used as defined in
Rule 12b-2 under the Exchange Act.

     2.   Shares Subject to Agreement. Each of Union Oil and CEO agrees that all
          ---------------------------
shares of Capital Stock of the Company registered in its or his name or
beneficially owned by it or him as of the date hereof and any and all other
Capital Stock of the Company legally or beneficially acquired by Union Oil or
CEO, as applicable, after the date hereof shall be subject to the provisions of
this Agreement.

     3.   Term; Termination.   This Agreement shall not become effective until
          -----------------
the Effective Time of the Merger, and shall terminate and be of no force or
effect if the Merger Agreement is terminated in accordance with its terms.
After the Effective Time of the Merger, this Agreement shall terminate upon the
earlier to occur of (i) the sale or transfer by Union Oil or its affiliates of
such number of shares of Capital Stock that causes the Union Oil Ownership
Percentage to decline to 10% or less, or (ii) the date on which CEO is no longer
Chief Executive Officer of the Company.  This Agreement may also be terminated
by the written agreement of all parties hereto.  In the event of the termination
of this Agreement pursuant to this Section 3,  this Agreement shall become void
and have no effect. Nothing contained in this Section 3 shall relieve any party
from liability for damages actually incurred as a result of any breach of this
Agreement.

     4.   Merger Agreement.  The parties acknowledge that pursuant to the Merger
          ----------------
Agreement,  Union Oil has agreed to cause the directors of the Company from and
after the Effective Time to consist of Darrell Chessum, Timothy H. Ling, Herbert
C. Williamson, III, Graydon H. Laughbaum, Jr. and H.D. Maxwell as designees of
Union Oil, and CEO and George G. Staley as designees of

                                       2
<PAGE>

CEO, until the next annual meeting of stockholders and until their respective
successors are duly qualified and elected.

     5.   Election of Directors.
          ---------------------

          (a)  At each election of directors of the Company during the term of
this Agreement, each of Union Oil and CEO shall vote (including the taking of
any action by written consent, as necessary or appropriate), and shall cause its
affiliates to vote (including the taking of any action by written consent, as
necessary or appropriate), all shares of Capital Stock which it or he is
entitled to vote (or control the voting of, directly or indirectly) in favor of
the slate of nominees as selected in accordance with Section 5(b) and 5(c) for
election to the Board.

          (b)  Subject to the terms and conditions of this Section 5(b), for
purposes of selecting the slate of nominees referred to in Section 5(a), Union
Oil shall be entitled to nominate (i) five members of the Board, if the Union
Oil Ownership Percentage is greater than 50%; (ii) four members of the Board, if
the Union Oil Ownership Percentage is greater than 35% but not more than 50%; or
(iii) two members of the Board, if the Union Oil Ownership Percentage is greater
than 10% but not more than 35%. No more than two of the persons nominated
pursuant to this Section 5(b) shall be Union Oil Affiliates. In the event that
the Union Oil Ownership Percentage is greater than 35%, one of the Union Oil
Affiliates nominated pursuant to this Section 5(b) must be approved by CEO and
any non-Union Oil Affiliate nominated pursuant to this Section 5(b) must be
approved by CEO, in each case such approval not to be unreasonably withheld.

          (c)  Subject to the terms and conditions of this Section 5(c), CEO
shall be entitled to nominate two members of the Board. Any person nominated
pursuant to this Section 5(c) (other than CEO) must be approved by Union Oil,
which approval shall not be unreasonably withheld.

          (d)  In the event that any director (a "Withdrawing Director")
nominated in the manner set forth above is unable to serve, or once having
commenced to serve, ceases for any reason to be a director, such Withdrawing
Director's replacement (the "Substitute Director") on the Board shall be
nominated by the party who nominated the Withdrawing Director, subject to the
other provisions of this Section 5. The Company and each of the parties agree to
take all action within their respective power, including, but not limited to,
the voting of Capital Stock entitled to vote, to cause the election of such
Substitute Director as soon as practicable following his designation, or
instructing the directors it has previously nominated to serve as members of the
Board, as the first order of business at the first meeting thereof after such
Substitute Director has been so nominated, to vote to seat such nominated
Substitute Director as a director in place of the Withdrawing Director. In the
event any party entitled to nominate a director or directors pursuant to this
Agreement fails to nominate a director or directors, such directorship or
directorships shall remain vacant.

          (e)  If the party who has nominated for election to the Board any
director serving on the Board pursuant to the preceding provisions of this
Section 5 requests that such director be removed (with or without cause) by
written notice thereof to the other parties, then such director shall be removed
(with or without cause) and each party hereby agrees to vote all shares of
Capital

                                       3
<PAGE>

Stock entitled to vote owned or held of record by such party to effect such
removal upon any such request. No director nominated by a party shall otherwise
be involuntarily removed as a director except for cause.

     6.   Successors, Assigns and Transferees.  The terms and provisions of this
          -----------------------------------
Agreement shall not bind, inure to the benefit of or be enforceable by or
against the successors, assigns or transferees of each of the parties hereto.
No party hereto may assign its rights under this Agreement provided that Union
Oil may assign its rights and obligations hereunder to any Affiliate who agrees
in writing to be bound by this Agreement.

     7.   Entire Agreement; Amendments.  This Agreement, and such additional
          ----------------------------
instruments as may be concurrently executed and delivered pursuant to this
Agreement, 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 herein or in the documents delivered concurrently herewith.
This Agreement may be amended only by a written instrument duly executed by all
the parties hereto.

     8.   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.

     9.   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 Union Oil:

               Union Oil Company of California
               One Sugar Creek Place
               14141 Southwest Freeway
               Sugar Land, Texas 77478
               Attention: Mr. Phil Ballard
               Fax No:  (281) 287-5170

          with a copy to:

               Union Oil Company of California
               2141 Rosecrans Avenue, Suite 4000
               El Segundo, California 90245
               Attention:  (1)  General Counsel, and
                           (2)  Vice President, Corporate Development
               Fax No:  (310) 726-7819

                                       4
<PAGE>

          If to the Company:

               Titan Resources Holdings, Inc.
               500 West Texas
               Suite 200
               Midland, Texas 79701
               Attention: Jack D. Hightower
               Fax: (915) 687-3863

          with a copy to:

               Thompson & Knight L.L.P.
               1700 Pacific Avenue
               Suite 3300
               Dallas, Texas 75201
               Attention: Mr. Joe Dannenmaier
               Fax: (214) 969-1751

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.

     10.  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.

     11.  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.

     12.  Challenges to Agreement.  In the event that any part of this Agreement
          -----------------------
or any transaction contemplated hereby is temporarily, preliminarily or
permanently enjoined or restrained by court of competent jurisdiction, the
parties hereto shall use their reasonable best 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.

     13.  Specific Performance.  Each of Union Oil and CEO 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,
each of Union Oil and CEO 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.

                                       5
<PAGE>

     14.  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.


                                 *  *  *  *  *

                                       6
<PAGE>

     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.

                                   TITAN RESOURCES HOLDINGS, INC.



                                   By: /s/ Phillip Ballard
                                      ----------------------------------------
                                       Phillip Ballard
                                       Vice President


                                   UNION OIL COMPANY OF CALIFORNIA



                                   By: /s/ Timothy H. Ling
                                      ----------------------------------------
                                      Timothy H. Ling
                                      Executive Vice President, North American
                                      Energy Operations and Chief Financial
                                      Officer



                                   /s/ Jack D. Hightower
                                   -------------------------------------------
                                   JACK D. HIGHTOWER

                                       7

<PAGE>

                                                                   EXHIBIT 2.2


                                 Schedule 1.6

               Directors and Officers of Titan After the Merger

Directors
- ---------

Darrell Chessum
Jack D. Hightower


Officers
- --------

Jack D. Hightower        President
William K. White         Vice President and Assistant Secretary
Susan D. Rowland         Secretary
Dan P. Colwell           Assistant Secretary
John L. Benfatti         Assistant Secretary

<PAGE>

                                                                     EXHIBIT 2.3


                         AGREEMENT AND PLAN OF MERGER


                                     among


                       UNION OIL COMPANY OF CALIFORNIA,

                        TITAN RESOURCES HOLDINGS, INC.,


                                   TRH, INC.

                                      and

                            TITAN EXPLORATION, INC.

                               December 13, 1999
<PAGE>

                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                       Page
<S>                                                                    <C>
ARTICLE I - THE MERGER...............................................     2
       1.1   The Merger..............................................     2
       1.2   Closing Date............................................     2
       1.3   Consummation of the Merger..............................     2
       1.4   Effects of the Merger...................................     2
       1.5   Certificate of Incorporation; Bylaws....................     2
       1.6   Directors and Officers..................................     3
       1.7   Conversion of Securities................................     3
       1.8   Rights as a Stockholder.................................     3
       1.9   Surrender and Payment...................................     4
       1.10  Taking of Necessary Action; Further Action..............     5
       1.11  Adjustment..............................................     5
       1.12  Titan Stock Options.....................................     6
       1.13  Fractional Shares.......................................     7
       1.14  Withholding Rights                                           7

ARTICLE II - TRANSFER OF ASSETS AND ASSUMPTION OF LIABILITIES........     7
       2.1   Transfer of Assets and Assumption of Liabilities........     7
       2.2   Assets..................................................     8
       2.3   Excluded Assets.........................................     9
       2.4   Cash Amount.............................................    10
       2.5   Transfer of Certain Contracts...........................    11

ARTICLE III - REPRESENTATIONS AND WARRANTIES OF UNION OIL, THE
       COMPANY AND SUB...............................................    12
       3.1   Organization and Qualification..........................    12
       3.2   No Subsidiaries.........................................    13
       3.3   Capitalization..........................................    13
       3.4   Authorization and Validity of Agreement.................    14
       3.5   Approvals; No Conflict..................................    14
       3.6   Financial Statements....................................    15
       3.7   Absence of Undisclosed Liabilities......................    15
       3.8   Absence of Certain Changes..............................    15
       3.9   Tax Matters.............................................    16
       3.10  Compliance With Laws....................................    16
       3.11  Litigation..............................................    17
       3.12  Employees; Employee Benefit Plans.......................    17
       3.13  Environmental Matters...................................    17
       3.14  Title to Assets.........................................    18
       3.15  No Well Abandonments, No P&A Liabilities................    18
       3.16  Production Marketing....................................    18
       3.17  Gas Balancing, Take or Pay, Allowables..................    18
</TABLE>

                                       i
<PAGE>

<TABLE>
<S>                                                                    <C>
       3.18  Leases and Contracts in Force, Operatorship.............  19
       3.19  Permits.................................................  19
       3.20  Current Commitments.....................................  19
       3.21  Tax Partnerships........................................  19
       3.22  No Demands..............................................  20
       3.23  No Other Activities.....................................  20
       3.24  Liability for Brokers' Fees.............................  20
       3.25  Registration Statement and Proxy Statement/Prospectus
             Information.............................................  20

ARTICLE IV - REPRESENTATIONS AND WARRANTIES OF TITAN.................  20
       4.1   Organization and Compliance with Law....................  20
       4.2   Capitalization..........................................  21
       4.3   Authorization and Validity of Agreement.................  22
       4.4   Approvals; No Conflict..................................  22
       4.5   Commission Filings; Financial Statements................  23
       4.6   Absence of Undisclosed Liabilities......................  24
       4.7   Absence of Certain Changes..............................  24
       4.8   Tax Matters.............................................  24
       4.9   Compliance With Laws....................................  25
       4.10  Litigation..............................................  26
       4.11  Voting Requirements.....................................  26
       4.12  Employees; Employee Benefit Plans.......................  26
       4.13  Environmental Matters...................................  27
       4.14  Title to Assets.........................................  27
       4.15  No Well Abandonments, No P&A Liabilities................  27
       4.16  Production Marketing....................................  27
       4.17  Gas Balancing, Take or Pay, Allowables..................  28
       4.18  Leases and Contracts in Force, Operatorship.............  28
       4.19  Permits.................................................  28
       4.20  Current Commitments.....................................  28
       4.21  Tax Partnerships........................................  29
       4.22  Liability for Brokers' Fees.............................  29
       4.23  Anti-Takeover Provisions................................  29
       4.24  Dissenters' Rights......................................  29
       4.25  Certain Discussions.....................................  29
       4.26  Registration Statement and Proxy Statement/Prospectus
              Information............................................  29

ARTICLE V - CONDUCT PENDING CLOSING..................................  30
       5.1   Conduct and Preservation of Business....................  30
       5.2   Conduct and Preservation of Business of Titan...........  31

ARTICLE VI - ADDITIONAL AGREEMENTS...................................  34
       6.1   Access to Information...................................  34
       6.2   Titan Acquisition Proposals.............................  35
       6.3   Company Acquisition Proposals...........................  37
</TABLE>

                                      ii
<PAGE>

<TABLE>
<S>                                                                   <C>
      6.4   Special Meeting; Proxy Statement/Prospectus;
            Registration Statement..................................  37
      6.5   Reservation of Company Common Stock.....................  38
      6.6   Notification of Certain Matters.........................  38
      6.7   HSR Act; Consents.......................................  39
      6.8   Disclosure Letters......................................  39
      6.9   Reasonable Efforts......................................  39
      6.10  Public Announcements....................................  40
      6.11  Fees and Expenses.......................................  40
      6.12  Employees and Employee Benefit Plans....................  40
      6.13  Indemnification of Claims of Brokers....................  43
      6.14  Amendment of Disclosure Letters.........................  43
      6.15  Transfer Taxes..........................................  43
      6.16  Amendment of Rights Plan................................  44
      6.17  Management Employee Agreements..........................  44
      6.18  Tax Treatment...........................................  44
      6.19  Company Board...........................................  44
      6.20  Stock Exchange Listing..................................  44
      6.21  Indemnification and Insurance...........................  44
      6.22  Affiliate Agreements....................................  46
      6.23  Ancillary Agreements....................................  46
      6.24  Dividend Restriction....................................  46
      6.25  Incentive Plan..........................................  46
      6.26  Registration Rights Agreement...........................  47

ARTICLE VII - CONDITIONS TO OBLIGATIONS OF UNION OIL................  47
      7.1   Representations and Warranties..........................  47
      7.2   Covenants and Agreements................................  47
      7.3   Certificate.............................................  47
      7.4   HSR Act.................................................  47
      7.5   Legal Proceedings.......................................  47
      7.6   Consents................................................  48
      7.7   Stockholder Approval....................................  48
      7.8   Registration Statement..................................  48
      7.9   Listing of Company Common Stock.........................  48
      7.10  Accounting Matters......................................  48
      7.11  Opinion of Tax Counsel..................................  48

ARTICLE VIII - CONDITIONS TO OBLIGATIONS OF TITAN...................  49
      8.1   Representations and Warranties..........................  49
      8.2   Covenants and Agreements................................  49
      8.3   Certificate.............................................  49
      8.4   HSR Act.................................................  49
      8.5   Legal Proceedings.......................................  49
      8.6   Consents................................................  49
      8.7   Stockholder Approval....................................  49
</TABLE>

                                      iii
<PAGE>

<TABLE>
<S>                                                                   <C>
      8.8   Registration Statement..................................  49
      8.9   Listing of Company Common Stock.........................  50
      8.10  Accounting Matters......................................  50
      8.11  Opinion of Tax Counsel..................................  50

ARTICLE IX - TAX MATTERS............................................  50
      9.1   Tax History of the Company..............................  50
      9.2   Proration of Taxes......................................  50
      9.3   Tax Benefit Payments....................................  51

ARTICLE X - TERMINATION, AMENDMENT AND WAIVER.......................  52
      10.1  Termination.............................................  52
      10.2  Effect of Termination...................................  53
      10.3  Amendment...............................................  53
      10.4  Waiver..................................................  54

ARTICLE XI - SURVIVAL MATTERS; CROSS INDEMNIFICATION................  54
      11.1  Survival of Representations and Warranties..............  54
      11.2  Survival of Covenants and Agreements....................  54
      11.3  Indemnification.........................................  54
      11.4  Indemnification Procedure...............................  55
      11.5  Insurance...............................................  56
      11.6  Definitions.............................................  57

ARTICLE XII - MISCELLANEOUS.........................................  57
      12.1  Notices.................................................  57
      12.2  Entire Agreement........................................  59
      12.3  Binding Effect; Assignment; No Third Party Benefit......  59
      12.4  Severability............................................  59
      12.5  Governing Law...........................................  59
      12.6  Descriptive Headings....................................  59
      12.7  Gender..................................................  59
      12.8  References..............................................  59
      12.9  Counterparts............................................  60
      12.10 Specific Performance....................................  60

ARTICLE XIII - DEFINITIONS..........................................  60
      13.1  Certain Defined Terms...................................  60
      13.2  Certain Additional Defined Terms........................  63
</TABLE>

                                      iv
<PAGE>

                               INDEX TO EXHIBITS

Exhibit A           Assets
Exhibit 6.17(a)     Executive Letter Agreement
Exhibit 6.17(b)     Executive Severance Arrangements
Exhibit 6.22        Affiliate Agreement
Exhibit 6.25        1999 Incentive Plan


                              INDEX TO SCHEDULES

Schedule 1.6        Directors and Officers of Surviving Corporation
Schedule 6.19       Directors and Officers of the Company
Schedule 6.25       Stock Option Grants

                                       v
<PAGE>

                         AGREEMENT AND PLAN OF MERGER


     This Agreement and Plan of Merger, dated as of the 13th day of December,
1999 (the "Agreement"), is among Union Oil Company of California, a California
corporation ("Union Oil") Titan Resources Holdings, Inc., a newly-formed
Delaware corporation and a wholly-owned subsidiary of Union Oil (the "Company"),
TRH, Inc., a newly-formed Delaware corporation and a wholly-owned subsidiary of
the Company ("Sub"), and Titan Exploration, Inc., a Delaware corporation
("Titan").

     WHEREAS, as of the Closing Date (as defined below), the Company will
conduct as an ongoing concern substantially all of the business and operations
of Union Oil and its subsidiaries relating to the exploration for and
development and production of oil and gas onshore in the Permian Basin and the
San Juan Basin including the business and operations relating to the gas plants
identified in Section 2.2 (the "Business");

     WHEREAS, the respective Boards of Directors of Union Oil, the Company, Sub
and Titan have determined that the acquisition by the Company of Titan is
desirable and in the best interests of the stockholders of the respective
companies;

     WHEREAS, the respective Boards of Directors of Union Oil, the Company, Sub
and Titan have approved this Agreement, and such Boards of Directors and Union
Oil, as the sole stockholder of the Company, and the Company, as the sole
stockholder of Sub, have approved the merger of Sub with and into Titan (the
"Merger"), whereby each issued and outstanding share of common stock, par value
$.01 per share, of Titan (the "Titan Common Stock"), not owned directly or
indirectly by Titan will be converted into the right to receive shares of common
stock, par value $.01 per share, of the Company ("Company Common Stock"), upon
the terms and subject to the conditions set forth herein;

     WHEREAS, as a material inducement for each party to enter into this
Agreement and consummate the transactions contemplated hereby, each of the
parties is, or will be at or prior to Closing, entering into each of the
Ancillary Agreements (as defined below) that it is a party to;

     WHEREAS, for federal income tax purposes, the parties intend that the
Merger shall qualify as a reorganization within the meaning of Section 368(a) of
the Internal Revenue Code of 1986, as amended (the "Code") and as part of a
transaction under Section 351 of the Code;

     WHEREAS, the parties intend that this Agreement, as it relates to the
Merger, shall constitute a "plan of reorganization" within the meaning of
Treasury Regulation Section 1.368-3;

     WHEREAS, the parties intend that Union Oil's transfer of the Assets (as
defined below) to the Company shall qualify as a transaction described in
Section 351(a) of the Code; and

     WHEREAS, the parties hereto desire to set forth certain representations,
warranties and covenants made by each to the other as an inducement to the
consummation of the Merger;

                                       1
<PAGE>

     NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements herein contained, and intending to be legally bound
hereby, Union Oil, the Company, Sub and Titan hereby agree as follows:


                                   ARTICLE I

                                  THE MERGER

     1.1  The Merger.  Subject to and in accordance with the terms and
          ----------
conditions of this Agreement and in accordance with the General Corporation Law
of the State of Delaware (the "DGCL"), at the Effective Time (as defined in
Section 1.3) Sub shall be merged with and into Titan.  As a result of the
Merger, the separate corporate existence of Sub shall cease and Titan shall
continue as the surviving corporation (sometimes referred to herein as the
"Surviving Corporation").

     1.2  Closing Date.  The closing of the transactions contemplated by this
          ------------
Agreement (the "Closing") shall take place at the offices of Thompson & Knight
L.L.P., 1700 Pacific Avenue, Suite 3300, Dallas, Texas 75201, at 10:00 a.m.,
local time, on the day which is five (5) consecutive Business Days after the day
on which the last of the conditions to the obligations of the parties set forth
in Articles VII and VIII is fulfilled or waived (subject to Applicable Law) or
is capable of being fulfilled at the Closing or (ii) at such other time or place
or on such other date as the parties hereto shall agree.  The date on which the
Closing occurs is herein referred to as the "Closing Date".

     1.3  Consummation of the Merger.  As soon as practicable on the Closing
          --------------------------
Date, the parties hereto will cause the Merger to be consummated by filing with
the Secretary of State of Delaware a certificate of merger in such form as
required by, and executed in accordance with, the relevant provisions of the
DGCL.  The "Effective Time" of the Merger as that term is used in this Agreement
shall mean such time as the certificate of merger is duly filed with the
Secretary of State of Delaware or at such later time (not to exceed 90 days from
the date the certificate is filed) as is specified in the certificate of merger
pursuant to the mutual agreement of Union Oil, the Company, Sub and Titan.

     1.4  Effects of the Merger.  The Merger shall have the effects set forth in
          ---------------------
the applicable provisions of the DGCL.  Without limiting the generality of the
foregoing, and subject thereto, at the Effective Time, all the properties,
rights, privileges, powers and franchises of Titan and Sub shall vest in the
Surviving Corporation, without any transfer or assignment having occurred, and
all debts, liabilities and duties of Titan and Sub shall attach to the Surviving
Corporation, all in accordance with the DGCL.

     1.5  Certificate of Incorporation; Bylaws.
          ------------------------------------

          (a) The Certificate of Incorporation of Sub, as in effect immediately
     prior to the Effective Time, shall be the Certificate of Incorporation of
     the Surviving Corporation and thereafter shall continue to be its
     Certificate of Incorporation until amended as provided therein and under
     the DGCL.

                                       2
<PAGE>

          (b) The bylaws of Sub, as in effect immediately prior to the Effective
     Time, shall be the bylaws of the Surviving Corporation and thereafter shall
     continue to be its bylaws until amended as provided therein and under the
     DGCL.

     1.6  Directors and Officers.  The directors of the Surviving Corporation at
          ----------------------
and after the Effective Time shall consist of the persons set forth on Schedule
1.6, each to hold office in accordance with the Certificate of Incorporation and
bylaws of the Company and the Surviving Corporation, and the officers of the
Surviving Corporation at and after the Effective Time shall consist of the
persons set forth on Schedule 1.6, in each case until their respective
successors are duly elected or appointed and qualified or until their earlier
death, resignation or removal in accordance with the Surviving Corporation's
Certificate of Incorporation and Bylaws.

     1.7  Conversion of Securities.  Subject to the terms and conditions of this
          ------------------------
Agreement, at the Effective Time, by virtue of the Merger and without any action
on the part of Union Oil, the Company, Sub, Titan or their stockholders:

          (a) Each share of Titan Common Stock, together with the attached
     preferred stock purchase rights, issued and outstanding immediately prior
     to the Effective Time, other than any shares of Titan Common Stock to be
     canceled pursuant to Section 1.7(b), shall be converted into the right to
     receive .4302314 (the "Exchange Ratio") of a share of Company Common Stock.

          (b) Each share of Titan Common Stock held in the treasury of Titan and
     each share of Titan Common Stock owned by any direct or indirect wholly-
     owned subsidiary of Titan immediately prior to the Effective Time shall be
     canceled and extinguished without any conversion thereof and no payment
     shall be made with respect thereto.

          (c) Each share of common stock, par value $.01 per share, of Sub
     issued and outstanding immediately prior to the Effective Time shall be
     converted into and become one share of common stock, $.01 par value per
     share, of the Surviving Corporation.

     The consideration to which the holders of shares of Titan Common Stock are
entitled as provided in Section 1.7(a), together with cash, if any, in lieu of
Fractional Shares (as defined below), is referred to herein as the "Merger
Consideration".

     The Company shall, following the Closing, except as provided in Section
1.9(d) and Section 1.13(b), pay all stamp duties and stamp duty reserve tax, if
any, imposed in connection with the issuance or creation of the shares of
Company Common Stock in connection with the Merger.

     1.8  Rights as a Stockholder.  From and after the Effective Time, all
          -----------------------
shares of Titan Common Stock converted in accordance with Section 1.7(a) into
the right to receive shares of Company Common Stock shall no longer be
outstanding and shall automatically be canceled and retired and shall cease to
exist, and each holder of a certificate representing any such shares of Titan
Common Stock shall cease to have any rights with respect thereto, except the
right to receive the Merger Consideration and any dividends payable pursuant to
Section 1.9(a). From and after the

                                       3
<PAGE>

Effective Time, all certificates representing the common stock of Sub shall be
deemed for all purposes to represent the number of shares of common stock of the
Surviving Corporation into which they were converted in accordance with Section
1.7(c).

     1.9  Surrender and Payment.
          ---------------------

          (a) Prior to the Effective Time, the Company shall designate a bank or
     trust company reasonably acceptable to the Company (the "Exchange Agent")
     for the purpose of effecting the exchange of certificates representing
     shares of Titan Common Stock (the "Certificates") for the Merger
     Consideration.  As soon as practicable after the Effective Time, the
     Company will make available to the Exchange Agent, for the benefit of the
     holders of shares of Titan Common Stock, for exchange in accordance with
     this Article I, certificates representing the number of whole shares of
     Company Common Stock issuable pursuant to Section 1.7 in exchange for
     outstanding shares of Titan Common Stock.  Promptly after the Effective
     Time, the Company will send, or will cause the Exchange Agent to send, to
     each holder of record at the Effective Time of shares of Titan Common Stock
     a letter of transmittal for use in such exchange (which shall specify that
     the delivery shall be effected, and risk of loss and title shall pass, only
     upon proper delivery of the Certificates to the Exchange Agent) in such
     form as the Company and Titan may reasonably agree, for use in effecting
     delivery of shares of Titan Common Stock to the Exchange Agent acting on
     behalf of the Company.

          (b) Each holder of shares of Titan Common Stock that have been
     converted into a right to receive the Merger Consideration, upon surrender
     to the Exchange Agent of a Certificate, together with a properly completed
     letter of transmittal, will be entitled to receive the Merger Consideration
     in respect of the shares of Titan Common Stock represented by such
     Certificate.  Until so surrendered and exchanged, each such Certificate
     that prior to the Effective Time represented Titan Common Stock shall
     represent solely the right to receive such Merger Consideration.

          (c) All shares of Company Common Stock issued upon the surrender for
     exchange of Certificates in accordance with the terms hereof (including any
     cash paid pursuant to Section 1.13) shall be deemed to have been issued in
     full satisfaction of all rights pertaining to such shares of Titan Common
     Stock.  At and after the Effective Time, there shall be no further
     registration of transfers on the stock transfer books of the Surviving
     Corporation of Titan Common Stock that were outstanding immediately prior
     to the Effective Time.  If, after the Effective Time, Certificates are
     presented to the Surviving Corporation or the Exchange Agent for any
     reason, they shall be canceled and exchanged as provided in this Article I.

          (d) If any portion of the Merger Consolidation is to be paid to a
     person other than the person in whose name the Certificate surrendered is
     registered, it shall be a condition to
     such payment that the Certificate so surrendered shall be properly endorsed
     and otherwise in proper form for transfer and that the person requesting
     such exchange shall have paid to the Exchange Agent any transfer or other
     taxes required by reason of the issuance of a

                                       4
<PAGE>

     certificate for shares of Company Common Stock in any name other than that
     of the registered holder of the Certificate surrendered, or established to
     the satisfaction of the Exchange Agent that such tax has been paid or is
     not payable.

          (e) None of Union Oil, the Company, Sub, Titan, the Surviving
     Corporation or their transfer agents shall be liable to a holder of the
     shares of Titan Common Stock for any amount paid in good faith to a public
     official pursuant to applicable property, escheat or similar laws.

          (f) Any holder whose Certificates have been lost or destroyed may
     nevertheless obtain the Merger Consideration and other amounts to which
     such holder is entitled pursuant to this Article I, provided such holder
     delivers to the Exchange Agent a statement certifying such loss or
     destruction and providing for indemnity reasonably satisfactory to the
     Company and the Surviving Corporation against any loss or expense either of
     them may incur with respect to such Certificate.

          (g) No dividends or other distributions with respect to shares of
     Company Common Stock issued in the Merger shall be paid to the holder of
     any unsurrendered Certificates until such Certificates are surrendered as
     provided in this Agreement. Subject to the effect of applicable laws,
     following such surrender, there shall be paid, without interest, to the
     record holder of the shares of Company Common Stock issued in exchange
     therefor (i) at the time of such surrender, all dividends and other
     distributions payable in respect of such shares of Company Common Stock
     with a record date after the Effective Time and a payment date on or prior
     to the date of such surrender and not previously paid and (ii) at the
     appropriate payment date, the dividends or other distributions payable with
     respect to such shares of Company Common Stock with a record date after the
     Effective Time but with a payment date subsequent to such surrender.

     1.10 Taking of Necessary Action; Further Action.  The parties hereto shall
          ------------------------------------------
take all such reasonable and lawful action as may be necessary or appropriate in
order to effectuate the Merger as promptly as possible.  If, at any time after
the Effective Time, any such further action is necessary or desirable to carry
out the purposes of this Agreement and to vest the Surviving Corporation with
full right, title and possession to all assets, property, rights, privileges,
powers and franchises of Titan or Sub, such parties shall direct their
respective officers and directors to take all such lawful and necessary action.

     1.11 Adjustment.  In the event of any stock split, combination,
          ----------
reclassification, recapitalization, exchange, stock dividend or other
distribution payable in Company Common Stock with respect to shares of Company
Common Stock (or if a record date with respect to any of the foregoing actions
should occur) during the period between the date of this Agreement and the
Effective Time, then the number of shares of Company Common Stock into which
each share of Titan Common Stock is to be converted pursuant to this Agreement
shall be adjusted to reflect any such action.

                                       5
<PAGE>

     1.12 Titan Stock Options.  Subject to the consummation of the Merger and
          -------------------
effective at the Effective Time, the Company and Titan will take such action as
is necessary to assume, effective at the Effective Time, each option to purchase
shares of Titan Common Stock (each, a "Titan Employee Option") that remains as
of such time unexercised in whole or in part and to substitute shares of Company
Common Stock as purchasable under each such assumed option ("Assumed Option"),
with such assumption and substitution to be effected as follows:

          (a) The Assumed Option shall not give the optionee additional benefits
     which he did not have under the Titan Employee Option before such
     assumption and shall be assumed on the same terms and conditions as the
     Titan Employee Options being assumed, subject to Section 1.12(b) and (c)
     (it being recognized that each existing Titan Employee Option shall vest on
     the Closing Date insofar as such Titan Employee Option vests as a result of
     the Merger);

          (b) The number of shares of Company Common Stock purchasable under the
     Assumed Option shall be equal to the nearest whole number of shares of
     Company Common Stock that the holder of the Titan Employee Option being
     assumed would have received (without regard to any vesting schedule) upon
     consummation of the Merger had such Titan Employee Option been exercised in
     full immediately prior to consummation of the Merger; and

          (c) The per share exercise price of such Assumed Option shall be an
     amount equal to the per share exercise price of the Titan Employee Option
     being assumed divided by the Exchange Ratio.

     The Company shall take all corporate action necessary to reserve for
issuance a sufficient number of shares of Company Common Stock for delivery upon
exercise of the Assumed Options, and, as soon as practicable after the Effective
Time, the Company shall file a registration statement on Form S-8 (or other
appropriate form) with respect to the shares of Company Common Stock subject to
the Assumed Options, and shall use its best efforts to maintain the
effectiveness of such registration statement (and maintain the current status of
any prospectus contained therein) for so long as any of the Assumed Options
remain outstanding.  The Company agrees that the Company's Board of Directors or
the Compensation Committee of the Company's Board of Directors shall at or prior
to the Effective Time adopt resolutions specifically approving, for purposes of
Rule 16b-3 under the Exchange Act, the receipt of (i) Company Common Stock
pursuant to Section 1.7 and (ii) Company stock options pursuant to this Section
1.12 by persons who will become officers or directors of the Company subject to
Section 16 of the Exchange Act.  The parties acknowledge that on or before the
date of this Agreement, the Company's board of directors has adopted resolutions
specifically approving, for purposes of Rule 16b-3 under the Exchange Act, the
receipt by Jack D. Hightower ("CEO") of the put rights contained in the
agreement referenced in Section 6.23(f) and the purchase by the Company of
Company Common Stock pursuant thereto.

                                       6
<PAGE>

     1.13 Fractional Shares.
          -----------------

     (a)  No certificates or scrip representing fractional shares of Company
Common Stock ("Fractional Shares") shall be issued upon the surrender for
exchange of Certificates, no dividend or distribution of the Company shall
relate to such Fractional Shares and such Fractional Shares will not entitle the
owner thereof to vote or to any rights of a stockholder of the Company.  All
holders of Titan Common Stock who would otherwise be entitled to receive
Fractional Shares shall be entitled to receive, in lieu thereof, an amount in
cash equal to the product obtained by multiplying (A) the number of Fractional
Shares to which such holder (after taking into account all shares of Titan
Common Stock held at the Effective Time by such holder) would otherwise be
entitled by (B) the closing price for a share of Company Common Stock as
reported in The Wall Street Journal, or, if not reported thereby, any other
authoritative source, on the first full trading day in the United States public
securities markets immediately following the Closing Date.

     (b)  The parties acknowledge that payment of the cash consideration in lieu
of issuing Fractional Shares was not separately bargained for consideration but
merely represents a mechanical rounding off for purposes of simplifying the
corporate and accounting problems that would otherwise be caused by the issuance
of Fractional Shares.

     1.14 Withholding Rights.  Each of the Surviving Corporation and the Company
          ------------------
shall be entitled to deduct and withhold from the consideration otherwise
payable to any person pursuant to this Article I such amounts as it is required
to deduct and withhold with respect to the making of such payment under any
provision of federal, state, local or foreign tax law. To the extent that
amounts are so withheld by the Surviving Corporation or the Company, as the case
may be, such withheld amounts shall be treated for all purposes of this
Agreement as having been paid to the holder of the shares of Titan Common Stock
in respect of which such deduction and withholding was made by the Surviving
Corporation or the Company, as the case may be.


                                  ARTICLE II

               TRANSFER OF ASSETS AND ASSUMPTION OF LIABILITIES

     2.1  Transfer of Assets and Assumption of Liabilities.  Simultaneously with
          ------------------------------------------------
the Closing, Union Oil shall, or shall cause its subsidiaries to, contribute and
convey, the Assets (as defined below) to the Company or, at the Company's
direction, to a subsidiary of the Company which is reasonably satisfactory to
both parties (as used herein, the term the "Company" shall be deemed to mean the
Company and/or such subsidiary, as appropriate) in exchange for (i) the issuance
by the Company to Union Oil of 32,708,067 shares of Company Common Stock, and
(ii) the assumption by the Company of all Liabilities related to the assets or
operations comprising the Business or the Assets or otherwise reflected or
reserved in the Financial Statements, in each case regardless of whether such
Liabilities exist or arise before, at or after January 1, 2000 (whether
contingent or otherwise), except for (A) any Liabilities required by generally
accepted accounting principles ("GAAP") to be disclosed in the Financial
Statements that are not disclosed in the Financial Statements, (B) any Liability
for trade payables arising out of the ownership and operation of the

                                       7
<PAGE>

Assets prior to January 1, 2000, (C) any Liability relating to payment of or
failure to pay any royalty, overriding royalty, compensatory royalty, working
interests or net profits interests prior to the Closing Date, other than
Liabilities relating to legal suspense amounts for royalties included among the
Assets, (D) any Liability for which the Company is indemnified pursuant to
Section 6.12 or Section 6.13, (E) Liabilities for Taxes of the Company or the
Business relating to periods prior to January 1, 2000, (F) any liabilities in
respect of the claims or Proceedings described in Section 3.9 or 3.11 of the
Union Oil Disclosure Letter or (G) any Liabilities of Union Oil or any of its
affiliates relating to the Excluded Assets (the matters in clauses (A) through
(G) are collectively referred to herein as the "Excluded Liabilities").  Union
Oil shall provide proposed forms of conveyance, assignment and assumption
documents to Titan not less than 10 days prior to the Closing Date, and such
documents as finally executed shall be reasonably acceptable to Titan.

     2.2  Assets.  As used in this Agreement, "Assets" shall mean the Cash
          ------
Amount (as determined in Section 2.4) and the aggregate of all right, title and
interest owned by Union Oil and/or any of its affiliates, or any of them,
insofar as they relate to the Business,  including without limitation the
following:

          (a) the interests specified on Exhibit A hereto in and to the oil and
     gas leases, real property, real property leases, mineral classified lands
     and other interests described on such Exhibit A (and any ratifications and
     amendments thereof, whether or not the same are described on Exhibit A);

          (b) without limitation of the foregoing, subject to Section 2.5, all
     other right, title and interest (of whatever kind or character, whether
     legal or equitable, and whether vested or contingent) of Union Oil or any
     subsidiary of Union Oil in and to the oil, gas and other minerals produced
     in association therewith in and under or that may be produced from the
     lands described on Exhibit A hereto at all depths or described in any of
     the leases or other instruments described on such Exhibit A (including,
     without limitation, interests in oil, gas and/or mineral leases, overriding
     royalties, production payments, net profits interests, fee mineral
     interests, fee royalty interests and other interests insofar as they cover
     such lands and depths), even though Union Oil's or such subsidiary's
     interest therein may be incorrectly described in, or omitted from, such
     Exhibit A; and

          (c) subject to Section 2.5, all rights, titles and interests of Union
     Oil or any subsidiary of Union Oil in and to, or otherwise derived from,
     all presently existing and valid oil, gas and/or mineral unitization,
     pooling, and/or communitization agreements, declarations, designations
     and/or orders relating to the foregoing (including, without limitation,
     those described on Exhibit A hereto) and in and to the properties covered
     and the units created thereby (including, without limitation, all units
     formed under orders, rules, regulations, or other official acts of any
     federal, state, or other authority having jurisdiction, and voluntary
     unitization agreements, designations and/or declarations) primarily
     relating to the properties described in subsections (a) and (b) above;

          (d) subject to Section 2.5, all rights, titles and interests of Union
     Oil or any subsidiary of Union Oil in and to all presently existing and
     valid production sales contracts,

                                       8
<PAGE>

     operating agreements, and other agreements and contracts which relate
     primarily to any of the properties described in subsections (a), (b) and
     (c) above;

          (e) subject to Section 2.5, all rights, titles and interests of Union
     Oil or any subsidiary of Union Oil in and to all materials, supplies,
     machinery, equipment, improvements and other personal property and fixtures
     (including, but not by way of limitation, all wells, wellhead equipment,
     pumping units, flowlines, tanks, platforms, buildings, saltwater disposal
     facilities, injection facilities, compression facilities, gathering
     systems, service contracts, seismic data, trucks, well site equipment,
     geological data (including maps and interpretations thereof), telephone,
     communication equipment, computers (including any geological or geophysical
     aids relating to software or hardware), hedges entered into at Titan's
     request, suspense files and accounts, bonds, contracts, legal claims,
     furniture and other equipment, personal property leases, prepaid expenses,
     and books and records) used primarily in connection with the exploration,
     development, operation, maintenance or administration of the properties
     described in subsections (a), (b) and (c) above, and in and to all permits
     and licenses (including, without limitation, all environmental and other
     governmental permits, licenses and authorizations), rights of way,
     easements, and other rights of surface use, water rights and other rights
     and interests used in connection with the exploration, development,
     operation, maintenance or administration of the properties described in
     subsections (a), (b) and (c) above;

          (f) all rights, titles and interests of Union Oil or any subsidiary of
     Union Oil in and to the gas plants and gathering and transmission lines
     listed on Exhibit A, including the gas plants in the Dollarhide, Massey,
     Sacrock and Coyonosa Fields;

          (g) all rights, titles and interests of Union Oil or any subsidiary of
     Union Oil in and to all accounts receivable and other rights to receive
     payment with respect to production from or operation of the Properties on
     or after January 1, 2000; and

          (h) all rights, titles and interests of Union Oil or any subsidiary of
     Union Oil in and to rights to receive proceeds with respect to the exercise
     of preferential purchase rights relating to any Asset after the date
     hereof.

     The properties, rights and interests described in subsections (a) through
(c) above are herein sometimes called the "Properties."

     2.3  Excluded Assets.  Notwithstanding any provision contained in this
          ---------------
Agreement to the contrary, the following shall be excluded from the Assets
(collectively, the "Excluded Assets"):

          (a) Union Oil's or its subsidiaries' capital stock in Tom Brown, Inc.
     and Matador Petroleum Corporation and all assets or properties of such
     corporations;

          (b) All tools, vehicles or other rolling stock, communication
     equipment, computer equipment, software, office premises, and office
     equipment that is not owned by Union Oil or is located outside of the
     Permian Basin and San Juan Basin;

                                       9
<PAGE>

          (c) Storage or warehouse agreements (for locations outside of the
     Permian Basin and San Juan Basin), service contracts and constructor
     agreements, unless such contract or agreement is associated primarily with
     the production from or operation of the Assets or is otherwise reasonably
     necessary to the ongoing ownership, operation or maintenance of the Assets
     consistent with past practice;

          (d) All pipelines, gas storage land or facilities, equipment and
     rights of any kind whether owned and/or operated, directly or indirectly,
     by Union Oil or any affiliate of Union Oil that are not expressly
     identified on Exhibit A, unless such pipeline, equipment or right of way is
     associated primarily with the production from or operation of the Assets or
     is otherwise reasonably necessary to the ongoing ownership, operation or
     maintenance of the Assets consistent with past practice; provided, however,
     that any assets owned by Unocal Pipeline Company shall be Excluded Assets;

          (e) All assets of whatever kind that are held by Union Oil or its
     subsidiaries that are used in owning, operating or maintaining assets and
     that are not primarily used in owning, operating or maintaining the Assets
     and are not related primarily to the Business;

          (f) The marketing agreement relating to the Assets between Unocal
     Global Trade and Union Oil; and

          (g) cash other than (1) the Cash Amount and (2) any preferential
     purchase rights proceeds referred to in Section 2.2(h).

     2.4  Cash Amount.  (a)  The Assets shall include the amount of cash equal
          -----------
to the following (the "Cash Amount"):

          (i)    the amount of revenues (or estimated revenues as agreed)
                 received by Union Oil in connection with sales of oil, gas
                 and/or other minerals and associated products from the Assets,
                 together with any other revenue from the Assets, with respect
                 to production and/or operations on or after January 1, 2000
                 through the Closing Date; plus

          (ii)   the amount of legal suspense as of the Closing Date; less

          (iii)  the amount of expenditures (or estimated expenditures as
                 agreed) paid by Union Oil that are attributable to the Assets
                 for the period beginning on January 1, 2000 and ending on the
                 Closing Date, including, without limitation, royalties, taxes,
                 rentals and similar charges and expenses, including those
                 billed under applicable operating agreements, and all prepaid
                 expenses.

          (b)    Three days prior to, and for the purposes of, the Closing,
     Union Oil and Titan shall determine, based upon the best information
     reasonably available to them, the amount of the Cash Amount. In the event
     that the Cash Amount determined at Closing is a negative

                                       10
<PAGE>

     number, such amount shall be an outstanding obligation of the Company
     payable, if applicable, to Union Oil in accordance with Section 2.4(d).

          (c) On or before February 15, 2001, Union Oil and the Company shall
     review any additional information which may then be available pertaining to
     the Cash Amount, and the Company shall prepare and deliver to Union Oil a
     reconciliation of the Cash Amount to determine whether any adjustment
     should be made to the Cash Amount as it was determined for the Closing
     (whether the same be made to account for funds received and expenditures
     paid that are attributable to the operations of the Assets for the period
     from and after January 1, 2000 until the Closing Date that were not
     considered in making the determination of the Cash Amount at Closing, or to
     correct errors made in such determination).  In the event that Union Oil
     acting in good faith disputes the reconciliation prepared by the Company,
     Union Oil shall give written notice thereof to the Company on or before the
     tenth Business Day after the reconciliation was given to Union Oil, which
     notice shall set forth the basis for such dispute in reasonable detail.
     Union Oil and the Company shall use all reasonable efforts to resolve any
     such dispute, but if any such dispute cannot be resolved by such parties
     within ten Business Days after the date the dispute notice is given, all
     unresolved disputes shall be referred to the Arbitrating Firm for
     resolution.  Union Oil and the Company shall seek to cause the Arbitrating
     Firm to make its determination within ten Business Days after referral of a
     dispute to it.  Union Oil and the Company shall each provide the
     Arbitrating Firm with all information which it reasonably requires.  The
     determination of the Arbitrating Firm shall be conclusive and binding on
     each party.  The fees of the Arbitrating Firm shall be allocated and paid
     by Union Oil or the Company on a basis determined by the Arbitrating Firm
     to be fair taking into account the correctness of the positions asserted by
     Union Oil and the Company.

          (d) Following the determination pursuant to Section 2.4(c) of the
     adjustments, if any, to the Cash Amount as determined at Closing, (i) if
     the Cash Amount as finally determined pursuant to Section 2.4(c) minus the
     Cash Amount  determined at Closing is greater than zero, then Union Oil
     shall promptly pay such amount to the Company and (ii) if  the Cash Amount
     as finally determined pursuant to Section 2.4(c) minus the Cash Amount
     determined at Closing is a negative number, then the Company shall promptly
     pay such amount to Union Oil.

          (e) Following the adjustments pursuant to this Section 2.4, no further
     adjustments shall be made to the Cash Amount.

     2.5  Transfer of Certain Contracts.
          -----------------------------

          (a) Without limiting the generality of Section 2.2, Union Oil agrees
     that between the date hereof and the Closing Date it will use its
     reasonable efforts to obtain or cause to be obtained the necessary consents
     to the transfer to the Company of each contract, license or permit included
     in the Assets which by its terms requires the consent of any other
     contracting party thereto or the issuer thereof (for purposes of this
     section, "Consent Required Asset").  In no event, however, shall Union Oil
     be obligated to pay any money to any person or to offer

                                       11
<PAGE>

     or grant other financial or other accommodations to any person in
     connection with obtaining any consent with respect to any contract, license
     or permit.  If Union Oil shall have failed prior to the Closing Date to
     obtain consents to the transfer of any Consent Required Asset, the terms of
     this Section 2.5 shall govern the transfer of the benefits of each such
     contract, license or permit.

          (b) Notwithstanding any provision contained in this Agreement to the
     contrary, the parties hereto acknowledge and agree that at the Closing
     Union Oil shall not transfer or cause to be transferred to the Company any
     Consent Required Asset the consent to which has not been obtained prior to
     the Closing Date.

          (c) With respect to each such unassigned Consent Required Asset, after
     the Closing Date Union Oil shall continue to deal with the other
     contracting party or parties to such Consent Required Asset as the prime
     contracting party and shall continue to use its reasonable efforts to
     obtain the consent of all required parties to the transfer of such Consent
     Required Asset to the Company, but the Company shall be entitled to the
     benefits of such Consent Required Asset accruing after the Closing Date to
     the extent that Union Oil may provide the Company with such benefits
     without violating the terms of such Consent Required Asset or Applicable
     Law; provided, however, that Union Oil's obligation to maintain any such
     arrangement shall terminate upon the earliest to occur of (1) the
     expiration or termination of such Consent Required Asset in accordance with
     its terms (without regard to any extensions, automatic or otherwise) or (2)
     with regard to a permit, such time as the Company shall obtain a permit in
     reasonable substitution therefor, or have its application for such
     substitute permit denied.  In any such arrangement, (i) Union Oil shall
     promptly pay to the Company when received all moneys relating to the period
     after the Closing Date received by it under any contract included in the
     Assets or any claim, right or benefit arising thereunder not transferred
     pursuant to this Section 2.5 and (ii) the Company shall promptly pay,
     perform or discharge when due any obligation or liability arising
     thereunder after the Closing Date.

          (d) Union Oil shall not incur any liability to Titan or the Company if
     such "pass through" arrangement shall not enable the Company to use or
     benefit from such Consent Required Asset.


                                  ARTICLE III

                       REPRESENTATIONS AND WARRANTIES OF
                        UNION OIL, THE COMPANY AND SUB

     Union Oil, the Company and Sub jointly and severally represent and warrant
to Titan that:

     3.1  Organization and Qualification.  Each of the Company and Sub is a
          ------------------------------
corporation duly organized, validly existing and in good standing under the laws
of the State of Delaware and has all requisite corporate power and authority and
all necessary governmental authorizations to own, lease

                                       12
<PAGE>

and operate all of its properties and assets and to carry on its business as now
being conducted.  Except as set forth in Section 3.1 of the disclosure letter
delivered by Union Oil and the Company to Titan on the date hereof (the "Union
Oil Disclosure Letter"), each of the Company and Sub is duly qualified as a
foreign corporation to do business, and is in good standing, in each
jurisdiction in which the property owned, leased or operated by it or the nature
of the business conducted by it makes such qualification necessary, except in
such jurisdictions where the failure to be duly qualified is not and would not
be, either individually or in the aggregate, reasonably expected to have a
Material Adverse Effect on the Assets or the Company.  No actions or proceedings
to dissolve the Company or Sub are pending.  Each of the Company and Sub has
heretofore made available to Titan true and complete copies of (i) such
company's Certificate of Incorporation and bylaws as currently in effect, (ii)
the stock records of the Company and Sub and (iii) the minutes of all meetings
of the Boards of Directors of the Company and Sub, any committees of such
Boards, and the stockholder of the Company and Sub (and all consents in lieu of
such meetings).  Such records, minutes and consents accurately reflect the stock
ownership of the Company and Sub and all actions taken by such Boards of
Directors, committees and stockholders.

     3.2  No Subsidiaries.  Except as set forth in Section 3.2 of the Union Oil
          ---------------
Disclosure Letter, neither the Company nor Sub owns, directly or indirectly, the
capital stock or other securities of any corporation or partnership or has any
direct or indirect equity or ownership interest in any other person, except for
the Company's ownership of Sub and except as contemplated by this Agreement.

     3.3  Capitalization.
          --------------

          (a) The authorized capital stock of the Company consists of (i) 200
     million shares of Company Common Stock, par value $.01 per share and (ii)
     10 million shares of preferred stock, par value $.01 per share.  As of the
     date of this Agreement, there were issued and outstanding 1,000 shares of
     Company Common Stock, all of which are owned by Union Oil, and no shares of
     capital stock of the Company are held as treasury shares.  At the Closing
     Date, after the completion of the contribution and assumption contemplated
     by Section 2.1, there will be issued and outstanding 32,709,067 shares of
     Company Common Stock, all of which will be owned by Union Oil.  All
     outstanding shares of capital stock of the Company have been validly issued
     and are fully paid and nonassessable, and no shares of capital stock of the
     Company are subject to, nor have any been issued in violation of,
     preemptive or similar rights.  Except as contemplated by this Agreement,
     neither Union Oil nor the Company is a party to, nor is aware of, any
     voting agreement, voting trust or similar agreement or arrangement relating
     to any class or series of the Company's capital stock, or any agreement or
     arrangement providing for registration rights with respect to any capital
     stock or other securities of the Company.  All shares of Company Common
     Stock to be issued pursuant to the Merger, when issued in accordance with
     this Agreement, will be validly issued, fully paid and nonassessable and
     will not violate the pre-emptive rights of any person.

          (b) As of the date of this Agreement, except as contemplated by this
     Agreement and other than as set forth in Section 3.3(a) or 3.3(d), there
     are not now, and at the Closing Date there will not be, any (A) shares of
     capital stock or other equity securities of the

                                       13
<PAGE>

     Company or Sub outstanding or (B) outstanding options, warrants, scrip,
     rights to subscribe for, calls or commitments of any character whatsoever
     relating to, or securities or rights convertible into or exchangeable for,
     shares of any class of capital stock of the Company or Sub, or contracts,
     understandings or arrangements to which Union Oil, the Company, Sub, any
     affiliate of Union Oil, the Company or Sub is a party, or by which Union
     Oil, the Company, Sub, any affiliate of Union Oil, the Company or Sub is or
     may be bound, to issue additional shares of  capital stock or equity
     interests or options, warrants, scrip or rights to subscribe for, or
     securities or rights convertible into or exchangeable for, any additional
     shares of  capital stock or equity interests of the Company or Sub.

          (c) All securities which have been offered or sold by the Company and
     Sub have been registered pursuant to the Securities Act and applicable
     state securities laws or were offered and sold pursuant to valid exemptions
     therefrom.

          (d) As of the date hereof, the authorized capital stock of Sub
     consists of 1,000 shares of common stock, par value $.01 per share, all of
     which are validly issued, fully paid and nonassessable and are owned by the
     Company.

     3.4  Authorization and Validity of Agreement.  Each of the Company, Sub and
          ---------------------------------------
Union Oil has all requisite corporate power and authority to enter into this
Agreement and to perform its obligations hereunder, and the execution and
delivery by the Company, Sub and Union Oil of this Agreement and the
consummation by each of them of the transactions contemplated hereby have been
duly authorized by all necessary corporate action.  This Agreement has been duly
executed and delivered by each of the Company, Sub and Union Oil and
constitutes, and each other agreement, instrument or document executed or to be
executed by the Company, Sub or Union Oil in connection with the transactions
contemplated hereby has been, or when executed will be, duly executed and
delivered by the Company, Sub or Union Oil, as applicable, and constitutes, or
when executed and delivered will constitute, the valid and binding obligation of
the Company, Sub and Union Oil, enforceable against the Company, Sub and Union
Oil, as applicable, to the extent it is a party thereto,  in accordance with
their respective terms, except that such enforceability may be limited by (i)
applicable bankruptcy, insolvency, reorganization, moratorium and similar laws
affecting creditors' rights generally and (ii) equitable principles which may
limit the availability of certain equitable remedies (such as specific
performance) in certain instances.

     3.5  Approvals; No Conflict.  Neither the execution and delivery of this
          ----------------------
Agreement nor the performance by any of the Company, Sub or Union Oil of its
obligations hereunder, nor the consummation of the transactions contemplated
hereby by the Company, Sub or Union Oil, will (i) conflict with the charter or
bylaws, or partnership or joint venture agreement, of the Company, Sub or Union
Oil; (ii) assuming satisfaction of the requirements set forth in clause (iii)
below, violate any provision of law applicable to the Company, Sub or Union Oil;
(iii) except for (A) requirements of federal or state securities laws and (B)
requirements arising out of the HSR Act, if applicable, require any consent or
approval of, or filing with or notice to, any Governmental Entity, domestic or
foreign, under any provision of law applicable to the Company, Sub or Union Oil;
or (iv) except as set forth in Section 3.5 of the Union Oil Disclosure Letter or
Exhibit A, require any consent, approval or notice under, or violate, breach, be
in conflict with or constitute a default (or any event

                                       14
<PAGE>

that, with notice or lapse of time or both, would constitute a default) under,
or permit the termination of any provision of, or result in the creation or
imposition of any lien upon the Assets or any other properties, assets or
business of the Company, Sub or Union Oil under, any note, bond, indenture,
mortgage, deed of trust, lease, franchise, permit, authorization, license,
contract, instrument, partnership agreement or other agreement or commitment or
any order, judgment or decree to which such entity is a party or by which it or
any of its assets or properties is bound or encumbered, except (A) those that
have already been given, obtained or filed and (B) those that, in the aggregate,
would not reasonably be expected to have a Material Adverse Effect on the
Company or the Assets.  No Asset is subject to a preferential right to purchase
that is applicable to the transactions contemplated by this Agreement, except
for such rights that, in the aggregate and if exercised, would not have a
Material Adverse Effect on the Company following the Merger.

     3.6  Financial Statements.  Attached as Section 3.6 of the Union Oil
          --------------------
Disclosure Letter are accurate and complete copies of (i) Union Oil's Permian
Basin Properties' audited consolidated balance sheets as of December 31, 1997
and 1998, and the related audited consolidated statements of earnings, owner's
net investment and cash flows for the years ended December 31, 1996, 1997 and
1998, and the notes and schedules thereto (excluding supplemental information on
oil and gas exploration and production disclosure ("SMOG Data"), together with
the unqualified report thereon of PricewaterhouseCoopers, independent public
accountants (the "Audited Financial Statements"), and (ii) Union Oil's Permian
Basin Properties' unaudited consolidated balance sheets as of September 30, 1998
and 1999, and the related unaudited consolidated statements of earnings, parent
company investment and cash flows for the nine-months ended September 30, 1998
and 1999 (the "Unaudited Financial Statements"), certified by Union Oil's chief
financial officer (collectively, the "Financial Statements"), which (i) have
been prepared from the books and records of Union Oil in conformity with GAAP
applied on a consistent basis and (ii) fairly present the financial position of
Union Oil's Permian Basin Properties (which does not include the Excluded
Assets) as of the respective dates thereof and its results of operations and
cash flows for the periods then ended.  For purposes of this Agreement, the
"Latest Balance Sheet" means the balance sheet dated September 30, 1999 set
forth in the Unaudited Financial Statements.

     3.7  Absence of Undisclosed Liabilities.  Neither the Company nor Sub has
          ----------------------------------
any liabilities or obligations of the type required to be reflected on the
Financial Statements, except (i) liabilities reflected on the Financial
Statements, (ii) liabilities which have arisen since the date of the Latest
Balance Sheet in the ordinary course of business, (iii) liabilities arising
under contracts entered into in the ordinary course of business and (iv) other
liabilities which, in the aggregate, would not have a Material Adverse Effect on
the Company or the Assets.

     3.8  Absence of Certain Changes.  Since the date of the Latest Balance
          --------------------------
Sheet, (i) there has not been any change, development, or effect on the Assets
or the Company, individually or in the aggregate, that has had, or might
reasonably be expected to have, a Material Adverse Effect on the Company or the
Assets; (ii) the operation of the Assets and the  business of the Company have
been conducted in the ordinary course consistent with past practice; (iii) the
Company has not incurred any material liability, engaged in any transaction or
entered into any agreement outside the ordinary course of business consistent
with past practice; (iv) the Company or the Assets have not suffered any loss,
damage, destruction or other casualty (whether or not covered by insurance)
which has had,

                                       15
<PAGE>

or might reasonably be expected to have, a Material Adverse Effect on the
Company; and (v) neither Union Oil nor the Company has taken any action that
would not be permitted to be taken by such entity under Section 5.1.

     3.9  Tax Matters.
          -----------

          (a) Except as set forth in Section 3.9 of the Union Oil Disclosure
     Letter, all Tax Returns of or relating to any Tax that are required to be
     filed on or before the Closing Date by or with respect to the Company, Sub
     or the Assets have been or will be duly and timely filed other than those
     returns on which an immaterial amount of Taxes would properly be shown the
     failure of which to file would not have a Material Adverse Effect on the
     Company, Sub or the Assets, and all Taxes, including interest and
     penalties, due and payable pursuant to such Tax Returns have been or will
     be paid.  Except as set forth in Section 3.9 of the Union Oil Disclosure
     Schedule, there is no material claim against the Company, Sub or the Assets
     with respect to any Taxes, and no material assessment, deficiency or
     adjustment has been asserted or proposed with respect to any Tax Return of
     or with respect to the Company, Sub or the Assets that has not been
     adequately provided for in reserves established by the Company.  The
     Company has (and as of the Closing Date will have) made all deposits
     required with respect to Taxes.  No waiver or extension of any statute of
     limitations as to any federal, local or foreign Tax matter has been given
     by or requested from the Company or Sub.  Except for statutory liens for
     current Taxes not yet due, no lien for Taxes exists upon the Assets of the
     Company or Sub.

          (b) All ad valorem, property, production, severance and similar Taxes
     and assessments based on or measured by the ownership of property or the
     production or removal of hydrocarbons or the receipt of proceeds therefrom
     and relating to the Assets, to the extent such taxes and assessments have
     become due and payable, have been timely paid and all applicable Tax
     Returns required to be filed have been filed and there are no material
     claims by any applicable Taxing Authority pending against Union Oil, the
     Company, Sub or any other subsidiary or parent of Union Oil applicable to
     the Assets.

     3.10 Compliance With Laws.  To the knowledge of the Company, Sub and Union
          --------------------
Oil, each of the Company, Sub and (to the extent related to the Assets) Union
Oil and the other subsidiaries of Union Oil (i) has complied with, and is in
compliance with, all Applicable Laws (including without limitation Applicable
Laws relating to securities, properties, production, sales, gathering and
transportation of hydrocarbons, occupational safety and health and product
safety), except for matters which would not reasonably be expected to have a
Material Adverse Effect on the Assets or the Company; (ii) has not received any
written notice, which has not been dismissed or otherwise disposed of, that it
has not so complied; (iii) has not been charged or, to the best knowledge of the
Company, Sub and Union Oil, threatened with or under investigation with respect
to any violation of any Applicable Law; and (iv) except for routine orders of
the Texas Railroad Commission, is not a party to or subject to the provisions of
any judgment, order, writ, injunction, decree or award of any court, arbitrator,
board, panel or Governmental Entity.

                                       16
<PAGE>

     3.11 Litigation.  Except as otherwise identified in Section 3.11 of
          ----------
the Union Oil Disclosure Letter, there are no Proceedings pending or, to the
knowledge of the Company, Sub and Union Oil, threatened against or affecting the
Assets, the Company, Sub or any of the Company's properties at law or in equity,
or before or by any Governmental Entity or before any arbitration board or
panel, wherever located, that individually or in the aggregate if adversely
determined would reasonably be expected to have a Material Adverse Effect on the
Company or the Assets, or that involve the risk of criminal liability.

     3.12 Employees; Employee Benefit Plans.
          ---------------------------------

          (a) All "employee benefit plans," as defined in Section 3(3) of ERISA,
     maintained or contributed to by the Company, Sub or its affiliates are in
     compliance with all applicable provisions of ERISA and the Code, and the
     Company, Sub, and its affiliates do not have any liabilities or obligations
     with respect to any such employee benefit plans, whether or not accrued,
     contingent or otherwise, except for instances of noncompliance or
     liabilities or obligations that would not, individually or in the aggregate
     have a Material Adverse Effect on the Company.  Except as set forth in
     Section 3.12 of the Company Disclosure Letter, no employee of the Company
     or Sub will be entitled to any additional benefits or any acceleration of
     the time of payment or vesting of any benefits under any employee incentive
     or benefit plan, program or arrangement as a result of the transactions
     contemplated by this Agreement.

          (b) Neither the Company nor Sub: (i) is a party to or otherwise bound
     by any collective bargaining agreement, contract or other agreement or
     understanding with a labor union or labor organization, nor is any such
     contract or agreement presently being negotiated; (ii) is a party to, or
     bound by, any consent decree with, or citation by, any governmental agency
     relating to employees or employment practices which would reasonably be
     expected to have a Material Adverse Effect on the Company; or (iii) is the
     subject of any proceeding asserting that it has committed an unfair labor
     practice or is seeking to compel it to bargain with any labor union or
     labor organization nor, as of the date of this Agreement, is there pending
     or, to the knowledge of the Company and Union Oil, threatened, any labor
     strike, dispute, walkout, work stoppage, slow-down or lockout involving
     Union Oil with respect to the operation of the Assets which, with respect
     to any event described in this clause (iii), would reasonably be expected
     to have a Material Adverse Effect on the Company.

     3.13 Environmental Matters.  Except as set forth in Section 3.13 of the
          ---------------------
Union Oil Disclosure Letter, and except for matters that would not have a
Material Adverse Effect on the Company or the Assets:  (i) the properties,
operations and activities of the Company and of Union Oil with respect to the
Assets are in compliance with all applicable Environmental Laws; (ii) the
Company and its properties and operations and the Assets and the operations
thereon are not subject to any existing, pending or, to the knowledge of Union
Oil, threatened action, suit, investigation, inquiry or proceeding by or before
any court or Governmental Entity under any Environmental Law; (iii) all Permits,
if any, required to be obtained or filed by Union Oil with respect to the Assets
or by the Company in connection with the business of the Company under any
Environmental Law have been obtained or filed and are valid and currently in
full force and effect; (iv) there has been no

                                       17
<PAGE>

release of any Hazardous Material, pollutant or contaminant into the environment
by Union Oil on or with respect to the Assets or the Company or in connection
with the Company's properties or operations; (v) there has been no exposure of
any Person or property to any Hazardous Material, pollutant or contaminant in
connection with the properties, operations and activities of the Company or the
Assets; and (vi) Union Oil has made available to Titan all internal and external
environmental audits and studies and all correspondence on substantial
environmental matters (in each case relevant to the Company or the Assets) in
the possession of Union Oil.

     3.14 Title to Assets.  Union Oil has, and on the Closing Date the Company
          ---------------
will (subject to Section 2.5) have, good and indefeasible title to the Assets,
subject to Permitted Encumbrances.  Without limiting the generality of the
foregoing, Union Oil has, and on the Closing Date the Company will have,
ownership of each well, unit or lease, royalty interest set forth in Exhibit A
which (i) entitles it to receive, after giving effect to the Permitted
Encumbrances, a decimal share of the oil, gas and other hydrocarbons produced
from such well, unit or lease not less than the decimal share set forth in
Exhibit A as the net revenue interest for such well, unit or lease under the
heading "N.I." and (ii) causes it to be obligated to bear a decimal share of the
cost of operation of such well, unit or lease not greater than the decimal share
set forth in Exhibit A as the working interest for such well, unit or lease
under the heading "W.I.", and such shares of production and shares of expenses
are not subject to change except as indicated on Exhibit A or as a result of
non-consent operations.

     3.15 No Well Abandonments, No P&A Liabilities.  Except as set forth in
          ----------------------------------------
Section 3.15 of the Union Oil Disclosure Letter, to the knowledge of the
Company, Sub and Union Oil, no proposals are currently outstanding (whether made
by Union Oil, the Company or by any other party) to deepen, plug back, rework or
abandon any wells included in the Assets, to conduct other operations with
respect to the Assets for which consent is required under the applicable
operating agreement, or to conduct any other operations with respect to the
Assets other than routine operation of the producing wells located on the
Properties the cost of which, individually, would not exceed $250,000.

     3.16 Production Marketing.  The Assets are not subject to any contractual
          --------------------
or other arrangements for the sale, processing or transportation of production,
or otherwise relating to the marketing of production, other than contracts or
other arrangements which either (i) will terminate in 92 days or less, or are
subject to cancellation on not more than 92 days' notice, in each case without
penalty or other detriment or (ii) are set forth in Section 3.16 of the Union
Oil Disclosure Letter.

     3.17 Gas Balancing, Take or Pay, Allowables.  Except as set forth in
          --------------------------------------
Section 3.17 of the Union Oil Disclosure Letter, as of the date set forth
therein there was no well included in the Assets with respect to which Union Oil
or its subsidiaries has taken more (referred to herein as "overproduced") or
less (referred to herein as "underproduced") production from such well than the
ownership of such party would entitle such party (absent any gas balancing
agreement or arrangement) to receive.  The overproduced and underproduced
positions disclosed in Section 3.17 of the Union Oil Disclosure Letter on a
field by field basis are, in each case, accurate in all material respects as of
the dates shown on such schedule.

                                       18
<PAGE>

     3.18 Leases and Contracts in Force, Operatorship.  The oil, gas and/or
          -------------------------------------------
mineral leases, interests that comprise parts of the Assets, and all other
material contracts and agreements, including but not limited to transportation
agreements, gas contracts, saltwater disposal agreements, road use agreements,
farmin agreements, farmout agreements, unit agreements, pooling agreements,
joint venture agreements, areas of mutual interest, contract alliances, water
injection agreements, line well injection agreements, gas balancing agreements,
and licenses and permits relating to the Assets (such leases and such material
contracts, agreements, licenses, and permits being herein called the "Union Oil
Basic Documents"), are to Union Oil's knowledge, in full force and effect and
constitute valid and binding obligations of the parties thereto, except for such
agreements, licenses and permits that would not have a Material Adverse Effect
on the Assets or the Company, and, to Union Oil's knowledge, all royalties and
other payments have been and are being properly paid thereunder, except for
royalties held in suspense in accordance with applicable law and customary
industry practice and except for such royalties and other payments of which the
failure to pay would not have a Material Adverse Effect on the Assets or the
Company.  Except as set forth in Section 3.18 of the Union Oil Disclosure
Letter, neither Union Oil nor the Company is in breach or default (and, to Union
Oil's knowledge, no situation exists which with the passing of time or giving of
notice would create a breach or default) of its obligations under the Union Oil
Basic Documents, and (to Union Oil's knowledge) no breach or default by any
third party (or situation which with the passage of time or giving of notice
would create a breach or default) exists except for such breaches and defaults
as would not have a Material Adverse Effect on the Assets or the Company.  Union
Oil (as of the date of this Agreement) operates, and (on the Closing Date) the
Company will operate, the Assets shown in Exhibit A as being operated by Union
Oil.

     3.19 Permits.  Except as would not have a Material Adverse Effect on the
          -------
Company or the Assets, Union Oil or one of its subsidiaries, as applicable, has
all Permits necessary or appropriate to own and operate the Assets that it
operates as presently being owned and operated, and such Permits are in full
force and effect, and, except as would not have a Material Adverse Effect on the
Company or the Assets, to Union Oil's knowledge, there have not been any
violations with respect to any such Permits.  The execution and delivery of this
Agreement and the consummation of the transactions contemplated hereby will not
result in any revocation cancellation, suspension or modification of any such
Permit except as would not have a Material Adverse Effect on the Assets or the
Company.

     3.20 Current Commitments.  To Union Oil's and the Company's knowledge,
          -------------------
Section 3.20 of the Union Oil Disclosure Letter contains a true and complete
list as of the date of this Agreement of all authorities for expenditures
("AFEs") to drill or rework any of the Properties, or for other capital
expenditures, involving amounts in excess of $250,000 pursuant to any of the
contracts included in the Assets  for which all of the activities anticipated in
such AFEs or commitments have not been completed by the date of this Agreement.

     3.21 Tax Partnerships.  Except as set forth in Section 3.21 of the Union
          ----------------
Oil Disclosure Letter, to Union Oil's and the Company's knowledge, none of the
Assets is subject to a tax partnership, including, without limitation, any
operating agreement or other arrangement under which the parties thereto have
not made an effective election pursuant to Section 761 of the Code,

                                       19
<PAGE>

and the Treasury Regulations promulgated thereunder, to be excluded from the
application of Subchapter K, Chapter 1, Subtitle A, of the Code.

     3.22  No Demands.  Except as set forth in Section 3.22 of the Union Oil
           ----------
Disclosure Letter, neither Union Oil nor the Company has received any notice of
any claimed defaults, offsets or cancellations from any lessors with respect to
the Assets, and to the best knowledge of the Company and Union Oil, there exists
no default existing with respect to any of the Assets or any express or implied
term of any Asset.

     3.23  No Other Activities.  Except as contemplated by this Agreement, the
           -------------------
Company has not engaged in any material business activity.

     3.24  Liability for Brokers' Fees.  No broker, finder or investment banker
           ---------------------------
(other than Donaldson, Lufkin & Jenrette, the fees and expenses of which will be
paid by Union Oil) is entitled to any brokerage, finder's fee or other fee or
commission payable by the Company, Union Oil, its parent or any of Union Oil's
subsidiaries in connection with the transactions contemplated by this Agreement
based upon arrangements made by or on behalf of Union Oil or any of its
subsidiaries or its parent.

     3.25  Registration Statement and Proxy Statement/Prospectus Information.
           -----------------------------------------------------------------
None of the information furnished by Union Oil or the Company for inclusion in
the Registration Statement and Proxy Statement/Prospectus, at the time the
Registration Statement becomes effective or the Proxy Statement/Prospectus is
first mailed to Titan's stockholders or at the time Titan's stockholders vote on
the transaction or at the Closing Date, will contain any untrue statement of a
material fact or omit to state any material fact required to be stated therein
or necessary in order to make the statements contained therein, in light of the
circumstances under which they are made, not misleading.


                                  ARTICLE IV

                    REPRESENTATIONS AND WARRANTIES OF TITAN

    Titan represents and warrants to, Union Oil, the Company and Sub that:

     4.1   Organization and Compliance with Law.  Each of Titan and its
           ------------------------------------
consolidated subsidiaries (the "Titan Subsidiaries") is a corporation or
partnership duly organized, validly existing and, to the extent applicable, in
good standing under the laws of the jurisdiction in which it is chartered or
organized and has all requisite corporate or partnership power and corporate or
partnership authority and all necessary governmental authorizations to own,
lease and operate all of its properties and assets and to carry on its business
as now being conducted, except where the failure to be so organized, existing or
in good standing or to have such authority would not reasonably be expected to
have a Material Adverse Effect on Titan and the Titan Subsidiaries. Except as
set forth in Section 4.1(a) of the disclosure letter delivered by Titan to Union
Oil and the Company the date hereof (the "Titan Disclosure Letter"), each of
Titan and the Titan Subsidiaries is duly qualified as a foreign corporation or
partnership to do business, and, to the extent applicable, is in good standing,

                                       20
<PAGE>

in each jurisdiction in which the property owned, leased or operated by it or
the nature of the business conducted by it makes such qualification necessary,
except in such jurisdictions where the failure to be duly qualified does not and
would not, either individually or in the aggregate, reasonably be expected to
have a Material Adverse Effect on Titan and the Titan Subsidiaries. Each of
Titan and the Titan Subsidiaries is in compliance with all applicable laws,
judgments, orders, rules and regulations, domestic and foreign, except where
failure to be in such compliance would not reasonably be expected to have a
Material Adverse Effect on Titan and the Titan Subsidiaries, taken as a whole.
Except as set forth in Section 4.1(b) of the Titan Disclosure Schedule, no
action or proceedings to dissolve Titan or any Titan Subsidiary are pending.
Titan has heretofore made available to Union Oil true and complete copies of (i)
Titan's Certificate of Incorporation, as amended, and bylaws as in existence on
the date hereof and (ii) the minutes of all meetings of the Board of Director of
Titan, and committees of such Board, and the stockholders of Titan. Other than
the Titan Subsidiaries, Titan does not beneficially own or control, directly or
indirectly, 5% or more of any class of equity or similar securities of any
person, whether incorporated or unincorporated.

     4.2   Capitalization.
           --------------

           (a)   The authorized capital stock of Titan consists of 60,000,000
     shares of Titan Common Stock and 10,000,000 shares of preferred stock, par
     value $.01 per share (of which 515,000 shares are designated as Series A
     Junior Participating Preferred Stock). As of the date of this Agreement,
     there were issued and outstanding 40,189,843 shares of Titan Common Stock,
     3,804,000 shares of Titan Common Stock were held as treasury shares and no
     shares of Series A Junior Participating Preferred Stock were outstanding
     (all of which shares of Series A Junior Participating Preferred Stock are
     reserved for issuance in accordance with the Rights Agreement (the "Titan
     Rights Agreement"), dated as of June 10, 1999, between Titan and First
     Union National Bank, as Rights Agent, as amended, pursuant to which Titan
     has issued rights ("Titan Rights") to purchase the Series A Junior
     Participating Preferred Stock). As of the date of this Agreement, an
     aggregate of 1,133,175 shares of Titan Common Stock were reserved for
     issuance and issuable pursuant to the Titan Exploration, Inc. Option Plan,
     1996 Incentive Plan and 1999 Non-Officer Stock Option Plan and the Offshore
     Energy Development Corporation 1996 Stock Awards Plan or upon the exercise
     of outstanding employee or non-employee director stock options granted
     under Titan's stock option plans and agreements. All issued shares of Titan
     Common Stock are validly issued, fully paid and nonassessable and were not
     issued in violation of any preemptive rights. Except as contemplated by
     this Agreement or set forth in Section 4.2(a) of the Titan Disclosure
     Schedule, Titan is not a party to, and is not aware of, any voting
     agreement, voting trust or similar agreement or arrangement relating to any
     class or series of its capital stock, or any agreement or arrangement
     providing for registration rights with respect to any capital stock or
     other securities of Titan or any Common Stock issuable in respect of
     securities of Titan upon consummation of the Merger.

          (b)   As of the date of this Agreement, there were outstanding options
     to purchase 1,067,743 shares of Titan Common Stock pursuant to the plans
     referenced in Section 4.2(a) above (the "Titan Options"). Other than as set
     forth in this Section 4.2 and except for issuances contemplated by this
     Agreement, there are not now, and at the Closing Date there

                                       21
<PAGE>

     will not be, any (A) shares of capital stock or other equity securities of
     Titan outstanding (other than Titan Common Stock issued pursuant to the
     exercise of Titan Options as described herein) or (B) except for (i)
     options granted pursuant to any of the plans referenced above, and (ii) the
     Titan Rights Agreement, outstanding options, warrants, scrip, rights to
     subscribe for, calls or commitments of any character whatsoever relating
     to, or securities or rights convertible into or exchangeable for, shares of
     any class of capital stock of Titan, or contracts, understandings or
     arrangements to which Titan is a party, or by which it is or may be bound,
     to issue, transfer, sell, redeem or repurchase shares of its capital stock
     or options, warrants, scrip or rights to subscribe for, or securities or
     rights convertible into or exchangeable for, any additional shares of its
     capital stock.

          (c)   Except as set forth in Section 4.2 of the Titan Disclosure
     Letter, all outstanding shares of capital stock of the Titan Subsidiaries
     are validly issued, fully paid and nonassessable and are owned by Titan or
     a wholly-owned subsidiary of Titan. As of the date of this Agreement, there
     were no outstanding options, warrants, scrip, rights to subscribe for,
     calls or commitments of any character whatsoever relating to, or securities
     or rights convertible into or exchangeable for, shares of any class of
     capital stock of any Titan Subsidiary, or contracts, understandings or
     arrangements to which any Titan Subsidiary is a party, or by which it is or
     may be bound, to issue, transfer, sell, redeem or repurchase shares of its
     capital stock or options, warrants, scrip or rights to subscribe for, or
     securities or rights convertible into or exchangeable for, any additional
     shares of capital stock of any Titan Subsidiary.

     4.3   Authorization and Validity of Agreement.  Titan has all requisite
           ---------------------------------------
corporate power and authority to enter into this Agreement and to perform its
obligations hereunder, and the execution and delivery by Titan of this Agreement
and the consummation by it of the transactions contemplated hereby have been
duly authorized by all necessary corporate action (subject only to the approval
thereof by the stockholders of Titan described in Section 6.4 ("Stockholder
Approval")). On or prior to the date of this Agreement, (i) the Board of
Directors of Titan has received an opinion of Petrie Parkman & Co. dated the
date hereof to the effect that the Exchange Ratio is fair, from a financial
point of view, to the stockholders of Titan (a copy of which opinion has been
delivered to Union Oil), and (ii) the Board of Directors of Titan has
unanimously determined to recommend the approval of the transaction to the
stockholders of Titan, and such determination is in effect as of the date
hereof. This Agreement has been duly executed and delivered by Titan and
constitutes, and each other agreement, instrument or document executed or to be
executed by Titan in connection with the transactions contemplated hereby has
been, or when executed will be, duly executed and delivered by Titan and
constitutes, or when executed and delivered will constitute, the valid and
binding obligation of Titan, enforceable against Titan, in accordance with their
respective terms, except that such enforceability may be limited by (i)
applicable bankruptcy, insolvency, reorganization, moratorium and similar laws
affecting creditors' rights generally and (ii) equitable principles which may
limit the availability of certain equitable remedies (such as specific
performance) in certain instances.

     4.4   Approvals; No Conflict.  Subject to Stockholder Approval, neither the
           ----------------------
execution and delivery of this Agreement nor the performance by Titan of its
obligations hereunder, nor the

                                       22
<PAGE>

consummation of the transactions contemplated hereby by Titan, will (i) conflict
with the charter or bylaws, or partnership or joint venture agreement, of Titan
or of any of the Titan Subsidiaries; (ii) assuming satisfaction of the
requirements set forth in clause (iii) below, violate any provision of law
applicable to Titan or any of the Titan Subsidiaries; (iii) except for (A)
requirements of federal or state securities laws and (B) requirements arising
out of the HSR Act, if applicable, require any consent or approval of, or filing
with or notice to, any Governmental Entity, domestic or foreign, under any
provision of law applicable to Titan or any of the Titan Subsidiaries; or (iv)
except as set forth in Section 4.4 of the Titan Disclosure Letter, require any
consent, approval or notice under, or violate, breach, be in conflict with or
constitute a default (or any event that, with notice or lapse of time or both,
would constitute a default) under, or permit the termination of any provision
of, or result in the creation or imposition of any lien upon any properties,
assets or business of Titan or any of the Titan Subsidiaries under, any note,
bond, indenture, mortgage, deed of trust, lease, franchise, permit,
authorization, license, contract, instrument, partnership agreement or other
agreement or commitment or any order, judgment or decree to which such entity is
a party or by which it or any of its assets or properties is bound or
encumbered, except (A) those that have already been given, obtained or filed,
(B) those that are required pursuant to bank loan agreements, which will be
obtained prior to the Closing Date, and (C) those that if not obtained, in the
aggregate, would not reasonably be expected to have a Material Adverse Effect on
the Surviving Corporation. No property of Titan or any of the Titan Subsidiaries
is subject to a preferential right to purchase that is applicable to the
transactions contemplated by this Agreement, except for such rights that, in the
aggregate and if exercised, would not have a Material Adverse Effect on Titan
following the Merger .

     4.5   Commission Filings; Financial Statements.
           ----------------------------------------

           (a)  Titan and each of the Titan Subsidiaries have filed all reports,
     registration statements and other filings, together with any amendments
     required to be made with respect thereto, that they have been required to
     file with the Commission under the Securities Act and the Exchange Act. All
     reports, registration statements and other filings (including all notes,
     exhibits and schedules thereto and documents incorporated by reference
     therein) filed by Titan with the Commission since December 31, 1996,
     through the date of this Agreement, together with any amendments thereto,
     are sometimes collectively referred to as the "Titan Commission Filings."
     As of the respective dates of their filing with the Commission, the Titan
     Commission Filings complied in all material respects with the Securities
     Act, the Exchange Act and the rules and regulations of the Commission
     thereunder, and did not contain any untrue statement of a material fact or
     omit to state a material fact required to be stated therein or necessary to
     make the statements made therein, in light of the circumstances under which
     they were made, not misleading.

          (b)   Each of the consolidated financial statements (including any
     related notes or schedules) included in the Titan Commission Filings was
     prepared in accordance with GAAP applied on a consistent basis (except as
     may be noted therein or in the notes or schedules thereto) and complied
     with all applicable rules and regulations of the Commission. Such
     consolidated financial statements fairly present the consolidated financial
     position of Titan and the Titan Subsidiaries as of the dates thereof and
     the results of operations, cash flows and changes in shareholders' equity
     for the periods then ended (subject, in the case of the

                                       23
<PAGE>

     unaudited interim financial statements, to normal year-end audit
     adjustments on a basis comparable with past periods).

     4.6   Absence of Undisclosed Liabilities.  Neither Titan nor any Titan
           ----------------------------------
Subsidiary has any liabilities or obligations of the type required to be
reflected on the financial statements of Titan included in the Commission
Filings, except (i) liabilities which have arisen in the ordinary course of
business, (ii) liabilities arising under contracts entered into in the ordinary
course of business and (iii) other liabilities which, in the aggregate, would
not have a Material Adverse Effect on Titan.

     4.7   Absence of Certain Changes.  Except as set forth in Section 4.7 of
           --------------------------
the Titan Disclosure Letter or (with respect to the period from the date of this
Agreement to and including the Closing) as contemplated by this Agreement, since
September 30, 1999, (i) there has not been any change, development, or effect on
Titan or the Titan Subsidiaries, individually or in the aggregate, that has had,
or might reasonably be expected to have, a Material Adverse Effect on Titan;
(ii) the business of Titan has been conducted in the ordinary course consistent
with past practice; (iii) neither Titan nor any Titan Subsidiary has incurred
any material liability or engaged in any transaction or entered into any
agreement outside the ordinary course of business consistent with past practice;
(iv) neither Titan nor any Titan Subsidiary has suffered any loss, damage,
destruction or other casualty to any of its assets (whether or not covered by
insurance) which has had, or might reasonably be expected to have, a Material
Adverse Effect on Titan; and (v) neither Titan nor any Titan Subsidiary has
taken any action that would not be permitted to be taken by such entity under
Section 5.2.

     4.8  Tax Matters.
          -----------

          (a)  Except as set forth in Section 4.8 of the Titan Disclosure
Schedule, Titan and the Titan Subsidiaries have timely filed, or has had filed
on its behalf in a timely manner (within any applicable extension periods), with
the appropriate Taxing Authority all Tax Returns with respect to Taxes of Titan
and each of the Titan Subsidiaries, other than those returns on which an
immaterial amount of Taxes would properly be shown the failure of which to file
would not have a Material Adverse Effect on Titan.  All such Tax Returns were
correct and complete in all material respects.  All Taxes, including interest
and penalties, owed by Titan and the Titan Subsidiaries (whether or not shown on
any Tax Return) have been or will be paid.

          (b)  Except as set forth in Section 4.8 of the Titan Disclosure
Schedule, all ad valorem, property, production, severance and similar Taxes and
assessments based on or measured by the ownership of property or the production
or removal of hydrocarbons or the receipt of proceeds therefrom and relating to
the assets of Titan and the Titan Subsidiaries, to the extent such Taxes and
assessments have become due and payable, have been timely paid and all
applicable Tax Returns required to be filed have been filed and there are no
claims by any applicable Taxing Authority pending against Titan and the Titan
Subsidiaries applicable to the assets of Titan and the Titan Subsidiaries

                                       24
<PAGE>

          (c)   All Taxes shown to be due and payable on all filed Tax Returns
of or with respect to Titan and the Titan Subsidiaries have been paid in full or
have been provided for in Titan's filings with the Commission in accordance with
GAAP.

          (d)   Except as set forth in Section 4.8 of the Titan Disclosure
Schedule, there are no outstanding agreements or waivers extending the statutory
period of limitations applicable to any federal, state, local or foreign income
or other material Tax Returns required to be filed by or with respect to Titan
or any of the Titan Subsidiaries.

          (e)   Except as set forth in Section 4.8 of the Titan Disclosure
Schedule, none of the Tax Returns of or with respect to Titan or any of the
Titan Subsidiaries is currently being audited or examined by any Taxing
Authority; and no material claim has ever been made by an authority in a
jurisdiction where Titan and the Titan Subsidiaries do not file Tax Returns that
such parties are or may be subject to taxation by that jurisdiction.

          (f)   There is no material claim against Titan or any of the Titan
Subsidiaries with respect to any Taxes, and no material assessment, deficiency
or adjustment has been asserted or proposed with respect to any Tax Return of or
with respect to Titan or any of the Titan Subsidiaries that has not been
adequately provided for in reserves established by Titan or any of the Titan
Subsidiaries. Titan and the Titan Subsidiaries have (and as of the Closing Date
will have) made all deposits required with respect to Taxes.

          (g)   Except as set forth in Section 4.8 of the Titan Disclosure
Schedule, there are no liens on any of the assets of Titan or any of the Titan
Subsidiaries that arose in connection with any failure (or alleged failure) to
pay any Tax, other than liens for Taxes not yet due.

          (h)   Except as set forth in Section 4.8 of the Titan Disclosure
Schedule, the unpaid Taxes of Titan and the Titan Subsidiaries (A) did not
exceed the reserve for Tax Liability (rather than any reserve for deferred taxes
established to reflect timing differences between book and tax income) set forth
on the face of the most recent financial statements of Titan included in the
Titan Commission Filings (rather than in any notes thereto) and (B) will not
exceed by any material amount that reserve as adjusted for operations and
transactions through the Closing Date in accordance with past custom and
practice of Titan and the Titan Subsidiaries in filing their Tax Returns.

     4.9  Compliance With Laws.  To the knowledge of Titan, each of Titan and
          --------------------
Titan Subsidiaries (i) has complied with, and is in compliance with, all
Applicable Laws (including without limitation Applicable Laws relating to
securities, properties, production, sales, gathering and transportation of
hydrocarbons, occupational safety and health and product safety), except for
matters which would not reasonably be expected to have a Material Adverse Effect
on Titan; (ii) has not received any written notice, which has not been dismissed
or otherwise disposed of, that it has not so complied; (iii) has not been
charged or, to the best knowledge of Titan, threatened with or under
investigation with respect to any violation of any Applicable Law; and (iv)
except for routine orders of the Texas Railroad Commission, is not a party to or
subject to the provisions of any judgment, order, writ, injunction, decree or
award of any court, arbitrator, board, panel or Governmental Entity.

                                       25
<PAGE>

     4.10  Litigation.  Except as disclosed in the Titan Commission Filings or
           ----------
as set forth in Section 4.10 of the Titan Disclosure Letter, there are no
Proceedings pending or, to the knowledge of Titan, threatened against or
affecting Titan or any of the Titan Subsidiaries or any of their respective
properties at law or in equity, or before or by any Governmental Entity, or
before any arbitration board or panel, wherever located, that individually or in
the aggregate if adversely deter mined would reasonably be expected to have a
Material Adverse Effect on Titan, or that involve the risk of criminal
liability.

     4.11  Voting Requirements.  The affirmative vote of the holders of a
           -------------------
majority of the outstanding shares of Titan Common Stock and the affirmative
vote of the holders of a majority of the shares of Titan Common Stock, other
than shares held by officers of Titan, present at the Titan special
stockholders' meeting convened in accordance with Section 6.4 and entitled to
vote thereon are the only votes of the holders of any class or series of the
capital stock of Titan necessary to approve this Agreement.

     4.12  Employees; Employee Benefit Plans.
           ---------------------------------

           (a)  All "employee benefit plans," as defined in Section 3(3) of
     ERISA, maintained or contributed to by Titan or the Titan Subsidiaries are
     in compliance with all applicable provisions of ERISA and the Code, and
     Titan and the Titan Subsidiaries do not have any liabilities or obligations
     with respect to any such employee benefit plans, whether or not accrued,
     contingent or otherwise, except for instances of noncompliance or
     liabilities or obligations that would not, individually or in the
     aggregate, have a Material Adverse Effect on Titan. Except as set forth in
     Section 4.12 of the Titan Disclosure Letter, no employee of Titan or any of
     the Titan Subsidiaries will be entitled to any additional benefits or any
     acceleration of the time of payment or vesting of any benefits under any
     employee incentive or benefit plan, program or arrangement as a result of
     the transactions contemplated by this Agreement.

          (b)   Neither Titan nor any of the Titan Subsidiaries: (i) is a party
     to or otherwise bound by any collective bargaining agreement, contract or
     other agreement or understanding with a labor union or labor organization,
     nor is any such contract or agreement presently being negotiated, nor is
     there, nor has there been in the last five years, a representation question
     respecting any of the employees of Titan or the Titan Subsidiaries, and, to
     the knowledge of Titan, there are no campaigns being conducted to solicit
     cards from employees of Titan or the Titan Subsidiaries to authorize
     representation by any labor organization; (ii) is a party to, or bound by,
     any consent decree with, or citation by, any governmental agency relating
     to employees or employment practices which would reasonably be expected to
     have a Material Adverse Effect on Titan; or (iii) is the subject of any
     proceeding asserting that it has committed an unfair labor practice or is
     seeking to compel it to bargain with any labor union or labor organization
     nor, as of the date of this Agreement, is there pending or, to the
     knowledge of Titan, threatened, any labor strike, dispute, walkout, work
     stoppage, slow-down or lockout involving Titan or any of the Titan
     Subsidiaries which, with respect to any event described in this clause
     (iii), would reasonably be expected to have a Material Adverse Effect on
     Titan.

                                       26
<PAGE>

     4.13  Environmental Matters.  Except as set forth in Section 4.13 of the
           ---------------------
Titan Disclosure Letter and except for matters that would not have a Material
Adverse Effect on Titan: (i) the properties, operations and activities of Titan
and the Titan Subsidiaries are in compliance with all applicable Environmental
Laws; (ii) Titan, the Titan Subsidiaries and their properties and operations and
the operations thereon are not subject to any existing, pending or, to the
knowledge of Titan, threatened action, suit, investigation, inquiry or
proceeding by or before any court or Governmental Entity under any Environmental
Law; (iii) all Permits, if any, required to be obtained or filed by Titan and
the Titan Subsidiaries in connection with the business of Titan and the Titan
Subsidiaries under any Environmental Law have been obtained or filed and are
valid and currently in full force and effect; (iv) there has been no release of
any Hazardous Material, pollutant or contaminant into the environment by Titan
or the Titan Subsidiaries or in connection with their properties or operations;
(v) there has been no exposure of any Person or property to any Hazardous
Material, pollutant or contaminant in connection with the properties, operations
and activities of Titan or the Titan Subsidiaries; and (vi) Titan and the Titan
Subsidiaries have made available to Union Oil all internal and external
environmental audits and studies and all correspondence on substantial
environmental matters in the possession of Titan and the Titan Subsidiaries.

     4.14  Title to Assets.  Each of Titan and the Titan Subsidiaries has, and
           ---------------
on the Closing Date will have, good and indefeasible title to its assets.
Without limiting the generality of the foregoing, each of Titan and the Titan
Subsidiaries has, and on the Closing Date will have, ownership of each well,
unit, lease or royalty interest set forth in Section 4.14 of the Titan
Disclosure Schedule which (i) entitles it to receive, after giving effect to the
Permitted Encumbrances, a decimal share of the oil, gas and other hydrocarbons
produced from such well, unit or lease not less than the decimal share set forth
in Section 4.14 of the Titan Disclosure Schedule as the "Net Revenue Interest"
for such well, unit or lease and (ii) causes it to be obligated to bear a
decimal share of the cost of operation of such well, unit or lease not greater
than the decimal share set forth in Section 4.14 of the Titan Disclosure
Schedule as the "Working Interest" for such well, unit or lease, and such shares
of production and shares of expenses are not subject to change except as
indicated in Section 4.14 of the Titan Disclosure Schedule or as a result of
non-consent operations.

     4.15  No Well Abandonments, No P&A Liabilities.  Except as set forth in
           ----------------------------------------
Section 4.15 of the Titan Disclosure Letter, to the knowledge of Titan, no
proposals are currently outstanding (whether made by Titan, the Titan
Subsidiaries or by any other party) to deepen, plug back, rework or abandon any
wells included in the assets of Titan and the Titan Subsidiaries, to conduct
other operations with respect to the assets of Titan and the Titan Subsidiaries
for which consent is required under the applicable operating agreement, or to
conduct any other operations with respect to the assets of Titan and the Titan
Subsidiaries other than routine operation of the producing wells located on the
Properties the cost of which, individually, would not exceed $250,000.

     4.16  Production Marketing.  The assets of Titan and the Titan Subsidiaries
           --------------------
are not subject to any contractual or other arrangements for the sale,
processing or transportation of production, or otherwise relating to the
marketing of production, other than contracts or other arrangements which either
(i) will terminate in 92 days or less, or are subject to cancellation on not
more than 92 days' notice, in each case without penalty or other detriment or
(ii) are set forth in Section 4.16 of the Titan Disclosure Letter.

                                       27
<PAGE>

     4.17  Gas Balancing, Take or Pay, Allowables.  Except as set forth in
           --------------------------------------
Section 4.17 of the Titan Disclosure Letter, as of the date set forth therein
there was no well included in the assets of Titan and the Titan Subsidiaries
with respect to which Titan, or the Titan Subsidiaries, has taken more (referred
to herein as "overproduced") or less (referred to herein as "underproduced")
production from such well than the ownership of such party would entitle such
party (absent any gas balancing agreement or arrangement) to receive. The
overproduced and underproduced positions disclosed in Section 4.17 of the Titan
Disclosure Letter are on a field by field basis, in each case, accurate in all
material respects as of the dates shown on such schedule.

     4.18  Leases and Contracts in Force, Operatorship.  The oil, gas and/or
           -------------------------------------------
mineral leases, interests, and all other material contracts and agreements,
including but not limited to transportation agreements, gas contracts, saltwater
disposal agreements, road use agreements, farmin agreements, farmout agreements,
unit agreements, pooling agreements, joint venture agreements, areas of mutual
interest, contract alliances, water injection agreements, line well injection
agreements, gas balancing agreements, and licenses and permits relating to such
assets of Titan and the Titan Subsidiaries (such leases and such material
contracts, agreements, licenses, and permits being herein called the "Titan
Basic Documents"), are to Titan's knowledge, in full force and effect and
constitute valid and binding obligations of the parties thereto, except for such
agreements, licenses and permits that would not have a Material Adverse Effect
on Titan, and, to Titan's knowledge, all royalties and other payments have been
and are being properly paid thereunder, except for royalties held in suspense in
accordance with applicable law and customary industry practice and except for
such royalties and other payments of which the failure to pay would not have a
Material Adverse Effect on Titan. Neither Titan nor any of the Titan
Subsidiaries is in breach or default (and, to Titan's knowledge, no situation
exists which with the passing of time or giving of notice would create a breach
or default) of its obligations under the Titan Basic Documents, and (to Titan's
knowledge) no breach or default by any third party (or situation which with the
passage of time or giving of notice would create a breach or default) exists
except for such breaches and defaults as would not have a Material Adverse
Effect on Titan. Titan, or the Titan Subsidiaries (as of the date of this
Agreement), operates, and (on the Closing Date) Titan, or the Titan
Subsidiaries, will operate, the assets shown in Section 4.14 of the Titan
Disclosure Letter as being operated by Titan or the Titan Subsidiaries.

     4.19  Permits.  Except as would not have a Material Adverse Effect on
           -------
Titan, Titan or one of the Titan Subsidiaries, as applicable, has all Permits
necessary or appropriate to own and operate the assets that they operate as
presently being owned and operated, and such Permits are in full force and
effect, and, except as would not have a Material Adverse Effect on Titan, to
Titan's knowledge, there have not been any violations with respect to any such
Permits. Such Permits are in full force and effect, and to the knowledge of
Titan, there have not been any material violations with respect to any such
Permits. The execution and delivery of this Agreement and the consummation of
the transactions contemplated hereby will not result in any revocation
cancellation, suspension or modification of any such Permit except as would not
have a Material Adverse Effect on Titan.

     4.20  Current Commitments.  To Titan's knowledge, Section 4.20 of the Titan
           -------------------
Disclosure Letter contains a true and complete list as of the date of this
Agreement of all AFEs to drill or rework any of the properties of Titan and the
Titan Subsidiaries, or for other capital expenditures, involving amounts in
excess of $250,000 pursuant to any of the contracts included in the assets of
Titan and

                                       28
<PAGE>

the Titan Subsidiaries for which all of the activities anticipated in such AFEs
or commitments have not been completed by the date of this Agreement.

     4.21  Tax Partnerships.  Except as set forth in Section 4.21 of the Titan
           ----------------
Disclosure Letter, to Titan's knowledge, none of the assets of Titan or the
Titan Subsidiaries is subject to a tax partnership, including, without
limitation, any operating agreement or other arrangement under which the parties
thereto have not made an effective election pursuant to Section 761 of the Code,
and the Treasury Regulations promulgated thereunder, to be excluded from the
application of Subchapter K, Chapter 1, Subtitle A, of the Code.

     4.22  Liability for Brokers' Fees.  No broker, finder or investment banker
           ---------------------------
(other than Petrie Parkman & Co., Inc., the fees and expenses of which will be
paid by Titan) is entitled to any brokerage, finder's fee or other fee or
commission payable by Titan or any of the Titan Subsidiaries in connection with
the transactions contemplated by this Agreement based upon arrangements made by
or on behalf of Titan or any of the Titan Subsidiaries. True and correct copies
of all agreements and engagement letters currently in effect with Petrie Parkman
& Co., Inc. (the "Titan Engagement Letters") have been provided to Union Oil.

     4.23  Anti-Takeover Provisions.  Titan and the Board of Directors of Titan
           ------------------------
have each taken all action required to be taken by it in order to exempt this
Agreement, and the transactions contemplated hereby from, and this Agreement and
the transactions contemplated hereby are exempt from, the requirements of any
"moratorium," "control share," "fair price," "affiliate transaction," "business
combination" or other antitakeover laws and regulations of any state, including,
without limitation, the State of Delaware, and including, without limitation,
Section 203 of the DGCL. Neither the execution of this Agreement, the Voting
Agreement, the Stockholders Voting Agreement nor the consummation of any of the
transactions contemplated hereby or thereby will trigger any event under the
Titan Rights Agreement or result in any adverse consequence to Union Oil
thereunder. Titan has taken all action that may be necessary under the Titan
Rights Agreement so that (i) the execution of this Agreement, the Voting
Agreement, the Stockholders Voting Agreement or the consummation of any of the
transactions contemplated hereby or thereby shall not cause (A) Union Oil, the
Company or Sub to become an Acquiring Person (as defined in the Rights
Agreement), (B) a Distribution Date (as defined in the Titan Rights Agreement)
to occur, (C) a Flip-In Event (as defined in the Titan Rights Agreement) to
occur or (D) a Flip-Over Event (as defined in the Titan Rights Agreement) to
occur and (ii) the Rights Agreement is otherwise inapplicable to this Agreement
and the transactions contemplated hereby, including the Merger.

     4.24  Dissenters' Rights.  No holder of Titan Common Stock is entitled to
           ------------------
dissenters' rights of appraisal under the DGCL in connection with the Merger.

     4.25  Certain Discussions.  Titan has disclosed to Union Oil all
           -------------------
discussions it has had with any person relating to an Acquisition Proposal (as
defined in Section 6.2) since June 1, 1999.

     4.26  Registration Statement and Proxy Statement/Prospectus Information.
           -----------------------------------------------------------------
None of the information furnished by Titan for inclusion in the Registration
Statement and Proxy Statement/Prospectus, at the time the Registration Statement
becomes effective or the Proxy

                                       29
<PAGE>

Statement/Prospectus is first mailed to Titan's stockholders or at the time
Titan's stockholders vote on the Transaction or at the Closing Date, will
contain any untrue statement of a material fact or omit to state any material
fact required to be stated therein or necessary in order to make the statements
contained therein, in light of the circumstances under which they are made, not
misleading.


                                   ARTICLE V

                            CONDUCT PENDING CLOSING

     5.1  Conduct and Preservation of Business.  Union Oil and the Company
          ------------------------------------
covenant and agree as follows:

          (a)  Except as expressly provided in this Agreement, during the period
     from the date hereof to the Closing Date, Union Oil shall (i) conduct the
     operations of the Business according to the ordinary course of business
     consistent with past practice and in compliance with all Applicable Laws,
     (ii) use its reasonable efforts to preserve, maintain and protect the
     Assets and (iii) use its reasonable efforts to preserve intact the Business
     and, with respect to the Business, to keep available the services of its
     employees and to maintain existing relationships with licensors, licensees,
     suppliers, contractors, distributors, customers and others having business
     relationships with it.

          (b)  Except as otherwise expressly provided in this Agreement or as
     otherwise required by law, prior to the Closing Date, without the prior
     written consent of Titan, the Company shall not and shall not permit its
     subsidiaries, if any, to, and Union Oil shall not permit the Company or any
     subsidiary of the Company to, take any action other than as contemplated by
     this Agreement.

          (c)  Except as otherwise expressly provided in this Agreement, prior
     to the Closing Date, without the prior written consent of Titan, Union Oil
     shall not and shall not permit any of its other subsidiaries to:

               (i)   (A) create, incur, guarantee, or assume any indebtedness
          for borrowed money that will be assumed by the Company or (B) mortgage
          or pledge any of the Assets or create or suffer to exist any
          Encumbrance thereupon, other than the Permitted Encumbrances;

               (ii)  sell, lease, transfer, or otherwise dispose of, directly or
          indirectly, any of the Assets other than in the ordinary course of the
          Business consistent with past practice;

               (iii) for any quarter beginning on or after January 1, 2000,
          make any capital expenditure or expenditures relating to the Assets
          which, individually, is in excess of $3,500,000 or, in the aggregate,
          are in excess of the greater of $37,000,000

                                       30
<PAGE>

          or the total amount of cash flow relating to the Assets for the
          preceding quarter, except for expenditures approved by Titan;

               (iv)   make any Tax election material to the Company other than
          as contemplated by this Agreement;

               (v)    pay, discharge or satisfy any claims, liabilities or
          obligations relating to the Business (whether accrued, absolute,
          contingent, unliquidated or otherwise, and whether asserted or
          unasserted), other than the payment, discharge or satisfaction in the
          ordinary course of the Business consistent with past practice, or in
          accordance with their terms, of liabilities reflected or reserved
          against in the Balance Sheet or incurred since September 30, 1999, in
          the ordinary course of the Business consistent with past practice;

               (vi)   enter into any lease, contract, agreement, commitment,
          arrangement or transaction that is or will be part of the Assets,
          except in the ordinary course of the Business consistent with past
          practice;

               (vii)  amend, modify or change any lease, contract or agreement
          that is or will be part of the Assets outside of the ordinary course
          of the Business consistent with past practice;

               (viii) change any of the accounting principles or practices used
          by it relating to the Business, except for any change required by
          reason of a concurrent change in GAAP and notice of which is given in
          writing by Union Oil to Titan;

               (ix)   waive, release, grant or transfer any rights of value that
          are or will be part of the Assets, other than in the ordinary course
          of the Business consistent with past practice;

               (x)    take any action that would, or that reasonably could be
          expected to, result in any of the representations and warranties set
          forth in Article III becoming untrue or any material breach of this
          Agreement; or

               (xi)   authorize or propose, or agree in writing or otherwise to
          take, any of the actions described in this Section 5.1.

     5.2  Conduct and Preservation of Business of Titan.  Titan covenants and
          ---------------------------------------------
agrees as follows:

          (a) Except as expressly provided in this Agreement, during the period
     from the date hereof to the Closing Date, Titan shall, and shall cause each
     of the Titan Subsidiaries to,  (i) conduct its operations according to the
     ordinary course of business consistent with past practice and in compliance
     with all Applicable Laws, (ii) use its reasonable efforts to preserve,
     maintain and protect its properties and (iii)  use its reasonable efforts
     to preserve

                                       31
<PAGE>

     intact its business organization, to keep available the services of its
     officers and employees and to maintain existing relationships with
     licensors, licensees, suppliers, contractors, distributors, customers and
     others having business relationships with it.

          (b)  Except as otherwise expressly provided in this Agreement, prior
     to the Closing Date, without the prior written consent of Union Oil, Titan
     shall not and shall not permit any of the Titan Subsidiaries to:

               (i)   amend its charter, bylaws or other organizational document;

               (ii)  issue, sell or deliver (whether through the issuance or
          granting of options, warrants, commitments, subscriptions, rights to
          purchase or otherwise) any shares of its capital stock of any class,
          except upon the exercise of employee stock options outstanding on the
          date of this Agreement or any other securities or equity equivalents,
          or amend in any material respect any of the terms of any such
          securities outstanding as of the date hereof;

               (iii) (A) split, combine or reclassify any shares of its capital
          stock; (B) declare, set aside or pay any dividend or other
          distribution (whether in cash, stock or property or any combination
          thereof) in respect of its capital stock; (C) repurchase, redeem or
          otherwise acquire any of its securities; or (D) adopt a plan of
          complete or partial liquidation or resolutions providing for or
          authorizing a liquidation, dissolution, merger, consolidation,
          restructuring, recapitalization or other reorganization of Titan or
          any Titan Subsidiary;

               (iv)  (A) except for amounts borrowed under Titan's $5,000,000
          unsecured credit facility and amounts borrowed to fund severance
          obligations that will accrue as a result of the consummation of this
          Agreement, create, incur, guarantee or assume any indebtedness for
          borrowed money or otherwise become liable or responsible for the
          obligations of any other person in an aggregate amount in excess of
          $10,000,000, (B) make any loans, advances or capital contributions to,
          or investments in, any other person (other than to the wholly-owned
          Titan Subsidiaries and customary loans or advances to employees in
          amounts not material to the maker of such loan or advance), or (C)
          mortgage or pledge any of its material assets, tangible or intangible,
          or create any material lien thereupon;

               (v)   (A) enter into, adopt or (except as may be required by law)
          amend or terminate any bonus, profit sharing, compensation, severance,
          termination, stock appreciation right, restricted stock, performance
          unit, stock equivalent, stock purchase, pension, retirement, deferred
          compensation, employment, severance or other employee benefit
          agreement, trust, plan, fund or other arrangement for the benefit or
          welfare of any director, officer or employee, (B) increase in any
          manner the compensation or fringe benefits of any director, officer or
          employee of Titan or the Titan Subsidiaries or (C) pay to any
          director, officer or employee of Titan or the

                                       32
<PAGE>

          Titan Subsidiaries any benefit not required by any employee benefit
          agreement, trust, plan, fund or other arrangement as in effect on the
          date hereof;

               (vi)   acquire, sell, lease, transfer or otherwise dispose of,
          directly or indirectly, any assets other than those which are (x) in
          the ordinary course of business consistent with past practice and (y)
          in an aggregate amount less than $5,000,000;

               (vii)  acquire (by merger, consolidation or acquisition of stock
          or assets or otherwise) any corporation, partnership or other business
          organization or division thereof;

               (viii) (A) make any capital expenditure or expenditures before
          January 1, 2000 which in the aggregate are in excess of $10,000,000,
          except as contemplated by Titan's capital expenditure budget for 1999,
          a copy of which has been made available to Union Oil, (B) make any
          capital expenditure or expenditures during the quarter ending March
          31, 2000 or any subsequent quarter that in the aggregate are in excess
          of the greater of the total amount of cash flow for the preceding
          quarter or $20,000,000, or (C) make any individual well expenditures
          in excess of $3,500,000;

               (ix)   make any Tax election or settle or compromise any federal,
          state local or foreign income Tax liability material to Titan and the
          Titan Subsidiaries considered as a whole;

               (x)    pay, discharge or satisfy any claims, liabilities or
          obligations (whether accrued, absolute, contingent, unliquidated or
          otherwise, and whether asserted or unasserted), other than the
          payment, discharge or satisfaction in the ordinary course of business
          consistent with past practice, or in accordance with their terms, of
          liabilities reflected or reserved against in the financial statements
          included in the Titan Commission Filings in the ordinary course of
          business consistent with past practice;

               (xi)   enter into any lease, contract, agreement, commitment,
          arrangement or transaction outside the ordinary course of business
          consistent with past practice;

               (xii)  amend, modify, or change in any material respect any
          existing lease, contract, or agreement, other than in the ordinary
          course of business consistent with past practice;

               (xiii) change any of the accounting principles or practices used
          by it, except for any change required by reason of a concurrent change
          in GAAP and notice of which is given in writing by Titan to Union Oil;

               (xiv)  waive, release, grant, or transfer any rights of value,
          other than in the ordinary course of business consistent with past
          practice;

                                       33
<PAGE>

               (xv)    take any action that would, or that reasonably could be
          expected to, result in any of the representations and warranties set
          forth in Article IV becoming untrue or any material breach of this
          Agreement;

               (xvi)   amend the Titan Engagement Letters;

               (xvii)  enter into any hedging, swap, fixed price sale or
          purchase (having a term of more than 90 days) or other derivative
          contract;

               (xviii) take any action that would be prohibited following the
          Closing under the terms of the Business Opportunity Agreement dated of
          even date herewith among Union Oil, the Company, Sub and Titan; or

               (xix)   authorize or propose, or agree in writing or otherwise to
          take, any of the actions described in this Section 5.2.


                                  ARTICLE VI

                             ADDITIONAL AGREEMENTS

     6.1  Access to Information.
          ---------------------

          (a) Subject to Applicable Law, between the date hereof and the Closing
     Date, the Company and Union Oil (i) shall give Titan and its authorized
     representatives reasonable access, during regular business hours and upon
     reasonable advance notice, to all employees, all plants, offices,
     warehouses, properties and other facilities, and all books and records of
     the Company and Union Oil (to the extent relevant to the ownership and/or
     operation of the Assets), (ii) shall permit Titan and its authorized
     representatives to make such non-invasive inspections of the Assets as they
     may reasonably require and (iii) shall cause Union Oil's and the Company's
     officers to furnish Titan and its authorized representatives with such
     financial and operating data and other information with respect to the
     Company and the Assets as Titan may from time to time reasonably request;
     provided, however, (A) that no investigation pursuant to this Section 6.1
     shall affect any representation or warranty of the Company or Union Oil
     contained in this Agreement or in any agreement, instrument, or document
     delivered pursuant hereto or in connection herewith; (B) that the Company
     shall have the right to have a representative present at all times of any
     such inspections, interviews and examinations conducted at or on the
     offices or other facilities or properties of the Company or its affiliates
     or representatives and (C) that Titan shall hold in confidence all such
     information on the terms and subject to the conditions contained in the
     Confidentiality Agreement dated October 4, 1999 between Union Oil and
     Titan.

          (b) Subject to Applicable Law, between the date hereof and the Closing
     Date, Titan (i) shall give Union Oil and its authorized representatives
     reasonable access, during regular business hours and upon reasonable
     advance notice, to all employees, all plants,

                                       34
<PAGE>

     offices, warehouses, properties and other facilities, and all books and
     records of Titan and the Titan Subsidiaries, (ii) shall permit Union Oil
     and its authorized representatives to make such non-invasive inspections of
     the Assets as it may reasonably require and (iii) shall cause Titan's
     officers to furnish Union Oil and its authorized representatives with such
     financial and operating data and other information with respect to Titan
     and the Titan Subsidiaries as Union Oil may from time to time reasonably
     request;  provided, however, (A) that no investigation pursuant to this
     Section 6.1 shall affect any representation or warranty of Titan contained
     in this Agreement or in any agreement, instrument, or document delivered
     pursuant hereto or in connection herewith; (B) that Titan shall have the
     right to have a representative present at all times of any such
     inspections, interviews and examinations conducted at or on the offices or
     other facilities or properties of Titan or its affiliates or
     representatives and (C) that Titan shall hold in confidence all such
     information on the terms and subject to the conditions contained in the
     Confidentiality Agreement dated October 4, 1999 between Union Oil and
     Titan.

          (c) For a period of six years after the Closing Date, Union Oil and
     the Company shall, using procedures consistent with their current record
     retention procedures, (i) preserve and retain all books and records held by
     either of them or their subsidiaries that relate to the operation of the
     Assets on or before the Closing Date (the "Records") and (ii) subject to
     the provisions of this Article VI, make the Records available to each other
     and their respective agents upon reasonable notice and at reasonable times,
     it being understood that either party shall be entitled to make copies of
     any of the Records at the copying party's expense.  Union Oil and the
     Company further agree not to  dispose of any of the Records in their
     possession for a period of six years after the Closing Date unless the
     party proposing to destroy the Records, or some portion thereof, gives the
     other party notice of the proposed destruction and a reasonable
     opportunity, at the other party's cost and expense, to remove and retain
     all or any part of such Records as the other party may select.

     6.2  Titan Acquisition Proposals.
          ---------------------------

          (a) Titan will notify Union Oil immediately and in any event within
     twelve (12) hours of receipt of any proposals by, request for any
     information from, or initiation of or attempt or request to initiate any
     negotiations or discussions with, Titan or its officers, directors,
     employees, investment bankers, attorneys, accountants or other agents, in
     each case in connection with any Acquisition Proposal (as defined below) or
     the consideration of making of an Acquisition Proposal ("Acquisition
     Proposal Interest") indicating, in connection with such notice, the terms
     and conditions of any Acquisition Proposals or offers.  Titan agrees that
     as of the date hereof it shall cease and cause to be terminated any
     activities, discussions or negotiations with any parties conducted
     heretofore with respect to any Acquisition Proposal Interest.  Titan agrees
     that it shall keep Union Oil informed, on a reasonably current basis, of
     the status and terms of any Acquisition Proposal Interest.  The term
     "Acquisition Proposal," as used herein, means any tender or exchange offer
     involving Titan or the Titan Subsidiaries or any offer or proposal for a
     merger, consolidation or other business combination or joint venture
     involving Titan or the Titan Subsidiaries or the acquisition of any
     substantial equity interest in, or a substantial portion of the assets of,
     Titan

                                       35
<PAGE>

     or the Titan Subsidiaries or any offer or proposal with respect to any
     recapitalization or restructuring with respect to Titan or the Titan
     Subsidiaries, other than the transactions contemplated by this Agreement.

          (b) Except as provided in Section 6.2(c) or 6.2(d), from the date
     hereof until this Agreement is terminated in accordance with its terms,
     Titan shall not, and shall use its reasonable efforts to ensure that its
     directors, officers, employees, investment bankers, attorneys, accountants
     or other agents shall not, directly or indirectly (i) solicit, initiate or
     knowingly encourage, or take any action to facilitate the making of, any
     Acquisition Proposal, (ii) enter into any agreement with respect to any
     Acquisition Proposal or (iii) engage in discussions or negotiations with,
     or provide any information relating to Titan to any person relating to an
     Acquisition Proposal; provided, however, that nothing contained in this
     Section 6.2 shall prohibit Titan or its Board of Directors from taking and
     disclosing to Titan's stockholders its position with respect to a tender or
     exchange offer by a third party pursuant to Rules 14d-9 and 14e-2 under the
     Exchange Act to the extent required by Applicable Law.

          (c) Notwithstanding the foregoing, Titan may furnish information
     concerning its business, properties or assets to any person and may
     negotiate and participate in discussions and negotiations with such person
     concerning an Acquisition Proposal if (x) such entity or group has on an
     unsolicited basis submitted a bona fide written proposal to Titan relating
     to any such transaction which Titan's Board of Directors determines in good
     faith, after receiving advice from Petrie Parkman & Co., represents a
     financially superior transaction to the Transaction from the standpoint of
     the stockholders of Titan other than the officers and directors of Titan
     and (y) Titan's Board of Directors determines in good faith, upon advice of
     counsel, that the failure to provide such information or access or to
     engage in such discussions or negotiations would cause Titan's Board of
     Directors to violate its fiduciary duties to Titan's stockholders under
     Applicable Law (an Acquisition Proposal which satisfies clauses (x) and (y)
     being referred to herein as a "Superior Proposal").

          (d) Except as set forth herein, neither Titan's Board of Directors nor
     any committee thereof shall (i) withdraw or modify, or propose to withdraw
     or modify, in a manner adverse to  Union Oil, the approval or
     recommendation by such Board of Directors or any such committee of this
     Agreement or the Transaction, (ii) approve or recommend or propose to
     approve or recommend, any Acquisition Proposal or (iii) enter into any
     agreement with respect to any Acquisition Proposal.  Notwithstanding the
     foregoing, Titan's Board of Directors may (subject to the terms of this
     sentence and the following sentence) terminate this Agreement in accordance
     with Section 10.1(d) and enter into an agreement with respect to a Superior
     Proposal, in which event Titan may take any of the actions set forth in
     clauses (i) through (iii) of the immediately preceding sentence; provided,
                                                                      --------
     however, that Titan shall not enter into an agreement with respect to a
     -------
     Superior Proposal unless Titan shall have furnished Union Oil with written
     notice not later than 12:00 noon two (2) Business Days in advance of any
     date that it intends to enter into such agreement and afford Union Oil an
     opportunity to make a proposal that is superior to such Superior Proposal.

                                       36
<PAGE>

     6.3  Company Acquisition Proposals. From the date hereof until Closing or
          -----------------------------
earlier termination of this Agreement, none of the Company, Union Oil or any
affiliate, director, officer, employee or representative of the Company or Union
Oil  shall, directly or indirectly, (i) solicit, initiate or knowingly encourage
any Company Acquisition Proposal (as defined below) or (ii) engage in
discussions or negotiations with, or disclose any nonpublic information relating
to, the Company, or afford access to the properties, books or records of the
Company, Union Oil or any other subsidiary of Union Oil to, any person that is
considering making or has made a Company Acquisition Proposal. The term "Company
Acquisition Proposal", as used herein, means any offer or proposal for, or any
indication of interest in, a merger or other business combination with the
Company or the acquisition of the Assets or any equity interest in, or a
substantial portion of the assets of, the Company, other than the transactions
contemplated by this Agreement.

     6.4  Special Meeting; Proxy Statement/Prospectus; Registration Statement.
          -------------------------------------------------------------------

          (a) Titan shall take all action necessary in accordance with
     Applicable Law and its Certificate of Incorporation to duly call, give
     notice of, convene and hold a special meeting of its stockholders (the
     "Special Meeting") as promptly as practicable after the date hereof to
     consider and vote upon the adoption and approval of this Agreement, the
     Transaction and the matters required by any national securities exchange or
     interdealer quotation system.  The stockholder vote required for the
     adoption and approval of this Agreement and the Transaction contemplated
     thereby shall be the vote of  the holders of a majority of the outstanding
     shares of Titan Common Stock, and a majority of the shares of Titan Common
     Stock other than shares held by officers of Titan, present in person or by
     proxy at the Special Meeting, where a quorum is present either in person or
     by proxy.  Subject to Section 6.2(d), the Board of Directors of Titan shall
     (i) unanimously recommend to the stockholders of Titan that they vote in
     favor of the adoption and approval of this Agreement, the Transaction and
     the matters contemplated thereby, (ii) use its reasonable efforts to
     solicit from the stockholders of Titan proxies in favor of such adoption
     and approval and (iii) take all other action reasonably necessary to secure
     a vote of the stockholders of Titan in favor of such adoption and approval.

          (b) As soon as practicable following the date of this Agreement, Titan
     and Union Oil shall cooperate to prepare and file with the Commission
     preliminary proxy materials for the use at the Special Meeting, which will
     also constitute the Prospectus to be included in the Registration Statement
     referred to in Section 6.4(d) (the definitive proxy statement filed with
     the Commission, as amended or supplemented, is herein referred to as the
     "Proxy Statement/Prospectus").  Titan and Union Oil shall cooperate to use
     reasonable efforts to have the Proxy Statement/Prospectus cleared by the
     Commission as promptly as practicable.  Union Oil and Titan shall cooperate
     with each other in the preparation of the Proxy Statement/Prospectus and
     shall furnish such data and information relating to Titan, Union Oil, the
     Assets and the Company as may reasonably be required for the purpose of
     including the data and information in the Proxy Statement/Prospectus.
     Titan and Union Oil shall give each other and their counsel the opportunity
     to review any preliminary proxy materials and the Proxy
     Statement/Prospectus prior to their being filed with the Commission and
     shall give each other and their counsel the opportunity to review all
     amendments and supplements

                                       37
<PAGE>

     thereto and all responses to requests for additional information and
     replies to comments prior to their being filed with, or sent to, the
     Commission.  Neither Party shall file the Proxy Statement/Prospectus or any
     amendment thereto without the other party's prior consent.  Titan and Union
     Oil will provide promptly to each other copies of all correspondence
     between such party or any of its representatives and the Commission.  Union
     Oil and Titan each agrees promptly to correct any information provided by
     it for use in the Proxy Statement/Prospectus if and to the extent that such
     information shall have become false or misleading in any material respect.

          (c) Except as provided in Section 6.2(d), the Proxy
     Statement/Prospectus shall contain the unanimous recommendation of the
     Board of Directors of Titan that stockholders of Titan vote in favor of the
     adoption and approval of this Agreement and the Transaction.  Titan shall
     not mail or otherwise distribute the Proxy Statement/Prospectus to its
     stockholders without consultation with Union Oil and its counsel.

          (d) As soon as practicable following the date of this Agreement, Titan
     and Union Oil shall cooperate to prepare on the Company's behalf a
     registration statement (the "Registration Statement") to be filed by the
     Company on Form S-4 with the Commission under the Securities Act with
     respect to the offering, sale and delivery of the shares of Company Common
     Stock to be issued pursuant to the Merger, which will include the Proxy
     Statement/Prospectus; and Union Oil will use its reasonable efforts to
     cause such Registration Statement to become effective as soon as
     practicable after filing.  Titan agrees that the Registration Statement
     (except with respect to information concerning Union Oil, the Company and
     Sub furnished by or on behalf of Union Oil, the Company and Sub
     specifically for use therein, for which information Union Oil shall be
     responsible) will comply as to form in all material respects with the
     requirements of the Securities Act and the Exchange Act and the respective
     rules and regulations adopted thereunder, and will not contain any untrue
     statement of any material fact or omit to state any material fact required
     to be stated therein or necessary to make the statements made therein not
     misleading.  Titan and Union Oil will each advise the other party in
     writing if prior to the Effective Time it shall obtain knowledge of any
     fact that would, in its opinion, make it necessary to amend or supplement
     the Registration Statement in order to make the statements therein not
     misleading or to comply with applicable law.

     6.5  Reservation of Company Common Stock.  The Company shall reserve for
          -----------------------------------
issuance, out of its authorized but unissued capital stock, such number of
shares of Company Common Stock as may be issuable upon consummation of the
Merger and such number of shares of Company Common Stock as may be issuable upon
exercise of the Assumed Options and the options granted pursuant to Section
6.25.

     6.6  Notification of Certain Matters.  The Company and Union Oil shall give
          -------------------------------
prompt notice to Titan of (i) the discovery of any fact or circumstance which
would be likely to cause any representation or warranty contained in Article III
to be untrue or inaccurate in any material respect and (ii) any material failure
of the Company or Union Oil to comply with or satisfy any covenant, condition or
agreement to be complied with or satisfied by it hereunder.  Titan shall give
prompt

                                       38
<PAGE>

notice to the Company of (i) the discovery of any fact or circumstance which
would be likely to cause any representation or warranty contained in Article IV
to be untrue or inaccurate in any material respect and (ii) any material failure
of Titan to comply with or satisfy any covenant, condition or agreement to be
complied with or satisfied by Titan hereunder.  The delivery of any notice
pursuant to this Section 6.6 shall not be deemed to (i) modify the
representations or warranties hereunder of the party delivering such notice,
(ii) modify the conditions set forth in Articles VII and VIII or (iii) limit or
otherwise affect the remedies available hereunder to the party receiving such
notice.

     6.7  HSR Act; Consents.  If required, each of the parties hereto shall (i)
          -----------------
file or cause to be filed, as promptly as practicable but in no event later than
five (5) consecutive Business Days after the execution and delivery of this
Agreement, with the Federal Trade Commission and the United States Department of
Justice, all reports and other documents required to be filed by such party
under the HSR Act concerning the transactions contemplated hereby and (ii)
promptly comply with or cause to be complied with any requests by the Federal
Trade Commission or the United States Department of Justice for additional
information concerning such transactions, in each case so that the waiting
period applicable to this Agreement and the transactions contemplated hereby
under the HSR Act shall expire as soon as practicable after the execution and
delivery of this Agreement.  Each party hereto agrees to request, and to
cooperate with the other party or parties in requesting, early termination of
any applicable waiting period under the HSR Act.  Each of the parties also shall
use its reasonable efforts to obtain all other consents, approvals, orders,
authorizations and waivers of, and to effect all declarations, filings and
registrations with, all third parties (including Governmental Entities) that are
necessary, required or deemed to be desirable to enable the parties to effect
the transactions contemplated by this Agreement and to otherwise consummate the
transactions contemplated hereby.

     6.8  Disclosure Letters.
          ------------------

          (a) The Union Oil Disclosure Letter, executed by Union Oil and the
     Company as of the date hereof, and delivered to Titan on the date hereof,
     contains all disclosure required to be made therein.  Each item of
     disclosure set forth in the Union Oil Disclosure Letter specifically refers
     to the Article and Section of the Agreement to which such disclosure
     responds, and shall not be deemed to be disclosed with respect to any other
     Article or Section of the Agreement.

          (b) The Titan Disclosure Letter, executed by Titan as of the date
     hereof, and delivered to Union Oil and the Company on the date hereof,
     contains all disclosure required to be made therein.  Each item of
     disclosure set forth in the Titan Disclosure Letter specifically refers to
     the Article and Section of the Agreement to which such disclosure responds,
     and shall not be deemed to be disclosed with respect to any other Article
     or Section of the Agreement.

     6.9  Reasonable Efforts.  Each party hereto agrees that it will not
          ------------------
voluntarily undertake any course of action inconsistent with the provisions or
intent of this Agreement and will use its reasonable efforts to take, or cause
to be taken, all action and to do, or cause to be done, all things

                                       39
<PAGE>

reasonably necessary, proper or advisable under Applicable Law to consummate the
transactions contemplated by this Agreement, including, without limitation, (i)
cooperation in determining whether any other consents, approvals, orders,
authorizations, waivers, declarations, filings or registrations of or with any
Governmental Entity or third party are required in connection with the
consummation of the transactions contemplated hereby, (ii) using its reasonable
efforts to obtain any such consents, approvals, orders, authorizations and
waivers and to effect any such declarations, filings and registrations, (iii)
using its reasonable efforts to cause to be lifted or rescinded any injunction
or restraining order or other order adversely affecting the ability of the
parties to consummate the transactions contemplated hereby, (iv) using its
reasonable efforts to defend, and to cooperate in defending, all lawsuits or
other legal proceedings challenging this Agreement or the consummation of the
transactions contemplated hereby and (v) the execution of any additional
instruments necessary to consummate the transactions contemplated hereby.

     6.10 Public Announcements.  Except as may be required by Applicable Law or
          --------------------
required by any listing agreement with any national securities exchange or
interdealer quotation system, neither Titan, on the one hand, nor the Company or
Union Oil, on the other, shall issue any press release or otherwise make any
public statement with respect to this Agreement or the transactions contemplated
hereby without the prior written consent of the other party.

     6.11 Fees and Expenses.  Except as provided below, all Expenses (as defined
          -----------------
below) incurred by the parties hereto shall be borne solely and entirely by the
party that has incurred such Expenses; provided, however, that (i) the parties
acknowledge that Expenses incurred by or on behalf of Union Oil or any of its
subsidiaries shall be deemed for all purposes to have been incurred by the
Company and (ii) if this Agreement is terminated for any reason, then the
allocable share of Union Oil, the Company and Sub, as a group, and Titan for all
Expenses (including any fees and expenses of accountants, experts, and
consultants, but excluding the fees and expenses of legal counsel and investment
bankers) related to preparing, printing, filing and mailing the Registration
Statement, the Proxy Statement/Prospectus and all SEC and other regulatory
filing fees incurred in connection with the Registration Statement, Proxy
Statement/Prospectus and HSR, shall be one-half each.  "Expenses" as used in
this Agreement shall include all reasonable out-of-pocket expenses (including,
without limitation, all reasonable fees and expenses of counsel, accountants,
investment bankers, experts and consultants to a party hereto and its
affiliates) incurred by a party or on its behalf in connection with or related
to the authorization, preparation, negotiation, execution and performance of
this Agreement, the preparation, printing, filing and mailing of the
Registration Statement, the Proxy Statement/Prospectus, the solicitation of
Titan stockholder approval, requisite HSR filings and all other matters related
to the consummation of the transactions contemplated hereby.  Notwithstanding
the foregoing, all fees and expenses of Donaldson, Lufkin & Jenrette incurred by
Union Oil shall be paid by Union Oil.

     6.12 Employees and Employee Benefit Plans.
          ------------------------------------

          (a) On the Closing Date, Union Oil or its affiliates shall cause the
     termination of all of the employees of Union Oil or its affiliates employed
     in connection with the Business (the "Employees").  Prior to the Closing
     Date, Union Oil will assist or cause its affiliates to assist the Company
     in offering employment to and hiring those Employees designated by

                                       40
<PAGE>

     Titan in its sole discretion and on such terms and conditions designated by
     Titan in its sole discretion.  The Company and its affiliates are not
     obligated to hire any of the Employees.  The Company is not hereby, and at
     no time hereafter will be, adopting, accepting, or assuming any employee
     benefit plan or collective bargaining agreement of Union Oil or its
     affiliates relating to any of their employees or any other agreement,
     trust, plan, fund, or other arrangement of Union Oil or its affiliates
     (including, but not limited to flexible contribution plans) that provides
     for employee benefits or perquisites (collectively, "Employment
     Arrangements"), and the Company shall have no liability or obligation
     whatsoever under any Employment Arrangement to Union Oil or its affiliates
     or to any Employees of Union Oil or its affiliates, whether or not any of
     such employees are offered employment by or become employees of the
     Company.  The Company is not obligated to replace any of the Employment
     Arrangements for any Employees who become employees of the Company, nor is
     the Company obligated to provide such persons with any similar agreements,
     plans, or arrangements.  Union Oil and its affiliates are responsible for
     and shall timely pay all wages, salaries, employment benefits of any kind
     or nature, arising out of services performed by the Employees on or prior
     to the Closing Date including, without limitation, retirement, health and
     other benefits, vacation pay and any termination or severance pay, whether
     due immediately or at some future date, whether or not required under any
     collective bargaining agreement.  All wages, salaries, vacation and sick
     pay, termination or severance pay and any other employment benefit or other
     compensation earned or accrued with respect to or arising out of services
     performed by the Employees on or prior to the Closing Date shall be paid,
     or caused to be paid, by Union Oil in accordance with any agreement with
     any such Employees or within the time limits prescribed by law.  Any
     Employee terminated by the Company or any of its affiliates within 365 days
     of the Closing under circumstances that would have resulted in benefits
     being paid under Union Oil's Employee Redeployment Program and Termination
     Allowance Plan ("Severance Benefits") had the termination occurred while
     the Employee was employed by Union Oil, shall be eligible for payment of
     equivalent Severance Benefits from the Company.  Union Oil shall pay to the
     Company 50% of the cost of said Severance Benefits upon receipt of adequate
     documentation of said payment.  In connection with all matters related to
     this Section 6.12, Union Oil and its affiliates agree to comply with all
     Applicable Laws, including without limitation the Worker Adjustment and
     Retraining Notification Act or any similar law or regulation.  Union Oil
     agrees to indemnify and hold harmless the Company and its affiliates from
     any and all liability, including attorneys fees and costs, related in any
     way to claims arising from the employment relationship between Union Oil or
     its affiliates and the Employees (or the termination of that relationship).
     The Company agrees to indemnify and hold harmless Union Oil and its
     affiliates from any and all liability, including attorneys' fees and costs,
     related in any way to claims arising from the employment of Employees by
     the Company (and, subject to the forgoing provisions, the subsequent
     termination of that relationship).

          (b) The employee benefit plans offered by the Company or its
     affiliates to Employees hired by the Company or an affiliate of the Company
     in connection with the transaction shall recognize (or be amended to
     recognize) the services of Employees for periods of employment by Union Oil
     or an affiliate of Union Oil for purposes of eligibility, participation and
     vesting, but not for purposes of benefit accruals (other than for purposes

                                       41
<PAGE>

     of determining vacation benefits).  Employees hired by the Company or an
     affiliate of the Company who are eligible employees under the Company's (or
     its affiliate's) 401(k) and matching plans may participate in such plans.

          (c) Union Oil or its affiliates currently maintain one or more defined
     contribution plans (the "Union Oil DC Plans") which provide certain
     retirement benefits for the Employees.  Effective as of the Closing Date,
     with respect to Employees hired by the Company or an affiliate in
     connection with the transaction, Union Oil shall take all necessary and
     appropriate action to amend all Union Oil DC Plans in which such Employees
     participate to provide that (i) such Employees receive full and immediate
     vesting in any employer-derived benefits accrued under such plans; (ii)
     such Employees who have outstanding loans will not be in default on such
     loans unless and until each such Employee receives a distribution from such
     plan or fails to make a timely payment on such loan(s); and (iii) such
     Employees may receive a distribution of their individual accounts under
     such plans that are qualified cash or deferred arrangements within the
     meaning of Section 401(k) of the Code as soon as administratively feasible
     after the Closing Date; provided, however, that in the event that
     distributions to such Employees cannot be made from a Union Oil DC Plan
     which is a qualified cash or deferred arrangement under Section 401(k) of
     the Code because such distributions would jeopardize the tax-qualified
     status of such plan (as may be determined in Union Oil's sole discretion),
     then the individual accounts of such Employees shall continue to be
     maintained and administered under a Union Oil DC Plan.

          (d) Union Oil or its affiliates currently maintain one or more defined
     benefit pension plans (the "Union Oil DB Plans") which provide certain
     retirement benefits for the Employees.  Union Oil shall remain solely
     responsible for making all contributions to the Union Oil DB Plans
     (including the payment of Pension Benefit Guaranty Corporation premiums
     applicable thereto) and the Company and its affiliates shall have no
     obligation or liability whatsoever with respect to the Union Oil DB Plans.
     Effective as of the Closing Date, Union Oil will take all necessary and
     appropriate action to cause the Union Oil DB Plans to expressly provide
     that Employees hired by the Company or an affiliate who were participants
     in the Union Oil DB Plans prior to the Closing will be fully vested for
     purposes of early retirement eligibility.

          (e) Union Oil agrees to indemnify and hold harmless the Company and
     its affiliates from any and all liability, including attorneys fees and
     costs, related in any way to any plan, program or arrangement pursuant to
     which benefits are provided to employees or former employees of Union Oil
     or its affiliates in respect of employment by Union Oil or its affiliates.

          (f) Welfare benefit plans established by Union Oil or an affiliate
     applicable to the Employees shall be responsible for all claims incurred
     under those plans prior to the Closing, including all claims incurred but
     unreported as of that time.  Employees receiving disability benefits as of
     the Closing Date shall continue to receive benefits from plans sponsored by
     Union Oil or an affiliate of Union Oil while the disability continues or
     until their eligibility otherwise expires as provided in such plans.  The
     Company and its affiliates

                                       42
<PAGE>

     shall have no obligation to pay any medical, life, disability or any other
     benefits to any Employee who does not actively work for the Company or an
     affiliate after the Closing.  In addition, the Company and its affiliates
     shall have no obligation to pay any medical, life, disability or any other
     benefits to any Employee who actively works for the Company or an affiliate
     after the Closing unless such Employee becomes eligible to participate in
     the Company's (or its affiliate's) employee benefit plans which provide
     those benefits.

          (g) Union Oil shall use its reasonable efforts to enforce all non-
     compete, confidentiality and non-disclosure agreements with Employees of
     Union Oil or an affiliate with respect to the Assets.

          (h) The Company shall have sole responsibility for "continuation
     coverage" benefits provided after the Closing Date under the Company's
     group health plans to all Employees hired by the Company and "qualified
     beneficiaries" of such Employees, for whom a "qualifying event" has
     occurred after the Closing Date.  Union Oil shall have sole responsibility
     for "continuation coverage" benefits provided under Union Oil's (or its
     affiliates') group health plans to all current Employees of Union Oil (or
     an affiliate of Union Oil) hired by the Company and "qualified
     beneficiaries" of such Employees of Union Oil, for whom a "qualifying
     event" has occurred on or before the Closing Date.  The terms "continuation
     coverage," "qualified beneficiaries" and "qualifying event" shall have the
     meaning ascribed to thereunder Section 4908B of the Code and Sections 601
     through 608 of ERISA and the regulations thereunder.

     6.13 Indemnification of Claims of Brokers.  Union Oil, on the one hand, and
          ------------------------------------
Titan, on the other, shall indemnify and hold each other harmless from any claim
or demand for commission or other compensation by any broker, finder, agent or
similar intermediary claiming to have been employed by or on behalf of Union Oil
(or the Company) or Titan, as the case may be, and shall bear the cost of legal
fees and expenses incurred in defending against any such claim.

     6.14 Amendment of Disclosure Letters.  Each party hereto agrees that, with
          -------------------------------
respect to the representations and warranties of such party contained in this
Agreement, such party shall have the continuing obligation until the Closing to
supplement or amend the Disclosure Letter of such party with respect to any
matter hereafter arising or discovered which, if known at the date of this
Agreement, would have been required to be set forth or described in the
Disclosure Letter of such party. For all purposes of this Agreement, including
without limitation for purposes of determining whether the conditions set forth
in Sections 7.1 and 8.1 have been fulfilled, the Disclosure Letters shall be
deemed to include only that information contained therein on the date of this
Agreement and shall be deemed to exclude all information contained in any
supplement or amendment thereto.

     6.15 Transfer Taxes.  All sales, transfer, filing, recordation,
          --------------
registration, stamp, and similar Taxes and fees arising from or associated with
the sale and transfer of the Assets as contemplated hereunder, whether levied on
Titan, the Company or Union Oil, shall be borne by the Company, and the Company
shall file all necessary documentation with respect to, and make all payments
of, such Taxes and fees on a timely basis.

                                       43
<PAGE>

     6.16 Amendment of Rights Plan. Titan's Board of Directors shall take all
          ------------------------
necessary to amend or otherwise cause the Titan Rights Agreement to permit the
transactions contemplated hereby.

     6.17 Management Employee Agreements.  The parties agree that Titan shall be
          ------------------------------
permitted at or prior to Closing to enter into an agreement in the form attached
hereto as Exhibit 6.17(a) (the "Executive Letter Agreement") with each of its
executive officers and on the Closing Date to make the payments contemplated
thereby. The Company agrees on or as soon as practicable after the Closing Date
to enter into a new severance agreement in such form and on such terms as shall
be approved by the CEO and the Compensation Committee of the Board of Directors
(the "Company Severance Agreements") with each executive officer of Titan that
is to become an officer of the Company upon consummation of the transactions
contemplated by this Agreement; provided, however, that such Company Severance
Agreements shall have such further terms as are described on Schedule 6.17(b).

     6.18 Tax Treatment.  Each of Union Oil and Titan undertakes and agrees to
          -------------
use its reasonable efforts to cause the Merger to qualify, and to take no action
that would cause the Merger not to qualify, for treatment as a "reorganization"
within the meaning of Section 368(a) of the Code and as a transfer of property
to the Company by the stockholders of Titan governed by Section 351 of the Code.
Each of Union Oil and Titan undertakes and agrees to use its reasonable efforts
to cause Union Oil's transfer of the Assets to the Company to qualify, and to
take no action that would cause such transaction not to qualify, for treatment
under Section 351(a) of the Code.  Neither Union Oil, Titan nor the Company will
take a position on any Tax Return, or before any Taxing Authority, that is
inconsistent with the foregoing unless otherwise contemplated by Section 9.3.

     6.19 Company Board.  Union Oil shall cause the directors and officers of
          -------------
the Company from and after the Closing Date to consist of the persons set forth
on Schedule 6.19 hereto in each case until their respective successors have been
duly elected or appointed and qualified or until their earlier death,
resignation or removal in accordance with the Company's Certificate of
Incorporation and Bylaws and the Stockholder Voting Agreement.

     6.20 Stock Exchange Listing.  Each of Union Oil, Titan and the Company
          ----------------------
shall use its reasonable efforts to cause the Company Common Stock to be
approved for listing on a national securities exchange or designated as a
national market system security on an interdealer quotation system by the NASD
prior to the Effective Time, subject in either case to official notice of
issuance.

     6.21 Indemnification and Insurance.
          -----------------------------

     (a)  From and after the Effective Time, the Company shall cause the
Surviving Corporation to indemnify, defend and hold harmless to the fullest
extent permitted under applicable law each person who is, or has been at any
time prior to the Effective Time, an officer or director of Titan (or a Titan
Subsidiary or division thereof) and each person who served at the request of
Titan as a director, officer, trustee or fiduciary of another corporation,
partnership, joint venture, trust, pension or other employee benefit plan or
enterprise (individually, an "Indemnified Person" and, collectively, the
"Indemnified Persons") against all losses, claims, damages, liabilities, costs
or

                                       44
<PAGE>

expenses (including attorneys' fees), judgments, fines, penalties and amounts
paid in settlement in connection with any claim, action, suit, proceeding or
investigation arising out of or pertaining to acts or omissions, or alleged acts
or omissions, by them in their capacities as such, whether commenced, asserted
or claimed before or after the Effective Time. In the event of any such claim,
action, suit, proceeding or investigation (an "Action"), (i) the Company shall
cause the Surviving Corporation to pay, as incurred, the fees and expenses of
counsel selected by the Surviving Corporation, which counsel shall be reasonably
acceptable to the Indemnified Person, in advance of the final disposition of any
such Action to the fullest extent permitted by applicable law, and, if required,
upon receipt of any undertaking required by applicable law, and (ii) the Company
will, and will cause the Surviving Corporation to, cooperate in the defense of
any such matter; provided, however, the Company shall not be liable for any
settlement effected without its written consent (which consent shall not be
unreasonably withheld or delayed), and provided further, that the Surviving
Corporation shall not be obligated pursuant to this Section 6.21 to pay the fees
and disbursements of more than one counsel for all Indemnified Persons in any
single Action, unless, in the good faith judgment of any of the Indemnified
Persons, there is or may be a conflict of interests between two or more of such
Indemnified Persons, in which case there may be separate counsel for each
similarly situated group.

     (b) The parties agree that the rights to indemnification, including
provisions relating to advances of expenses incurred in defense of any action or
suit, in the certificate of incorporation, bylaws and any indemnification
agreement of Titan and the Titan Subsidiaries with respect to matters occurring
through the Effective Time, shall survive the Merger and shall continue in full
force and effect for a period of six years from the Effective Time; provided,
however, that all rights to indemnification in respect of any Action pending or
asserted or claim made within such period shall continue until the disposition
of such Action or resolution of such claim.

     (c) The parties agree that Titan shall be permitted on or before the
Closing Date to procure officers' and directors' liability insurance covering
the Indemnified Persons who are, on the date of this Agreement and/or at the
Effective Time, officers or directors of Titan with respect to, among other
things, acts or omissions, or alleged acts or omissions, prior to the Effective
Time (whether claims, actions or other proceedings relating thereto are
commenced, asserted or claimed before or after the Effective Time); provided,
however, that without the consent of Union Oil the aggregate premiums for such
insurance for the full term thereof shall not exceed $700,000.

     (d) The rights of each Indemnified Person hereunder shall be in addition to
any other rights such Indemnified Person may have under the certificate of
incorporation or bylaws of Titan or the Titan Subsidiaries, under the DGCL or
otherwise. The provisions of this Section 6.21 shall survive the consummation of
the Merger and expressly are intended to benefit each of the Indemnified
Parties.

     (e) In the event the Company or any of its successors or assigns (i)
consolidates with or merges into any other person and shall not be the
continuing or surviving corporation or entity in such consolidation or merger or
(ii) transfers all or substantially all of its properties and assets to any
person, then and in either such case, proper provision shall be made so that the
successors and

                                       45
<PAGE>

assigns of the Company, as the case may be, shall assume the obligations set
forth in this Section 6.21.

     6.22 Affiliate Agreements.  Titan shall identify in a letter to Union Oil
          --------------------
all persons who are, on the date hereof, "affiliates" of Titan, as such term is
used in Rule 145 under the Securities Act.  Titan shall use its reasonable
efforts to cause such persons to deliver to Union Oil not later than ten (10)
days prior to the date of the Titan Special Meeting, a written agreement
substantially in the form attached hereto as Exhibit 6.22 and shall use its
reasonable efforts to cause persons who become "affiliates" after the date
hereof but prior to the Closing Date to execute and deliver agreements at least
five (5) days prior to the Closing Date.

     6.23 Ancillary Agreements.  Simultaneously with the execution of this
          --------------------
Agreement, Union Oil, the Company and Titan, to the extent that they are a party
thereto, are entering into each of the following agreements (collectively, the
"Ancillary Agreements") that they are a party thereto:

     (a)  Business Opportunities Agreement, dated as the date hereof but
effective as of and conditioned upon the Closing, among Union Oil, the Company
and Titan (the "Business Opportunities Agreement");

     (b)  Non-Dilution Agreement, dated as of the date hereof but effective as
of and conditioned upon the Closing, between Union Oil and the Company (the
"Non-Dilution Agreement");

     (c)  Registration Rights Agreement, dated as of the date hereof but
effective as of and conditioned upon the Closing, between Union Oil and the
Company (the "Registration Rights Agreement");

     (d)  Stockholders Voting Agreement, dated as of the date hereof but
effective as of and conditioned upon the Closing, among Union Oil, the Company
and CEO (the "Stockholder Voting Agreement");

     (e)  Voting Agreement, dated as of the date hereof, between Union Oil and
CEO (the "Voting Agreement"); and

     (f)  Employment Agreement, dated as of the date hereof but effective as of
and conditioned upon the Closing, between the Company and CEO.

     6.24 Dividend Restriction.  For a period of three years following the
          --------------------
Closing Date, the Company shall not pay any dividend in cash or property (other
than capital stock) in excess of $5,000,000 per year on the outstanding shares
of Company Common Stock unless approved by a majority of the Board of Directors
of the Company who are not affiliates of Union Oil.

     6.25 Incentive Plan.  The Company, subject to the consummation of the
          --------------
Merger, has (i) adopted the Company's 1999 Incentive Plan in the form attached
hereto as Exhibit 6.25 (the "Company Incentive Plan"), which adoption has been
approved by Union Oil as sole stockholder of

                                       46
<PAGE>

the Company, and (ii) has approved the grant of options (subject to consummation
of the Merger) pursuant to such plan to the persons and on the terms set forth
on Schedule 6.25.

     6.26 Registration Rights Agreement.  On or prior to Closing, the Company
          -----------------------------
shall enter into a registration rights agreement with CEO in substantially the
form of the Amended and Restated Registration Rights Agreement dated September
30, 1996 among Titan, CEO and others, with conforming changes so that such
agreement covers the shares of Company Common Stock owned by CEO, provides him
with two demand rights, does not contain a percentage threshold for exercising
the demand registration rights and provides that the shares to be registered
pursuant to the demand registration rights must have an estimated aggregate
offering price to the public of at least $10 million (or $20 million in the
first occasion CEO completes an offering pursuant to his demand registration
rights).


                                  ARTICLE VII

                    CONDITIONS TO OBLIGATIONS OF UNION OIL

     The obligations of Union Oil, the Company and Sub to consummate the
transactions contemplated by this Agreement shall be subject to the fulfillment
on or prior to the Closing Date of each of the following conditions:

     7.1  Representations and Warranties.  As of the date hereof and (except for
          ------------------------------
any representation or warranty that states specifically that it is made as of
the date hereof or as of an earlier date) on the Closing Date, all the
representations and warranties of Titan  contained in this Agreement shall be
true and correct without regard to any materiality qualification thereto,
provided such condition shall be deemed satisfied if the value of Titan is not
more than $20,000,000 less than it would have been if all such breached
representations and warranties had been true and correct.

     7.2  Covenants and Agreements.  Titan and the Titan Subsidiaries shall have
          ------------------------
performed and complied with in all material respects all covenants and
agreements required by this Agreement to be performed or complied with by them
on or prior to the Closing Date.

     7.3  Certificate.  Union Oil shall have received a certificate executed on
          -----------
behalf of Titan by the president of Titan, dated the Closing Date, representing
and certifying that the conditions set forth in this Article VII have been
fulfilled.

     7.4  HSR Act.  All waiting periods (and any extensions thereof) applicable
          -------
to this Agreement and the transactions contemplated hereby under the HSR Act
shall have expired or been terminated.

     7.5  Legal Proceedings.  No Proceeding shall, on the Closing Date, be
          -----------------
pending or threatened seeking to restrain, prohibit or obtain damages or other
relief in connection with this Agreement or the consummation of the transactions
contemplated hereby.

                                       47
<PAGE>

     7.6  Consents.  All consents, approvals, orders, authorizations and waivers
          --------
of, and all declarations, filings and registrations with, third parties
(including Governmental Entities) required to be obtained or made by or on the
part of the parties hereto, or otherwise reasonably necessary for the
consummation of the transactions contemplated hereby, shall have been obtained
or made, and all thereof shall be in full force and effect at the time of
Closing, unless the failure to obtain or make any such consent, approval, order,
authorization, waiver, declaration, filing or registration would not have a
Material Adverse Effect on the Company, the Surviving Corporation, its
subsidiaries or the Assets.

     7.7  Stockholder Approval.  Titan shall have received stockholder approval
          --------------------
of the Merger and the consummation of the transactions contemplated by this
Agreement as described in Section 6.4(a).

     7.8  Registration Statement.  The Registration Statement shall have become
          ----------------------
effective in accordance with the provisions of the Securities Act and no stop
order suspending the effectiveness of the Registration Statement shall be in
effect and no proceeding for such purpose shall be pending before or threatened
by the Commission.

     7.9  Listing of Company Common Stock.  The Company Common Stock shall have
          -------------------------------
been approved for listing on a national securities exchange or designated as a
national market system security on an interdealer quotation system by the NASD,
subject, in either case, to official notice of issuance.

     7.10 Accounting Matters.  The Company shall have received a "comfort"
          ------------------
letter from Titan's independent accountants, dated the effective date of the
Proxy Statement/Prospectus and addressed to the Company, of the kind
contemplated by the Statement on Auditing Standards with respect to Letters to
Underwriters promulgated by the American Institute of Certified Public
Accountants (the "AICPA Statement"), in form reasonably acceptable to the
Company, in connection with the procedures undertaken by Titan's independent
accountants with respect to the financial statements of Titan included in the
Registration Statement and the other matters with respect to Titan contemplated
by the AICPA Statement and customarily included in comfort letters relating to
transactions similar to the Merger.

     7.11 Opinion of Tax Counsel.  Union Oil and the Company shall have received
          ----------------------
a written opinion, in form reasonably satisfactory to each (the "Union Oil Tax
Opinion"), to the effect that the transfer of the Assets and the assumption of
the Liabilities specified in Section 2.1 will not result in gain or loss to
Union Oil or the Company.  In rendering such Union Oil Tax Opinion, such counsel
shall be entitled to rely upon representations of officers of Union Oil and
Titan and of their respective "affiliates" reasonably satisfactory in form and
substance to such counsel.

                                       48
<PAGE>

                                 ARTICLE VIII

                      CONDITIONS TO OBLIGATIONS OF TITAN

     The obligations of Titan to consummate the transactions contemplated by
this Agreement shall be subject to the fulfillment on or prior to the Closing
Date of each of the following conditions:

     8.1  Representations and Warranties.  As of the date hereof and (except for
          ------------------------------
any representation or warranty that states specifically that it is made as of
the date hereof or as of an earlier date) on the Closing Date, all the
representations and warranties of the Company and Union Oil contained in this
Agreement shall be true and correct without regard to any materiality
qualification thereto, provided such condition shall be deemed satisfied if the
value of the Assets is not more than $35,000,000 less than it would have been if
all such breached representations and warranties had been true and correct.

     8.2  Covenants and Agreements.  The Company and Union Oil shall have
          ------------------------
performed and complied with in all material respects all covenants and
agreements required by this Agreement to be performed or complied with by them
on or prior to the Closing Date.

     8.3  Certificate.  Titan shall have received a certificate executed on
          -----------
behalf of Union Oil and the Company by an officer of each, dated the Closing
Date, representing and certifying that the conditions set forth in this Article
VIII have been fulfilled.

     8.4  HSR Act.  All waiting periods (and any extensions thereof) applicable
          -------
to this Agreement and the transactions contemplated hereby under the HSR Act
shall have expired or been terminated.

     8.5  Legal Proceedings.  No Proceeding shall, on the Closing Date, be
          -----------------
pending or threatened seeking to restrain, prohibit or obtain damages or other
relief in connection with this Agreement or the consummation of the transactions
contemplated hereby.

     8.6  Consents.  All consents, approvals, orders, authorizations and waivers
          --------
of, and all declarations, filings and registrations with, third parties
(including Governmental Entities) required to be obtained or made by or on the
part of the parties hereto, or otherwise reasonably necessary for the
consummation of the transactions contemplated hereby, shall have been obtained
or made, and all thereof shall be in full force and effect at the time of
Closing, unless the failure to obtain or make any such consent, approval, order,
authorization, waiver, declaration, filing or registration would not have a
Material Adverse Effect on the Company and Sub considered as a whole.

     8.7  Stockholder Approval.  Titan shall have received stockholder approval
          --------------------
of the Merger and the consummation of the transactions contemplated by this
Agreement as described in Section 6.4(a).

     8.8  Registration Statement.  The Registration Statement shall have become
          ----------------------
effective in accordance with the provisions of the Securities Act and no stop
order suspending the effectiveness

                                       49
<PAGE>

of the Registration Statement shall be in effect and no proceeding for such
purpose shall be pending before or threatened by the Commission.

     8.9  Listing of Company Common Stock.  The Company Common Stock shall have
          -------------------------------
been approved for listing on a national securities exchange or designated as a
national market system security on an interdealer quotation system by the NASD,
subject, in either case, to official notice of issuance.

     8.10 Accounting Matters.  Titan shall have received a "comfort" letter from
          ------------------
the Company's independent accountants, dated the effective date of the Proxy
Statement/Prospectus and addressed to Titan, of the kind contemplated by the
Statement on Auditing Standards with respect to Letters to Underwriters
promulgated by the AICPA Statement, in form reasonably acceptable to Titan, in
connection with the procedures undertaken by the Company's independent
accountants with respect to the financial statements of the Company included in
the Registration Statement and the other matters with respect to the Assets
contemplated by the AICPA Statement and customarily included in comfort letters
relating to transactions similar to the Merger.

     8.11 Opinion of Tax Counsel.  Titan shall have received a written opinion
          ----------------------
from Thompson & Knight L.L.P., in form reasonably satisfactory to such party
(the "Tax Opinion"), to the effect that (i) the Merger will constitute a
reorganization within the meaning of Section 368(a) of the Code and/or a
transfer of property to the Company by the stockholders of Titan governed by
Section 351 of the Code, and (ii) the exchange in the Merger of Titan Common
Stock for Merger Consideration will not give rise to gain or loss to the
shareholders of Titan with respect to such exchange (except to the extent of any
cash received).  In rendering such Tax Opinion, such counsel shall be entitled
to rely upon representations of officers of Union Oil and Titan and of their
respective "affiliates" reasonably satisfactory in form and substance to such
counsel.

                                  ARTICLE IX

                                  TAX MATTERS

     9.1  Tax History of the Company.  As of the Closing Date, the Company is a
          --------------------------
newly-formed entity with no tax or operational history.

     9.2  Proration of Taxes.  The Company and Union Oil shall apportion all ad
          ------------------
valorem and similar taxes on the Assets, as well as severance or other Taxes
imposed upon any of the Assets, or with respect to any production from the
Assets, as of the Closing Date.  Union Oil shall pay and be responsible for all
such Taxes apportioned to the period ending on December 31, 1999, and the
Company shall pay and be responsible for all such Taxes apportioned to the
period beginning January 1, 2000.

                                       50
<PAGE>

     9.3  Tax Benefit Payments.
          --------------------

          (a)  In the event there is a Final Determination (as defined below)
     applicable to Union Oil's federal income tax return for the year of the
     Closing Date which results in the transfer of Union Oil's Assets to the
     Company not qualifying under Section 351(a) of the Code, the Company will
     amend its prior year Tax Returns (to the extent allowed by law) to take
     into account the larger deductions resulting from the Stepped-up-Basis (as
     defined below) of the Assets.

          (b)  The Company will pay to Union Oil an amount equal to the realized
     actual cash reduction in Taxes resulting from the Stepped-up Basis ("Tax
     Benefit").  Such Tax Benefit shall be calculated for each taxable year
     (including those for which amended returns are filed pursuant to subsection
     9.3(a) above) by determining the difference between the amount of tax that
     would have been paid for such year without the adjustments to the tax basis
     resulting from the Final Determination referenced in subsection 9.3(a)
     above and the amount of tax paid with the Stepped-up Basis and will include
     any refund interest resulting from amending the Company's Tax Returns as
     provided in subsection 9.3(a) above.

          (c)  The payment for any year shall be adjusted to take into account
     any increase or decrease in the Tax Benefit for any prior year, whether
     resulting from the filing of an amended return, a Final Determination with
     respect to such year, or otherwise.

          (d)  "Final Determination" shall mean (i) a final decision with
     respect to the proposed adjustment by an IRS appeals officer as evidenced
     by the issuance of a 90-day letter, IRS Form 870-AD or like notice unless
     judicial proceedings are initiated, (ii) a final non-appealable decision
     with respect to the proposed adjustment by a court of competent
     jurisdiction, or (iii) the settlement of the proposed adjustment with the
     consent of Titan and the Company (which consent shall not be unreasonably
     withheld).

          (e)  "Stepped-up Basis" shall mean a tax basis for the Assets as
     adjusted pursuant to the Final Determination referenced in subsection
     9.3(a) above.

          (f)  The parties agree to treat all payments pursuant to this Section
     9.3 as adjustments to the purchase price for federal income tax purposes.

          (g)  At the Company's option, any payments required hereunder may be
     made in either cash or Company Common Stock, with the number of shares to
     be determined by dividing the amount of the payment by the average of the
     closing prices for the Common Stock for the twenty trading days previous to
     the date of payment on a national securities exchange or the Nasdaq
     National Market, as applicable.

                                       51
<PAGE>

                                   ARTICLE X

                       TERMINATION, AMENDMENT AND WAIVER

     10.1 Termination.  This Agreement may be terminated and the transactions
          -----------
contemplated hereby abandoned at any time prior to the Closing in the following
manner:

          (a)  By mutual written consent of Union Oil and Titan; or

          (b)  By Union Oil or Titan, if:

               (i)    The Closing shall not have occurred on or before May 31,
          2000, unless such failure to close shall be due to a material breach
          of this Agreement by the party seeking to terminate this Agreement
          pursuant to this clause (i);

               (ii)   There shall be any Applicable Law that makes consummation
          of the transactions contemplated hereby illegal or otherwise
          prohibited or a Governmental Entity shall have issued an order, decree
          or ruling or taken any other action permanently restraining, enjoining
          or otherwise prohibiting the consummation of the transactions
          contemplated hereby, and such order, decree, ruling or other action
          shall have become final and nonappealable; or

               (iii)  The approval of the stockholders of Titan contemplated by
          this Agreement shall not have been obtained by reason of the failure
          to obtain the required vote specified in Section 6.4 at a duly held
          meeting of stockholders or any adjournment thereof.

          (c)  By Union Oil, if (i) any of the representations and warranties of
     Titan contained in this Agreement shall not be true and correct such that
     the condition set forth in Section 7.1 would not be satisfied or (ii) Titan
     shall have failed to fulfill in any material respect any of its material
     obligations under this Agreement, which failure is material to the
     obligations of Titan under this Agreement, and, in the case of each of
     clauses (i) and (ii), such misrepresentation, breach of warranty or failure
     (provided it can be cured) has not been cured within 30 days of notice
     thereof by Union Oil;

          (d)  By Titan, if (i) any of the representations and warranties of the
     Company or Union Oil contained in this Agreement shall not be true and
     correct such that the condition set forth in Section 8.1 would not be
     satisfied, (ii) the Company or Union Oil shall have failed to fulfill in
     any material respect any of its material obligations under this Agreement,
     which failure is material to the obligations of the Company or Union Oil
     under this Agreement, and, in the case of each of clauses (i) and (ii),
     such misrepresentation, breach of warranty or failure (provided it can be
     cured) has not been cured within 30 days of notice thereof by Titan, or
     (iii) such termination is necessary to allow Titan to enter into an
     agreement in accordance with Section 6.2 hereof with respect to a Superior
     Proposal which

                                       52
<PAGE>

     Titan's Board of Directors has determined is more favorable to the
     stockholders of Titan than the transactions contemplated hereby; or

          (e)  By Union Oil, if (i) the Board of Directors shall withdraw,
     modify or change its recommendation or approval in respect of this
     Agreement in a manner adverse to Union Oil or (ii) a tender offer or
     exchange offer for outstanding shares of capital stock of Titan then
     representing 30% or more of the combined power to vote generally for the
     election of directors is commenced, and the Board of Directors of Titan
     does not recommend that stockholders not tender their shares into such
     tender or exchange offer.

     10.2 Effect of Termination.
          ---------------------

     (a)  In the event of the termination of this Agreement pursuant to Section
10.1 by Titan or Union Oil, written notice thereof shall forthwith be given to
the other party specifying the provision hereof pursuant to which such
termination is made, and this Agreement shall become void and have no effect,
and there shall be no liability hereunder on the part of Titan, Union Oil, the
Company, Sub or any of their respective directors, officers, employees,
stockholders or representatives, except that the agreements contained in this
Section 10.2 and in Sections 6.11 and 6.13 and in Article XII shall survive the
termination hereof.  Nothing contained in this Section 10.2 shall otherwise
relieve any party from liability for damages actually incurred as a result of
any breach of this Agreement.  No termination of this Agreement shall affect the
obligations of the parties pursuant to the confidentiality agreements referred
to in Section 6.1(a) and 6.1(b).

     (b)  If (i) Union Oil shall have terminated this Agreement pursuant to
Section 10.1(e), (ii) Titan shall have terminated this Agreement pursuant to
Section 10.1(d)(iii), or (iii) the Agreement is terminated by Union Oil pursuant
to Section 10.1(c)(ii) and (with respect to the foregoing clause (iii) only)
within 180 days after such termination (A) a transaction is consummated, which
transaction, if offered or proposed, would constitute an Acquisition Proposal,
(B) an agreement for such a transaction is entered into or (C) any person shall
have acquired beneficial ownership or the right to acquire beneficial ownership
of, or any "group" (as such term is defined under Section 13(d) of the Exchange
Act and the rules and regulations promulgated hereunder) shall have been formed
that beneficially owns, or has the right to acquire beneficial ownership of,
outstanding shares of capital stock of Titan then representing 50% or more of
the combined power to vote generally for the election of directors, then in any
such case Titan shall pay in immediately available funds simultaneously with
such termination if pursuant to Section 10.1(d)(iii) and promptly, but in no
event later than two (2) business days after the date of such termination if
pursuant to Section 10.1(e), and promptly after the occurrence of the event
specified in clause (iii) above in the case of such an event, to Union Oil a
termination fee of $7,500,000, which fee shall be payable by wire transfer to
such account as Union Oil may designate in writing to Titan.  No fee shall be
paid pursuant to this Section 10.2(b) if either Union Oil or the Company shall
be in material breach of its obligations hereunder, after Titan has afforded
Union Oil and the Company a 30 day period after notice in which to cure such
breach.

     10.3 Amendment.  Any provision of this Agreement (including the Exhibits
          ---------
hereto) may be amended, to the extent permitted by law, prior to the Effective
Time if, and only if, such

                                       53
<PAGE>

amendment is in writing and signed, in the case of an amendment, by the Company,
Union Oil, Sub and Titan; provided that after the adoption of this Agreement by
the stockholders of Titan, no such amendment shall, without the further approval
of such stockholders, alter or change (i) the amount or kind of consideration to
be received in exchange for any shares of Titan Common Stock or (ii) any of the
other terms or conditions of this Agreement if such alteration or change would
adversely affect such stockholders.

     10.4 Waiver.  Each of Union Oil, the Company and Sub and Titan may (i)
          ------
waive any inaccuracies in the representations and warranties of the other
contained herein or in any document, certificate or writing delivered pursuant
hereto or (ii) waive compliance by the other with any of the other's agreements
or fulfillment of any conditions to its own obligations contained herein.  Any
agreement on the part of a party hereto to any such waiver shall be valid only
if set forth in an instrument in writing signed by or on behalf of such party.
No failure or delay by a party hereto in exercising any right, power or
privilege hereunder shall operate as a waiver thereof nor shall any single or
partial exercise thereof preclude any other or further exercise thereof or the
exercise of any other right, power or privilege.

                                  ARTICLE XI

                    SURVIVAL MATTERS; CROSS INDEMNIFICATION

     11.1 Survival of Representations and Warranties.  The representations and
          ------------------------------------------
warranties of the parties contained in this Agreement shall not survive the
Closing.

     11.2 Survival of Covenants and Agreements.  The covenants and agreements of
          ------------------------------------
the parties to be performed after the Closing contained in this Agreement shall
survive the Closing.

     11.3 Indemnification.
          ---------------

     (a)  The Company shall defend, indemnify and hold harmless the Union Oil
Indemnified Parties against any and all the Company Liabilities, whether or not
the result of the sole or partial negligence or otherwise culpable conduct or
fault of one or more of the Union Oil Indemnified Parties,  including, without
limitation, any such loss resulting from or caused in whole or in part by the
Company Indemnified Parties' or their predecessors' violation of or failure to
fulfill duties imposed by, or incurrence of liability under, any Environmental
Laws. UNION OIL AND THE COMPANY AGREE THAT THE PROVISIONS OF THIS SECTION SHALL
APPLY REGARDLESS OF WHETHER THE UNION OIL INDEMNIFIED PARTIES OR THEIR
PREDECESSORS ARE OR WERE WHOLLY OR PARTIALLY OR CONCURRENTLY, ACTIVELY OR
PASSIVELY, NEGLIGENT OR OTHERWISE AT FAULT, AND WHETHER OR NOT THE LOSSES ARISE
OUT OF A THEORY OF NEGLIGENCE, NEGLIGENCE PER SE, TRESPASS, NUISANCE, STRICT
LIABILITY, PRODUCTS LIABILITY, PREMISES LIABILITY, LIABILITY BASED ON STATUTE,
LIABILITY BASED ON CONTRACT, OR ANY OTHER THEORY OF LIABILITY, AND REGARDLESS OF
WHO ASSERTS THE LOSS, INCLUDING, WITHOUT LIMITATION, PRIVATE CITIZENS, PERSONS
OR

                                       54
<PAGE>

ORGANIZATIONS, OR ANY FOREIGN, FEDERAL, STATE, MUNICIPAL OR LOCAL GOVERNMENT OR
THEIR REPRESENTATIVES IN EACH CASE WITHOUT REGARD TO SOLE, PARTIAL OR CONCURRENT
NEGLIGENCE, STRICT LIABILITY, GROSS NEGLIGENCE, WILLFUL MISCONDUCT OR OTHER
FAULT OF THE UNION OIL INDEMNIFIED PARTIES.

     (b)  Union Oil shall defend, indemnify and hold harmless the Company
Indemnified Parties against any and all Union Oil Liabilities, whether or not
the result of the sole or partial negligence or otherwise culpable conduct or
fault of one or more of the Company Indemnified Parties.  UNION OIL AND THE
COMPANY AGREE THAT THE PROVISIONS OF THIS SECTION SHALL APPLY REGARDLESS OF
WHETHER THE COMPANY INDEMNIFIED PARTIES OR THEIR PREDECESSORS ARE OR WERE WHOLLY
OR PARTIALLY OR CONCURRENTLY, ACTIVELY OR PASSIVELY, NEGLIGENT OR OTHERWISE AT
FAULT, AND WHETHER OR NOT THE LOSSES ARISE OUT OF A THEORY OF NEGLIGENCE,
NEGLIGENCE PER SE, TRESPASS, NUISANCE, STRICT LIABILITY, PRODUCTS LIABILITY,
PREMISES LIABILITY, LIABILITY BASED ON STATUTE, LIABILITY BASED ON CONTRACT, OR
ANY OTHER THEORY OF LIABILITY, AND REGARDLESS OF WHO ASSERTS THE LOSS,
INCLUDING, WITHOUT LIMITATION, PRIVATE CITIZENS, PERSONS OR ORGANIZATIONS, OR
ANY FOREIGN, FEDERAL, STATE, MUNICIPAL OR LOCAL GOVERNMENT OR THEIR
REPRESENTATIVES IN EACH CASE WITHOUT REGARD TO SOLE, PARTIAL OR CONCURRENT
NEGLIGENCE, STRICT LIABILITY, GROSS NEGLIGENCE, WILLFUL MISCONDUCT OR OTHER
FAULT OF THE COMPANY INDEMNIFIED PARTIES.

     (c)  The Company, Union Oil and Titan acknowledge and agree that the
provisions of this Section 11.3 and related provisions are the result of mutual
compromise and an allocation of risk with respect to the subject matter of this
Agreement.  The provisions of this Section 11.3 and related provisions of this
Article XI shall be effective notwithstanding the knowledge or lack of knowledge
of the Company, Union Oil or Titan with respect to the condition of the Assets
or any actual or potential liability or obligation arising under Environmental
Laws or relating to Hazardous Materials, known or unknown, contingent or
otherwise.  The Company, Union Oil and Titan further acknowledge and agree that
the provisions of this Section 11.3 and related provisions of this Article XI
have been given individual weight by them in connection with entering into this
Agreement.   The Company, Union Oil and Titan acknowledge and agree that the
allocations of risk and responsibility contained in this Section 11.3 and
related provisions are mutually intended by them to be given full effect.

     11.4 Indemnification Procedure.  Each person to be indemnified pursuant to
          -------------------------
this Article XI (an "Indemnified Party") agrees to give prompt notice to the
indemnifying party of the assertion of any claim, or the commencement of any
suit, action or proceeding, brought against or sought to be collected from such
Indemnified Party (each a "Third Party Claim"), in respect of which indemnity
may be sought by such Indemnified Party under this Article XI; provided that the
omission so to promptly notify the indemnifying party with respect to a Third
Party Claim brought against or sought to be collected from such Indemnified
Party will not relieve the indemnifying party from any Liability that it may
have to such Indemnified Party under this Article XI except to the extent that

                                       55
<PAGE>

such failure has materially prejudiced such indemnifying party with respect to
the defense of such Third Party Claim. If any Indemnified Party shall seek
indemnity under this Article XI with respect to a Third Party Claim brought
against or sought to be collected from such Indemnified Party, the indemnifying
party shall be entitled to participate therein and, to the extent that it
wishes, to assume and direct the defense and settlement thereof with counsel
satisfactory to such Indemnified Party. After notice from the indemnifying party
to an Indemnified Party of its election to assume and direct the defense and
settlement of a Third Party Claim brought against or sought to be collected from
such Indemnified Party that such indemnifying party is entitled to assume and
direct under the terms hereof, the indemnifying party shall not be liable to
such Indemnified Party under this Article XI for any legal or other expenses
subsequently incurred by such Indemnified Party in connection with the defense
thereof other than reasonable costs of investigation, unless the Indemnifying
Party and the Indemnified Party are both named parties to any such action, claim
or demand and representation of both parties by the same counsel would be
inappropriate due to actual or potential conflicts of interest between them.
Notwithstanding the foregoing provisions of this Section 11.4, the indemnifying
party shall not (A) without the prior written consent of an Indemnified Party,
effect any settlement of any pending or threatened proceeding in respect of
which such Indemnified Party is, or with reasonable foreseeability, could have
been a party and indemnity could have been sought hereunder by such Indemnified
Party for a Third Party Claim brought against or sought to be collected from
such Indemnified Party, unless such settlement includes an unconditional
release, in form and substance satisfactory to the Indemnified Party, of such
Indemnified Party from all Liability arising out of such proceeding (provided
that, whether or not such a release is required to be obtained, the indemnifying
party shall remain liable to such Indemnified Party in accordance with this
Article XI in the event that a Third Party Claim is subsequently brought against
or sought to be collected from such Indemnified Party) or (B) be liable for any
settlement of any Third Party Claim brought against or sought to be collected
from an Indemnified Party effected without such indemnifying party's written
consent (which shall not be unreasonably withheld), but if settled with such
indemnifying party's written consent, or if there is a final judgment for the
plaintiff in any such Third Party Claim, such indemnifying party agrees (to the
extent stated above) to indemnify the Indemnified Party from and against any
loss, liability, claim, damage or expense by reason or such settlement or
judgment. The indemnification required by this Article XI shall be made by
periodic payments of the amount thereof during the course of the investigation
or defense, as and when bills are received or loss, liability, claim, damage or
expense is incurred.

     11.5 Insurance.
          ---------

     (a)  Notwithstanding any provision to the contrary herein, an indemnifying
party hereunder shall have no obligation for a liability or any part thereof
sought to be indemnified by an Indemnified Party pursuant to this Article XI to
the extent that the Indemnified Party has received payment from an insurer on
account of such liability, which payment has not been offset through a matching
deductible or premium adjustments made on account of such payment.

     (b)  To the extent that an Indemnified Party may have insurance for a
liability or any part thereof sought to be indemnified under this Article XI,
until an insurer makes payment on account thereof, the parties shall proceed
with indemnification under this Article XI as if the Indemnified Party is not
covered by such insurance.  An indemnifying party which has paid all or any part
of an

                                       56
<PAGE>

indemnification claim shall then be reimbursed by the Indemnified Party from
insurance payment later received, if any, which payment has not been offset
through a matching deductible or premium adjustments made on account of such
payment.

     11.6 Definitions.  As used in this Article XI, each of the following terms
          -----------
has the meaning given it below:

          (a)  "Company Indemnified Parties" shall mean the Company and its
     Subsidiaries and any officer, director, employee, agent or other
     representative thereof (individually, a "Company Indemnified Party").

          (b)  "Company Liabilities" shall mean all Liabilities, known or
     unknown, absolute, accrued contingent or otherwise, to the extent (A)
     assumed by the Company pursuant to Section 2.1 or (B) directly or
     indirectly related to Titan or its subsidiaries or their assets, operations
     or businesses, in each case regardless of whether such Liabilities exist or
     arise before, at or after the Closing Date and in each case including all
     Liabilities attributable to damage to property, injury to or death of
     persons or other living things, natural resource damages, response,
     remediation restoration, investigation, monitoring, containment, cleanup,
     removal, closure, corrective action or other work of any kind or nature,
     abandonment expenses, violation of or non-compliance with environmental
     laws, the presence or release or threatened release of Hazardous Materials
     (any of the foregoing occurring or existing at any location), or the
     environmental condition of the property (including disposal of wastes on or
     from the property);  provided, however, that the Excluded Liabilities shall
     not constitute Company Liabilities; provided further, that, notwithstanding
     any provision to the contrary herein, any Liability constituting an Expense
     or obligation for which the Company is liable under the terms of this
     Agreement shall constitute a Company Liability.

          (c)  "Union Oil Indemnified Parties" shall mean Union Oil and its
     affiliates, other than the Company and its subsidiaries, and any officer,
     director, employee, agent or other representative thereof (individually, a
     "Union Oil Indemnified Party").

          (d)  "Union Oil Liabilities" shall mean the Excluded Liabilities and
     all other Liabilities known or unknown, absolute, accrued, contingent or
     otherwise, arising out of or associated with the affairs or operations of
     Union Oil, its parent and any of its subsidiaries and which are not the
     Company Liabilities.

                                  ARTICLE XII

                                 MISCELLANEOUS

     12.1 Notices.  All notices, requests, demands and other communications
          -------
required or permitted to be given or made hereunder by any party hereto shall be
in writing and shall be deemed to have been duly given or made if delivered
personally, or sent by prepaid overnight delivery

                                       57
<PAGE>

service, or sent telefax, to the parties at the following addresses (or at such
other addresses as shall be specified by the parties by like notice):

          (a)  If to Titan:

               Titan Exploration, Inc.
               500 West Texas, Suite 200
               Midland, Texas
               Attention: Jack Hightower
               Telefax: 915-687-3863

          with a copy to:

               Thompson & Knight L.L.P.
               1700 Pacific Avenue, Suite 3300
               Dallas, Texas 75201
               Attention: Joe Dannenmaier
               Telefax: 214-969-1751

          (b)  If to Union Oil, the Company or Sub:

               c/o Mr. Phil Ballard
               Manager, Corporate Development
               Union Oil Company of California
               One Sugar Creek Place
               14141 Southwest Freeway
               Sugar Land, Texas 77478
               Telefax: (281) 287-5170

          with a copy to:

               Jay Cuclis, Esq. / David Stone, Esq.
               Vinson & Elkins
               2300 First City Tower
               1001 Fannin Tower
               Houston, Texas 77002
               Telefax: (713) 615-5141

                                       58
<PAGE>

          and another copy to:

               Union Oil Company of California
               2141 Rosecrans Avenue, Suite 4000
               El Segundo, California 90245
               Attn:  (1) General Counsel, and
                      (2) Vice President, Corporate Development
               Telefax: (310) 726-7819

     12.2 Entire Agreement.  This Agreement, together with the Ancillary
          ----------------
Agreements, the schedules, exhibits and other writings referred to herein or
delivered pursuant hereto constitute the entire agreement between the parties
hereto with respect to the subject matter hereof and supersede all prior
agreements and understandings, both written and oral, between the parties with
respect to the subject matter hereof.

     12.3 Binding Effect; Assignment; No Third Party Benefit.  This Agreement
          --------------------------------------------------
shall be binding upon and inure to the benefit of the parties hereto and their
respective successors and permitted assigns; provided, however, that neither
this Agreement nor any of the rights, interests or obligations hereunder shall
be assigned by any of the parties hereto (by operation of law or otherwise)
without the prior written consent of the other parties.  Except as provided in
Article I and Section 6.21, nothing in this Agreement, express or implied, is
intended to or shall confer upon any person other than Titan, the Company and
Union Oil any rights, benefits or remedies of any nature whatsoever under or by
reason of this Agreement.

     12.4 Severability.  If any provision of this Agreement is held to be
          ------------
unenforceable, this Agreement shall be considered divisible and such provision
shall be deemed inoperative to the extent it is deemed unenforceable, and in all
other respects this Agreement shall remain in full force and effect; provided,
however, that if any such provision may be made enforceable by limitation
thereof, then such provision shall be deemed to be so limited and shall be
enforceable to the maximum extent permitted by Applicable Law.

     12.5 Governing Law.  This Agreement shall be governed by and construed and
          -------------
enforced in accordance with the laws of the State of Delaware.

     12.6 Descriptive Headings.  The descriptive headings herein are inserted
          --------------------
for convenience of reference only, do not constitute a part of this Agreement
and shall not affect in any manner the meaning or interpretation of this
Agreement.

     12.7 Gender.  Pronouns in masculine, feminine and neuter genders shall be
          ------
construed to include any other gender, and words in the singular form shall be
construed to include the plural and vice versa, unless the context otherwise
requires.

     12.8 References.  All references in this Agreement to Articles, Sections
          ----------
and other subdivisions refer to the Articles, Sections and other subdivisions of
this Agreement unless expressly provided otherwise.  The words "this Agreement",
"herein", "hereof", "hereby", "hereunder" and

                                       59
<PAGE>

words of similar import refer to this Agreement as a whole and not to any
particular subdivision unless expressly so limited.  Whenever the words
"include", "includes" and "including" are used in this Agreement, such words
shall be deemed to be followed by the words "without limitation".

     12.9  Counterparts. This Agreement may be executed by the parties hereto in
           ------------
any number of counterparts, each of which shall be deemed an original, but all
of which shall constitute one and the same agreement.  Each counterpart may
consist of a number of copies hereof each signed by less than all, but together
signed by all, the parties hereto.

     12.10 Specific Performance.  The parties hereto acknowledge and agree that
           --------------------
Titan would not have an adequate remedy at law for money damages in the event
that this Agreement were not performed in accordance with its specific terms. It
is accordingly agreed that Titan shall be entitled to enforce specifically the
provisions of this Agreement, in any court of the United States or any state
thereof having jurisdiction, in addition to any other remedy to which Titan may
be entitled under this Agreement or at law or in equity.

                                 ARTICLE XIII

                                  DEFINITIONS

     13.1  Certain Defined Terms.  As used in this Agreement, each of the
           ---------------------
following terms has the meaning given it below:

     "affiliate" shall mean, with respect to any person, any other person that,
directly or indirectly, through one or more intermediaries, controls, is
controlled by or is under common control with, such person.

     "Applicable Law" shall mean any statute, law, rule or regulation or any
judgment, order, writ, injunction or decree of any Governmental Entity to which
a specified person or property is subject.

     "Arbitrating Firm" shall mean one of the "big five" independent public
accounting firms (other than any such firm that audited the 1998 financial
statements of Titan, Union Oil or the Company) selected by agreement of Union
Oil and the Company or, if they cannot agree, chosen by lot by the Company from
among the eligible firms.

     "Business Day" shall mean a day on which national banks are open for the
transaction of business.

     "Commission" shall mean the Securities and Exchange Commission.

     "Encumbrances" shall mean liens, charges, pledges, options, mortgages,
deeds of trust, security interests, claims, restrictions (whether on voting,
sale, transfer, disposition or otherwise), easements and other encumbrances of
every type and description, whether imposed by law, agreement, understanding or
otherwise.

                                       60
<PAGE>

     "Environmental Laws" shall mean all federal, state and local laws and
regulations relating to pollution or protection of human health or the
environment, including without limitation, laws relating to Releases or
threatened Releases of Hazardous Materials into the indoor or outdoor
environment (including, without limitation, ambient air, surface water, ground
water, land surface or substance strata) or otherwise relating to the
manufacture, processing, distribution, use, treatment, storage, Release,
disposal, transport or handling of Hazardous Materials and all laws and
regulations with regard to record keeping, notification, disclosure and
reporting requirements respecting Hazardous Materials.

     "Environmental Liabilities" shall mean all obligations, duties, losses,
liabilities, claims, fines, expenses, damages, costs (including attorney's fees
and expenses) or penalties created by, related to, or arising out of any
Environmental Law, whether accruing before or after the Closing Date.

     "Environmental Response Measures" shall mean any of the following, to the
extent required to effectuate compliance with Applicable Environmental Laws:
the cost of investigation, remedial response obligations, removal response
obligations, interim response obligations, ecological investigation obligations,
natural resource damage remediation obligations, and obligations to comply with
orders of any Governmental Entity.

     "ERISA" shall mean the Employee Retirement Income Security Act of 1974, as
amended.

     "Exchange Act" shall mean the Securities Exchange Act of 1934.

     "Governmental Entity" shall mean any court or tribunal in any jurisdiction
(domestic or foreign) or any public, governmental, or regulatory body, agency,
department, commission, board, bureau or other authority or instrumentality
(domestic or foreign).

     "Hazardous Materials" shall mean all substances defined as Hazardous
Substances, Oil, Pollutants or Contaminants in the National Oil and Hazardous
Substances Pollution Contingency Plan, 40 C.F.R. (S) 300.5, or defined as such
by, or regulated as such under, any Environmental Law, including without
limitation, PCBs, mercury and NORM, or which otherwise may be the basis for any
person (including, without limitation, any federal, state, local or foreign
government, and natural persons) to require cleanup, removal, treatment or
remediation.

     "HSR Act" shall mean the Hart-Scott-Rodino Antitrust Improvements Act of
1976, as amended.

     "IRS" shall mean the Internal Revenue Service.

     "Liabilities" shall mean all losses, liabilities, claims, taxes, damages,
costs (including costs of investigation) and expenses (including reasonable
legal fees and expenses).

     "Lease" shall mean any oil and gas lease, oil, gas and mineral lease or
similar interest.

                                       61
<PAGE>

     "Material Adverse Effect" shall mean with respect to any person any adverse
change or adverse condition in or relating to the financial condition of such
person and its subsidiaries that is material to such person and its subsidiaries
taken as a whole; provided, however, that any prospective change or changes in
the conditions listed above or relating to or resulting from (i) any change or
changes in the prices of oil, gas, natural gas liquids or other hydrocarbon
products or (ii) general economic conditions or local, regional, national or
international industry conditions.

     "NASD" shall mean the National Association of Securities Dealers, Inc.

     "Permits" shall mean licenses, permits, variances, exemptions, orders,
franchises, approvals and  other authorizations of or from Governmental
Entities.

     "Permitted Encumbrances" shall mean:

          (a)  any materialman's, mechanic's, repairman's, employee's,
     contractor's, operator's or other similar liens or charges for unpaid
     liquidated amounts arising in the ordinary course of business which are not
     yet due;

          (b)  liens for Taxes which are not yet due;

          (c)  all lessors' royalties, overriding royalties, and other similar
     burdens which do not, with respect to Union Oil, the Company and the
     Assets, cause the representations set forth in Section 3.14 and, with
     respect to Titan and the Titan Subsidiaries, cause the representations in
     Section 4.14 to be untrue;

          (d)  unitization and pooling designations, declarations, orders and
     agreements which do not, with respect to Union Oil, the Company and the
     Assets, cause the representations set forth in Section 3.14 and, with
     respect to Titan and the Titan Subsidiaries, cause the representations in
     Section 4.14 to be untrue; and

          (e)  such other encumbrances as are not, either individually or in the
     aggregate, reasonably expected to have a Material Adverse Effect (i) on the
     Assets or the Business with respect to Union Oil, the Company and Sub and
     (ii) the assets of Titan and the Titan Subsidiaries with respect to Titan.

     "person" shall mean any individual, corporation, partnership, joint
venture, association, joint-stock company, trust, enterprise, unincorporated
organization or Governmental Entity.

     "Proceedings" shall mean all proceedings, actions, claims, suits,
investigations and inquiries by or before any arbitrator or Governmental Entity.

     "reasonable efforts" shall mean a party's best efforts in accordance with
reasonable commercial practice and without the incurrence of unreasonable
expense.

                                       62
<PAGE>

     "Release" shall mean any release, spill, emission, discharge, leaking,
pumping, injection, deposit, disposal, dispersal, leaching or migration into the
indoor or outdoor environment (including, without limitation, ambient air,
surface water, groundwater, land surface or subsurface strata) or into or out of
any property, including the movement of Hazardous Materials through or in air,
soil, surface water, groundwater or property.

     "Securities Act" shall mean the Securities Act of 1933, as amended.

     "Tax" shall mean any income taxes or similar assessments or any sales,
excise, occupation, use, ad valorem, property, production, severance,
transportation, employment, payroll, franchise or other tax imposed by any
United States federal, state or local (or any foreign or provincial) taxing
authority, including any interest, penalties or additions attributable thereto.

     "Taxing Authority" shall mean any governmental authority responsible for
the imposition of any Tax.

     "Tax Return" shall mean any return or report, including any related or
supporting information, with respect to Taxes.

     "To the knowledge" of a person (or similar references to a person's
knowledge) shall mean the actual knowledge of any of such person's officers, as
such knowledge has been obtained in the normal conduct of the business of such
person or its subsidiaries or in connection with the preparation of the
Schedules to this Agreement and the furnishing of information as contemplated by
this Agreement.

     "Transaction" means the Merger and the other transactions contemplated by
this Agreement.

     "Treasury Regulations" shall mean one or more treasury regulations
promulgated under the Code by the Treasury Department of the United States.

     13.2 Certain Additional Defined Terms.  In addition to such terms as are
          --------------------------------
defined in the opening paragraph of and the recitals to this Agreement and in
Section 12.1, the following terms are used in this Agreement as defined in the
Sections set forth opposite such terms:

                    Defined Term                       Section Reference
                    ------------                       -----------------

          Acquisition Proposal                              6.2(a)
          Acquisition Proposal Interest                     6.2(a)
          Action                                            6.21(a)
          AFEs                                              3.20
          Agreement                                         Preamble
          AICPA Statement                                   7.10
          Ancillary Agreements                              6.23
          Arbitrating Firm                                  2.4(c)

                                       63
<PAGE>

                    Defined Term                       Section Reference
                    ------------                       -----------------

          Assets                                            2.2
          Assumed Option                                    1.12
          Audited Financial Statements                      3.6
          Business                                          Preamble
          Business Opportunities Agreement                  6.23(a)
          Cash Amount                                       2.4
          CEO                                               1.12
          Certificates                                      1.9(a)
          Closing                                           1.2
          Closing Date                                      1.2
          Code                                              Preamble
          Common Shares Trust                               1.13(b)
          Company                                           Preamble
          Company Acquisition Proposal                      6.3
          Company Common Stock                              Preamble
          Company Incentive Plan                            6.25
          Company Indemnified Party                         11.6(c)
          Company Liabilities                               11.6(d)
          Company Severance Agreements                      6.17
          Consent Required Asset                            2.5
          DGCL                                              1.1
          Effective Time                                    1.3
          Employees                                         6.12(a)
          Employment Arrangements                           6.12(a)
          Excess Shares                                     1.13(a)
          Exchange Agent                                    1.9(a)
          Exchange Ratio                                    1.7(a)
          Excluded Assets                                   2.3
          Excluded Liabilities                              2.1
          Executive Letter Agreement                        6.17
          Expenses                                          6.11
          Final Determination                               9.3(d)
          Financial Statements                              3.6
          Fractional Shares                                 1.13
          GAAP                                              2.1
          Voting Agreement                                  6.23
          Indemnified Party                                 11.4
          Indemnified Person(s)                             6.21(a)
          Latest Balance Sheet                              3.6
          Merger                                            Preamble
          Merger Consideration                              1.7
          Non-Dilution Agreement                            6.23(b)
          Properties                                        2.2

                                       64
<PAGE>

                    Defined Term                       Section Reference
                    ------------                       -----------------

          Proxy Statement/Prospectus                        6.4(b)
          Records                                           6.1(c)
          Registration Rights Agreement                     6.23(c)
          Registration Statement                            6.4(d)
          Severance Benefits                                6.12(a)
          Special Meeting                                   6.4(a)
          Stepped-up Basis                                  9.3(e)
          Stockholder Approval                              4.3
          Stockholder Voting Agreement                      6.23
          Sub                                               Preamble
          Superior Proposal                                 6.2(c)
          Surviving Corporation                             1.1
          Tax Benefit                                       9.3(b)
          Tax Opinion                                       8.11
          Third Party Claim                                 11.4
          Titan Basic Documents                             4.18
          Titan Commission Filings                          4.5(a)
          Titan Common Stock                                9.3(b)
          Titan Disclosure Letter                           4.1
          Titan Employee Option                             1.12
          Titan Engagement Letter                           4.22
          Titan Options                                     4.2(b)
          Titan Rights                                      4.2(a)
          Titan Rights Agreement                            4.2(a)
          Titan Subsidiaries                                4.1
          Unaudited Financial Statements                    3.6
          Union Oil                                         Preamble
          Union Oil Basic Documents                         3.18
          Union Oil DB Plans                                6.12(d)
          Union Oil DC Plans                                6.12(c)
          Union Oil Disclosure Letter                       3.1
          Union Oil Indemnified Party                       11.6(a)
          Union Oil Liabilities                             11.6(b)
          Union Oil Tax Opinion                             7.11

                                       65
<PAGE>

     IN WITNESS WHEREOF, each of the parties has caused this Agreement to be
executed on its behalf by its representative thereunto duly authorized, all as
of the date first above written.


                                        UNION OIL COMPANY OF CALIFORNIA



                                        By: /s/ Timothy H. Ling
                                            --------------------
                                            Timothy H. Ling
                                            Chief Financial Officer and
                                            Executive Vice President,
                                            North American Energy Operations


                                        TITAN RESOURCES HOLDINGS, INC.



                                        By: /s/ Phillip Ballard
                                            -------------------
                                            Phillip Ballard
                                            Vice President

                                        TRH, INC.


                                        By: /s/ Phillip Ballard
                                            --------------------
                                            Phillip Ballard
                                            Vice President

                                        TITAN EXPLORATION, INC.


                                        By: /s/ Jack D. Hightower
                                            ---------------------
                                            Jack D. Hightower
                                            Chief Executive Officer and
                                            President

                                       66

<PAGE>

                                                                    EXHIBIT 2.4


                       BUSINESS OPPORTUNITIES AGREEMENT

     This BUSINESS OPPORTUNITIES AGREEMENT (this "Agreement"), dated as of
December 13, 1999, is entered into by Union Oil Company of California, a
California corporation ("Union Oil"), Titan Resources Holdings, Inc., a newly
formed Delaware corporation and wholly owned subsidiary of Union Oil (the
"Company"), TRH, Inc., a newly formed Delaware corporation and a wholly owned
subsidiary of the Company ("Sub"), and Titan Exploration, Inc., a Delaware
corporation ("Titan").

     This Agreement is being executed and delivered simultaneously with the
execution and delivery of the Agreement and Plan of Merger dated December 13,
1999 (the "Merger Agreement") among Union Oil, the Company, Sub and Titan.
Pursuant to the Merger Agreement, Sub will be merged with and into Titan, which
will be the Surviving Corporation. All capitalized terms used and not defined
herein (as well as the terms "affiliate" and "person") have the meanings
attributable to them in the Merger Agreement.  As a result of the Merger, Union
Oil will own a majority of the outstanding capital stock of the Company, and the
Company will own all of the outstanding capital stock of the Surviving
Corporation.

     Titan believes that it and its stockholders will benefit from the Merger
and that the Merger is in its best interest and in the best interest of its
stockholders.  Union Oil, however, is unwilling to enter into the Merger
Agreement unless Titan and the Company enter into this Agreement because Union
Oil engages in the exploration for and the development, production and marketing
of natural gas and crude oil in the United States.  The businesses in which
Union Oil engages are similar to those in which Titan and its subsidiaries
engage and in which the Company and its subsidiaries, including the Surviving
Corporation, will engage following the Merger.

     As the owner of a controlling interest in the Company following the Merger,
Union Oil may owe certain duties to the Company.  Pursuant to a Stockholders
Agreement entered into simultaneously with the execution and delivery of this
Agreement, Union Oil will have the right to nominate certain persons
("Designees") to serve on the board of directors of the Company following the
Merger. Certain of the Designees may be directors of or employed by Union Oil or
companies in which Union Oil has an interest, other than the Company and its
subsidiaries.  These Designees will have duties to the Company and duties to
Union Oil or such other companies.

     The law relating to duties that Union Oil or its Designees may owe to the
Company is not clear.  The application of such law to particular circumstances
is often difficult to predict, and if a court were to hold that Union Oil or one
of its Designees breached any such duty Union Oil or such Designee could be held
liable for damages in a legal action brought on behalf of the Company.

                                       1
<PAGE>

     In order to induce Union Oil to enter into the Merger Agreement, Titan and
the Company are willing to enter into this Agreement in order to renounce,
effective upon consummation of the Merger, any interest or expectancy either of
them or their subsidiaries may have in the classes or categories of business
opportunities specified herein that are presented to or identified by Union Oil
or any of its Designees, as more fully described herein.  As a result of this
Agreement, Union Oil may continue to conduct its business and to pursue certain
business opportunities without an obligation to offer such opportunities to the
Company or any of its subsidiaries, and any Designee may continue to discharge
his or her responsibilities as a director or employee of Union Oil or any
company in which Union Oil has an interest.

     In consideration of the foregoing, the mutual covenants, rights, and
obligations set forth in this Agreement, and the benefits to be derived
herefrom, and other good and valuable consideration, the receipt and the
sufficiency of which each of the parties hereto acknowledges and confesses, the
parties hereto agree as follows:

     1.   Scope of Business of the Company and its Subsidiaries Following the
          -------------------------------------------------------------------
Merger. The Company and Titan covenant and agree that, following consummation of
- ------
the Merger, except with the consent of Union Oil (which it may withhold in its
sole discretion), the Company and its subsidiaries will not engage in any
business other than the E&P Business and will not pursue any business
opportunity that involves any direct or indirect ownership interest in any
properties located outside the areas onshore shown on the map attached hereto
(collectively, the "Designated Areas"). The Company and Titan hereby renounce,
effective upon consummation of the Merger, any interest or expectancy in any
business opportunity that does not consist exclusively of the E&P Business
within the Designated Areas. "E&P Business" means the oil and gas exploration,
exploitation, development and production business and includes without
limitation (a) the ownership of oil and gas property interests (including
working interests, mineral fee interests and royalty and overriding royalty
interests), (b) the ownership and operation of real and personal property used
or useful in connection with exploration for Hydrocarbons, development of
Hydrocarbon reserves upon discovery thereof and production of Hydrocarbons from
wells located on oil and gas properties and (c) debt of or equity interests in
corporations, partnerships or other entities engaged in the exploration for
Hydrocarbons, the development of Hydrocarbon reserves and the production and
sale of Hydrocarbons from wells located on oil and gas properties in which the
entity conducting the E&P Business owns an interest; but such term does not
include the oilfield service business. "Hydrocarbons" means oil, gas or other
liquid or gaseous hydrocarbons or other minerals produced from oil and gas
wells. "Subsidiaries" means all entities controlled, directly or indirectly, by
the Company. Notwithstanding the foregoing, nothing in this Agreement shall
prohibit the Company and its subsidiaries from purchasing securities of any
class registered under Section 12 of the Securities Exchange Act of 1934
(regardless of the types or locations of businesses in which the issuer thereof
engages) if following any such purchase the Company and its subsidiaries own, in
the aggregate, less than 5% of such class.

     2.   Corporate Opportunities.  The Company and Titan recognize that Union
          -----------------------
Oil and its Designees (i) participate and will continue to participate in the
E&P Business, directly and through affiliates, (ii) may have interests in,
participate with, and maintain seats on the

                                       2
<PAGE>

boards of directors of or serve as officers or employees of other companies
engaged in the E&P Business and (iii) may develop business opportunities for
Union Oil and its affiliates and such other companies. The Company and Titan
recognize that Union Oil, its Designees and such affiliates and other companies
may be engaged in E&P Business in competition with the Company and/or its
subsidiaries. The Company and Titan (a) acknowledge and agree that neither Union
Oil, its affiliates nor its Designees nor any such company shall be restricted
or proscribed by the relationship between Union Oil and the Company, or
otherwise, from engaging in the E&P Business or any other business, regardless
of whether such business activity is in direct or indirect competition with the
business or activities of the Company and its subsidiaries, on any basis other
than that which is inconsistent with the standards set forth in Section 3
hereof, (b) acknowledge and agree that, as long as their activities are
conducted in accordance with the standards set forth in Section 3 hereof,
neither Union Oil nor any Designee or affiliate of Union Oil nor any such other
company shall have any obligation to offer the Company or any of its
subsidiaries any business opportunity, (c) renounce any interest or expectancy
in any business opportunity pursued by Union Oil, any affiliate of Union Oil,
any Designee or any such company in accordance with the standards set forth in
Section 3 hereof and (d) waive any claim that any business opportunity pursued
by Union Oil, any affiliate of Union Oil, any Designee or any such company
constitutes a corporate opportunity of the Company or any of its subsidiaries
that should have been presented to the Company, unless such business opportunity
was pursued in violation of the standards set forth in Section 3 hereof.

     3.   Standards for Separate Conduct of Business. Union Oil, any affiliate
          -------------------------------------------
of Union Oil, any Designee or any other company in which Union Oil has an
interest or of which a Designee is a director, officer or employee shall be
deemed to meet the standards set forth in this Section 3 if its businesses are
conducted through the use of its own personnel and assets and not with the use
of any personnel or assets of the Company. Without limiting the foregoing, such
standards will be met with respect to a business opportunity only if (a) it is
identified by or presented to personnel of Union Oil, such affiliate of Union
Oil, such Designee or such other company and developed and pursued solely
through the use of their personnel and assets (and not based on confidential
information disclosed by or on behalf of the Company in or during the course of
such Designee's relationship with the Company), and (b) it did not come to the
attention of such Designee solely in, and as a direct result of, his or her
capacity as a director of the Company; provided that (i) if such opportunity is
separately identified by Union Oil or one of its affiliates or such other
company or separately presented to Union Oil or one of its affiliates or such
other company by a person other than such Designee, Union Oil, such affiliate or
such company shall be free to pursue such opportunity even if it also came to
the Designee's attention solely as a result of and in his or her capacity as a
director of the Company and (ii) if such opportunity is presented to or
identified by a Designee other than solely as a result of and in his or her
capacity as a director of the Company, Union Oil or such affiliate or such other
company shall be free to pursue such opportunity even if it also came to the
Designee's attention as a result of and in his or her capacity as a director of
the Company.  Nothing in this Agreement will allow a Designee to usurp a
corporate opportunity solely for his or her personal benefit (as opposed to
pursuing, for the benefit of Union Oil, an affiliate or Union Oil or any such
other company, an opportunity in accordance with the standards set forth in this
Section 3).

                                       3
<PAGE>

     4.   Termination of Section 1.  Section 1 of this Agreement will terminate
          ------------------------
at such time as Union Oil no longer owns, directly or indirectly, capital stock
of the Company representing at least 35% of the ordinary voting power for the
election of directors of the Company.

     5.   Waiver. If the Company seeks a waiver of provisions of this Agreement,
          ------
the Company shall submit to Union Oil a written request, accompanied with
materials that provide a basis for the request and assist Union Oil in
considering the request.  Union Oil shall respond to the request within five
business days of its receipt of the request, unless it determines that it
requires additional information before responding, in which case it shall notify
the Company of its request for additional information.  Within five business
days of receipt of the Company's response to its request for additional
information, Union Oil shall notify the Company of its decision as to the
request for a waiver.  Union Oil may withhold such waiver in its sole discretion
or grant a conditional or limited waiver, and Union Oil shall have no duty,
fiduciary or otherwise, to grant any such waiver.

     6.   Miscellaneous.
          -------------

     This Agreement may be signed in any number of counterparts, each of which
when so executed and delivered shall be deemed an original, and such
counterparts together shall constitute one instrument.  This Agreement shall be
governed by and construed in accordance with the laws of the State of Delaware.

                                       4
<PAGE>

     IN WITNESS WHEREOF, the undersigned have duly executed this Agreement as of
the date set forth above.

                                   TITAN RESOURCES HOLDINGS, INC.


                                        By:   /s/ Phillip Ballard
                                           -------------------------------------
                                           Phillip Ballard
                                           Vice President


                                   UNION OIL COMPANY OF CALIFORNIA


                                        By: /s/ Timothy H. Ling
                                           -------------------------------------
                                           Timothy H. Ling
                                           Executive Vice President, North
                                           American Energy Operations and
                                           Chief Financial Officer


                                   TRH, INC.

                                        By: /s/ Phillip Ballard
                                           -------------------------------------
                                           Phillip Ballard
                                           Vice President


                                   TITAN EXPLORATION, INC.


                                        By: Jack D. Hightower
                                           ------------------------------------
                                            Jack D. Hightower
                                            President and Chief Executive
                                            Officer

                                       5

<PAGE>

                                                                   Exhibit 99.1


                            JOINT FILING AGREEMENT

     The undersigned each agree as follows:  (i) that certain statement on
Schedule 13D relating to the Common Stock, par value $.01 per share, of Titan
Exploration, Inc., a Delaware corporation, is filed on behalf of each of them,
(ii) such Statement on Schedule 13D is adopted by each of them, (iii) all future
amendments to such Statement on Schedule 13D will, unless written notice to the
contrary is delivered as described below, be jointly filed on behalf of each of
them, and (iv) the provisions of Rule 13d-1(f)(1) under the Securities Exchange
Act of 1934, as amended, apply to each of them.  This Agreement may be
terminated with respect to the obligation to file jointly future amendments to
such Statement on Schedule 13D as to any of the undersigned upon such person
giving written notice thereof to each of the other persons signatory hereto, at
the principal office thereof.

     EXECUTED as of December 23, 1999.

                                    UNOCAL CORPORATION


                                    By:  /s/ Joseph A. Householder
                                       -----------------------------------
                                       Name:   Joseph A. Householder
                                       Title:  Vice President, Corporate
                                               Development, and Assistant
                                               Chief Financial Officer


                                    UNION OIL COMPANY OF CALIFORNIA


                                    By:  /s/ Joseph A. Householder
                                       -----------------------------------
                                       Name:   Joseph A. Householder
                                       Title:  Vice President, Corporate
                                               Development, and Assistant
                                               Chief Financial Officer


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