<PAGE>   1



                                                                       EXHIBIT 4

================================================================================





                                WARRANT AGREEMENT


                                     between


                        RUTHERFORD-MORAN OIL CORPORATION


                                       and


                            THE CHASE MANHATTAN BANK

                                       and

                                 BANQUE PARIBAS


                          Dated as of December 3, 1997





================================================================================




<PAGE>   2




                                TABLE OF CONTENTS

<TABLE>
<CAPTION>

                                                                                                                   Page
                                                                                                                   ----  

<S>                                                                                                                  <C> 
SECTION 1.  Definitions; Accounting Terms and Determinations..........................................................l
              1.01    Definitions.....................................................................................1

1.02                Accounting Terms and Determinations...............................................................9

SECTION 2.  Purchase and Sale of Warrant.............................................................................10

2.01           Authorization and Issuance of Warrant Stock and
             Warrants................................................................................................10

2.02         Issuance of the Warrant.................................................................................10

2.03         Purchase for Investor's Account.........................................................................11

2.04         Securities Act Compliance...............................................................................11

SECTION 3.  Representations and Warranties...........................................................................11

3.01         Existence; Qualification................................................................................11

3.02         No Breach...............................................................................................12

3.03         Corporate Action........................................................................................12

3.04         Approvals...............................................................................................13

3.05         Investment Company Act..................................................................................13

3.06         Public Utility Holding Company Act......................................................................13

3.07         Capitalization..........................................................................................13

3.08         Private Offering........................................................................................14

3.09         Litigation..............................................................................................14

3.10         SEC Documents; Financial Statements.....................................................................15
</TABLE>



<PAGE>   3


<TABLE>

                                                                                                                   (ii)
<S>                                                                                                                  <C>
SECTION 4.  Restrictions on Transferability..........................................................................15

4.01         Transfers Generally.....................................................................................15

4.02           Transfers of Restricted Securities Pursuant to Registration Statements,
               Rule 144 and Rule 144A................................................................................16

4.03         Notice of Certain Transfers.............................................................................16

4.04         Restrictive Legends.....................................................................................16

4.04         Termination of Restrictions.............................................................................17

SECTION 5.  Dispositions of Securities...............................................................................17

5.01         Disposition of Securities...............................................................................17

5.02         Transfer Restriction....................................................................................19

5.03         Repurchase of Common Stock..............................................................................19

5.04         Transfer and Exchange...................................................................................19

SECTION 6.  Adjustment of Stock Unit.................................................................................20

6.01         Stock Dividends, Subdivisions and Combinations..........................................................20

6.02         Issuance of Additional Common Stock.....................................................................20

6.03         Issuance of Options.....................................................................................22

6.04         Issuance of Convertible Securities......................................................................23

6.05         Superseding Adjustment of Stock Unit....................................................................24

6.06         Other Provisions Applicable to Adjustments Under this
             Section 6...............................................................................................26

6.07         Merger, Consolidation or Disposition of Asset...........................................................28
</TABLE>



<PAGE>   4


<TABLE>

                                                                                                                   (iii)
<S>                                                                                                                 <C>
6.08          Distributions upon Declaration  of Dividend or Other
             Distribution............................................................................................29

6.09         Dilution in Case of Other Securities....................................................................30

6.10         Notice of Adjustments...................................................................................30

6.11         Notice of Certain Corporate Action......................................................................31

SECTION 7.  Registration.............................................................................................32

7.01         Notice..................................................................................................32

7.02         Proration...............................................................................................34

7.03         Registration Procedure..................................................................................35

7.04         Holdback on Sales.......................................................................................39

7.05         Expenses................................................................................................39

7.06         Indemnification.........................................................................................40

7.07         Option to Purchase Registrable Stock....................................................................43

7.08         No Other Registration Rights............................................................................44

SECTION 8.  Holders' Rights..........................................................................................44

8.01         Delivery Expenses.......................................................................................44

8.02         Taxes...................................................................................................44

8.03         Replacement of Instruments..............................................................................45

8.04         Indemnification.........................................................................................45

SECTION 9.  Other Covenants of Issuer................................................................................46

9.01         Financial Statements, Etc...............................................................................46
</TABLE>


<PAGE>   5


<TABLE>

                                                                                                                   (iv)
<S>                                                                                                                 <C>
9.02         Transactions with Affiliates............................................................................47

9.03   Restrictions on Performance...................................................................................48

9.04   Rule 144......................................................................................................48

SECTION 10.  Miscellaneous...........................................................................................48

10.01  Office of the Issuer..........................................................................................48

10.02  Waiver........................................................................................................48

10.03  Notices.......................................................................................................49

10.04  Expenses, Etc.................................................................................................50

10.05  Amendments, Etc...............................................................................................51

10.06  Successors and Assigns........................................................................................51

10.07  Survival......................................................................................................51

10.08  Specific Performance..........................................................................................51

10.09  Captions......................................................................................................52

10.10  Counterparts..................................................................................................52

10.11  Governing Law.................................................................................................52

10.12  Severability..................................................................................................52

10.13  Entire Agreement..............................................................................................53
</TABLE>

ANNEX 1 - FORM OF WARRANT
ANNEX 2 - FORM OF ASSIGNMENT



<PAGE>   6


            WARRANT AGREEMENT dated as of December 3, 1997 between
RUTHERFORD-MORAN OIL CORPORATION, a company duly organized and validly existing
under the laws of the State of Delaware (the "Issuer"), and each of the
investors signatory hereto (each, an "Investor" and collectively, the
"Investors").

            WHEREAS, the Issuer, the Subsidiary Guarantors listed on the
signature pages thereof and The Chase Manhattan Bank, and Banque Paribas
(collectively, the "Lenders"), are parties to an Amended and Restated Loan
Agreement dated as of December 3, 1997 (as originally executed, the "Loan
Agreement"; references to the Loan Agreement herein shall apply whether or not
the Loan Agreement is then in force and without regard to amendments thereto
unless such amendments thereto have been consented to by each of the Investors),
providing, subject to the terms and conditions thereof, for rendering loans to
the Issuer in principal amount up to $150,000,000 to be made by the Lenders to
the Issuer.

            WHEREAS, as a condition to the execution of the Loan Agreement, and
for other good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, the Issuer has agreed to issue a Warrant (as
hereinafter defined) providing for the purchase of shares of Stock Units (as
hereinafter defined) of the Issuer, under the circumstances and in the manner
hereinafter provided.

            NOW, THEREFORE, the parties hereto agree as follows:

            SECTION 1.  Definitions; Accounting Terms and Determinations.

            1.01 Definitions. (a) As used herein, the following terms shall have
the following meanings (all terms defined in this Section 1 or in other
provisions of this Agreement in the singular to have the same meanings when used
in the plural and vice versa):

            "Additional Common Stock" shall mean all shares of Common Stock
issued or sold by the Issuer on or after the date hereof, other than Excluded
Securities.


                                Warrant Agreement


<PAGE>   7



                                        2


            "Affiliate" means, as to any Person, any Subsidiary of such Person
and any other Person which, directly or indirectly, controls, is controlled by
or is under common control with such Person. For the purposes of this
definition, "control" means the possession of the power to direct or cause the
direction of management and policies of such Person, whether through the
ownership of voting securities, by contract or otherwise. Notwithstanding the
foregoing, (i) no individual shall be an Affiliate of any Person solely by
reason of his or her being a director, officer or employee of such Person and
(ii) none of the Issuer and the Wholly Owned Subsidiaries of the Issuer shall be
Affiliates of each other.

            "Board" shall mean the Board of Directors (or any duly authorized
committee thereof) of the Issuer.

            "Business Day" shall mean any day that is not a Saturday, Sunday or
other day on which commercial banks in New York City are authorized or required
by law to remain closed.

            "Closing Date" shall mean the date of this Agreement.

            "Commission" shall mean the Securities and Exchange Commission or
any other similar or successor agency of the Federal government administering
the Securities Act and/or the Exchange Act.

            "Common Stock" shall mean the Common Stock of the Issuer, par value
$0.01 per share, or any other common stock or other securities receivable
thereon, or into which the Common Stock is convertible or exchangeable, as a
result of any recapitalization, reclassification, merger or consolidation of, or
deposition of assets by, the Issuer.

            "Convertible Securities" shall mean evidences of indebtedness,
interests or other securities or rights which are exchangeable for or
exercisable or convertible into shares of Common Stock either immediately or
upon the arrival of a specified date or the occurrence of a specified event.



                                Warrant Agreement


<PAGE>   8



                                        3


            "Convertible Security Value" shall mean the fair market value of a
Convertible Security on the date of issuance, reasonably determined in good
faith by the Board, less the proceeds received by the Issuer for such conversion
or exchange.

            "Current Market Price", per share of Common Stock, for the purposes
of any provision hereof or of a Warrant at the date herein or therein specified,
shall be deemed to be (a) with respect to any Additional Common Stock issued (or
to be issued) in a public offering (other than a public offering effected as a
part of a merger or other acquisition transaction by the Issuer, in which case
paragraph (b) below shall apply), the offering price of such shares of
Additional Common Stock (less any customary underwriting discounts or
commissions) and (b) otherwise, the average of the daily market prices for each
day during the 15 consecutive trading days immediately preceding such date as of
which such a price can be established in the manner set forth in the next
sentence. The market price for each such trading day shall be the last sale
price on such day as reported in the Consolidated Last Sale Reporting System or
as quoted in the National Association of Securities Dealers Automated Quotation
System, or if such last sale price is not available, the average of the closing
bid and asked prices as reported in either such system. Notwithstanding the
foregoing, the "Current Market Price" per share of Common Stock for shares to be
issued in connection with an acquisition of assets or stock, a tender or
exchange offer, a merger or other business combination shall be deemed to be the
price per share as determined in such acquisition, tender or exchange offer,
merger or other business combination agreement.

            "Current Warrant Price", for the purpose of any provision hereof or
of a Warrant at the date herein or therein specified, shall mean the amount per
share of Common Stock equal to the quotient resulting from dividing the Exercise
Price per Stock Unit in effect on such date by the number of shares (including
any fractional share) of Common Stock comprising a Stock Unit on such date.





                                Warrant Agreement


<PAGE>   9



                                        4


            "Demand Registration" shall have the meaning assigned to such term
in Section 7.01 hereof.


            "Equity Securities" means Voting Securities, Convertible Securities
and Rights to Purchase Voting Securities.


            "Excluded Securities" shall mean (a) shares of Common Stock issued
or issuable upon exercise of any options or warrants and other securities
(including options and warrants) issued to employees, consultants, advisors,
officers and directors, or (b) securities issued in connection with any
acquisition or merger.


            "Exchange Act" shall mean the Securities Exchange Act of 1934, as
amended, or any similar Federal statute, and the rules and regulations of the
Commission thereunder, all as the same shall be in effect at the time.


            "Exercise Price" shall have the meaning assigned to such term in the
form of Warrant attached as Annex 1 hereto.


            "Expiration Date" shall have the meaning assigned to such term in
form of the Warrant attached as Annex 1 hereto.


            "GAAP" shall mean generally accepted accounting principles,
consistently applied throughout the specified period.


            "Governmental Authority" shall mean the government of the United
States of America, any other nation or any political subdivision thereof,
whether state or local, and any agency, authority, instrumentality, regulatory
body, court, central bank or other entity exercising executive, legislative,
judicial, taxing, regulatory, monetary or administrative powers or functions of
or pertaining to government.


            "Holder" shall mean any Person who acquires Warrants or Warrant
Stock pursuant to the provisions of this Agreement, including any transferees of
Warrants or Warrant Stock and, prior to the issuance of the Warrants shall mean
the Investors; provided, however, that a holder of Warrant Stock purchased




                                Warrant Agreement


<PAGE>   10



                                        5


pursuant to an effective registration statement or pursuant to Rule 144 shall
not be deemed a Holder.

            "include" and "including" shall be construed as if followed by the
phrase "without being limited to".

            "Independent Appraiser" shall mean an appraiser which is a
recognized independent expert (including any Investment Banking Firm)
experienced in valuing businesses similar or related to the principal business
of the Issuer and its Subsidiaries.

            "Investment Banking Firm" shall mean a nationally recognized
investment banking firm.

            "Investor" and "Investors" shall have the meanings assigned to each
such term in the preamble of this Agreement.

            "Issuer" shall have the meaning assigned to such term in the
preamble of this Agreement.

            "Lien" shall mean, with respect to any asset, any mortgage, lien,
pledge, charge, security interest or encumbrance of any kind in respect of such
asset. For purposes of this Agreement, a Person shall be deemed to own subject
to a Lien any asset which it has acquired or holds subject to the interest of a
vendor or lessor under any conditional sale agreement, capital lease or other
title retention agreement relating to such asset.

            "Loan Agreement" shall have the meaning assigned to such term in the
recital of this Agreement.

            "Majority Warrant Stock Holders" shall mean the Holders of a
majority of the Warrant Stock issued or issuable upon exercise of the Warrants.
For purposes of giving notices, waivers and consents hereunder, Holders of
Warrants shall be deemed holders of the Warrant Stock issued on exercise
thereof.

            "NASDAQ" shall mean the National Association of Securities Dealers
automated quotation system.




                                Warrant Agreement


<PAGE>   11




                                        6



            "Notice of Sale" shall mean (x) the issuance by the Issuer of a
press release or the filing by the Issuer of a Form 8-K (or any successor form)
with the Commission or (y) the delivery to the Investors of a certificate signed
by the Issuer's President or chief financial officer stating in either case that
(i) the Issuer is making substantial progress toward the sale of not less than
75% of the outstanding Common Stock of the Issuer (the "Required Amount") to a
Person other than an Affiliate of the Company, (ii) such financial services firm
is actively engaged in pursuing the sale of the Required Amount and (iii) such
firm and the Issuer have received either an executed Purchase and Sale Agreement
or firm written indications of interest to purchase the Required Amount, in the
form of a formal Letter of Intent, from one or more buyers. The Purchase and
Sale Agreement or the Letter of Intent must be from a party which is capable of
purchasing the Required Amount and providing and arranging such funds as are
required by the Issuer and its Subsidiaries to fulfill their obligations under
the Concession Agreement and the Operating Agreements (each as defined in the
Loan Agreement) as represented in writing by the aforementioned financial
services firms.

            "Option" shall mean any warrant, option or other right to subscribe
for or purchase shares of Common Stock.

            "Option Plan" shall mean an Employee Stock Option Plan of the Issuer
approved by a majority of the non-employee directors of the Board.

            "Other Equity Documents" shall mean any Option Plan, the certificate
of incorporation of the Issuer, the by-laws of the Issuer and any other
instrument or document of organization or governance of the Issuer.

            "Other Securities" shall mean any stock (other than Warrant Stock)
and other securities of the Issuer or any other Person (corporate or otherwise)
which a Holder at any time shall be entitled to receive, or shall have received,
upon exercise of the Warrants held by such Holder or pursuant to Section 6
hereof,




                                Warrant Agreement


<PAGE>   12



                                        7



in lieu of or in addition to Warrant Stock, or which at any time shall be
issuable or shall have been issued in exchange for or in replacement of Warrant
Stock or Other Securities received in an earlier exchange, exercise or
replacement of Warrant Stock.

            "Person" shall mean any individual, corporation, company, voluntary
association, partnership, joint venture, trust, unincorporated organization or
government (or any agency, instrumentality or political subdivision thereof).

            "Principal Shareholder" shall mean either of Patrick Rutherford or
John Moran.

            "Regulated Holder" shall mean a Holder which is a bank, a bank
holding company or an Affiliate of any of the foregoing.

            A Regulated Holder shall be deemed to have a "Regulatory Problem"
when (i) such Regulated Holder's investment in the Warrants and/or Warrant Stock
exceeds any limitation to which it is subject, or is otherwise not permitted,
under any law, rule or regulation of any Governmental Authority (including any
position to that effect taken by such Governmental Authority), or (ii)
restrictions are imposed on such Regulated Holder which, in its reasonable
judgment, make it illegal or unduly burdensome for such Regulated Holder to
continue to hold such Warrants and/or Warrant Stock.

            "Regulation Y" shall mean Regulation Y promulgated by the Board of
Governors of the Federal Reserve System (12 C.F.R. 225) or any successor
regulation.

            "Restricted Certificate" shall mean a certificate for Warrant Stock
or Warrants bearing or required to bear the restrictive legend set forth in
Section 4.03.

            "Restricted Securities" shall mean Restricted Warrant Stock and.
Restricted Warrants.

            "Restricted Warrant Stock" shall mean Warrant Stock evidenced by a
Restricted Certificate.



                                Warrant Agreement


<PAGE>   13



                                        8



            "Restricted Warrants" shall mean Warrants evidenced by a restricted
Certificate.

            "Rule 144" shall mean Rule 144 promulgated by the Commission under
the Securities Act (or any successor or similar rule then in force).

            "Rule 144A" shall mean Rule 144A promulgated by the Commission under
the Securities Act (or any successor or similar rule then in force).

            "Securities Act" shall mean the Securities Act of 1933, as amended,
or any similar Federal statute, and the rules and regulations of the Commission
thereunder, all as the same shall be in effect at the time.

            "Seller" shall have the meaning assigned to such term in Section
7.01 hereof.

            "Seller Notice" shall have the meaning assigned to such term in
Section 7.01 hereof.

            "Shareholder" shall mean any Person who directly or indirectly owns
any shares of Common Stock (including Warrant Stock).

            "Stock Unit" shall mean one share of Common Stock, as such Common
Stock is constituted on the date hereof, and thereafter shall mean such number
of shares (including any fractional shares) of Common Stock and other
securities, cash or other property as shall result from the adjustments
specified in Section 4.

            "Subsidiary" of a Person means (a) any corporation more than 50% of
the outstanding securities having ordinary voting power of which shall at the
time be owned or controlled, directly or indirectly, by such Person or by one or
more of its Subsidiaries or by such Person and one or more of its Subsidiaries,
or (b) any company, partnership, association, joint



                                Warrant Agreement


<PAGE>   14



                                        9


venture or similar business organization more than 50% of the ownership
interests having ordinary voting power of which shall at the time be so owned or
controlled. Unless otherwise expressly provided, all references herein to a
"Subsidiary" shall mean a direct or indirect Subsidiary of the Issuer.

            "Voting Securities" means the Common Stock and any other securities
of the Issuer of any kind or class having power generally to vote for the
election of directors; "Rights to Purchase Voting Securities" means options and
rights issued by the Issuer (whether presently exercisable or not) to purchase
Voting Securities or Convertible Voting Securities.

            "Warrant Stock" shall mean all shares of Common Stock issuable from
time to time upon exercise of a Warrant.

            "Warrant" and "Warrants" shall mean the Warrants, if any, issued by
the Issuer pursuant to this Agreement, evidencing rights to purchase up to an
aggregate of 200,000 Stock Units (which represents less than 1% of the
outstanding shares of Common Stock on a fully diluted basis on the date hereof),
and all Warrants issued upon transfer, division or combination of, or in
substitution for, any thereof.

            (b) Prior to the issuance of any Warrants hereunder, any reference
to the "holders" or the "holders of Warrants", "Warrant Stock Holders" or words
or phrases of similar meaning shall be deemed to be a reference to the
Investors.

            1.02 Accounting Terms and Determinations. Except as otherwise may be
expressly provided herein, all accounting terms used herein shall be
interpreted, and all financial statements and certificates and reports as to
financial matters required to be delivered to the Holders hereunder shall be
prepared, in accordance with GAAP. All calculations made for the purposes of
determining compliance with the terms of this Agreement shall (except as
otherwise may be expressly provided herein) be made by application of GAAP.




                                Warrant Agreement


<PAGE>   15



                                       10



            SECTION 2.  Purchase and Sale of Warrant.

            2.01 Authorization and Issuance of Warrant Stock and Warrants. The
Issuer has authorized: (a) the issuance of the Warrants evidenced by the warrant
certificate in the form of Annex 1; and (b) the issuance of such number of
shares of Common Stock as shall be necessary to permit the Issuer to comply with
its obligations to issue shares of Common Stock pursuant to the Warrants.

            2.02 Issuance of the Warrant. In consideration of the loans from
each Investor to the Issuer pursuant to the Loan Agreement, if after June 30,
1998 any amounts remain outstanding under the Loan Agreement in excess of
$60,000,000 (subject to a redetermination of the Threshold Amount pursuant to
Sections 1.04 and 2.09 of the Loan Agreement to be effective as of June 30,
1998), and provided that no Notice of Sale shall have been made:

            (a) on or before July 10, 1998 the Issuer shall issue to each
            Investor a Warrant representing the number of Stock Units set forth
            opposite such Investor's name in Annex 3 hereto;

            (b) the Issuer shall deliver to each Investor a single certificate
            for the Warrant, to be issued to such Investor registered in the
            name of such Investor, except that, if such Investor shall notify
            the Issuer in writing prior to such issuance that it desires
            certificates for Warrants to be issued in other denominations or
            registered in the name or names of any Affiliate, nominee or
            nominees of such Investor for its or their benefit, then the
            certificates for Warrants shall be issued to such Investor in the
            denominations and registered in the name or names specified in such
            notice; and

            (c) the Issuer shall deliver to each Investor a legal opinion from
            counsel to the Issuer in form and substance satisfactory to each
            Investor.



                                Warrant Agreement


<PAGE>   16



                                       11



            2.03 Purchase for Investor's Account. Each Investor represents and
warrants to the Issuer as follows:

            (a) If any Warrants is issued to such Investor, such Investor shall
purchase the Warrant for investment for its own account, without a view to the
distribution thereof, all without prejudice, however, to the right of the
Investor at any time, in accordance with this Agreement, lawfully to sell or
otherwise to dispose of all or any part of the Warrant or the Warrant Stock held
by it.

            (b) The Investor is an "accredited investor" within the meaning of
Regulation D under the Securities Act.

            2.04 Securities Act Compliance. The Investor understands that at the
time, if any, of the issuance of such Warrant, the Issuer has not registered the
Warrants or the Warrant Stock under the Securities Act or applicable state
securities laws, the Investor agrees that neither the Warrants nor the Warrant
Stock shall be sold or transferred or offered for sale or transfer without
registration or qualification under the Securities Act or applicable state
securities laws or the availability of an exemption therefrom, all as more fully
provided in Section 4.

            SECTION 3. Representations and Warranties. The Issuer represents and
warrants as follows:

            3.01 Existence; Qualification. Each of the Issuer and its
Subsidiaries is duly organized, validly existing and in good standing under the
laws of the jurisdiction of its organization. Each of the Issuer and its
Subsidiaries is duly qualified, licensed or admitted to do business and is in
good standing as a foreign corporation in every jurisdiction where the failure
to be so qualified would have a material adverse effect on the business,
financial condition, operations, assets, prospects, liabilities or
capitalization of the Issuer and its Subsidiaries taken as a whole and has all
requisite corporate power and authority to transact its business as now
conducted in all such jurisdictions.



                                Warrant Agreement


<PAGE>   17



                                       12



            3.02 No Breach. The execution, delivery and performance of this
Agreement and the Warrants, if issued, by the Issuer and the consummation by it
of the transactions contemplated hereby and thereby will not (a) violate the
certificate of incorporation or by-laws or any other instrument or document of
organization or governance of the Issuer, (b) violate, or result in a breach of
or default under, any other material instrument or agreement to which the Issuer
or any of its Subsidiaries is a party or is bound, (c) violate any judgment,
order, injunction, decree or award against or binding upon the Issuer or any of
its Subsidiaries, (d) result in the creation of any material Lien upon any of
the properties or assets of the Issuer or any of its Subsidiaries (other than as
contemplated by the Loan Agreement), or (e) violate any law, rule or regulation
relating to the Issuer or any of its Subsidiaries.

            3.03 Corporate Action. The Issuer has, and in the event the Issuer
is required to issue the Warrants will have, all necessary corporate power and
authority to execute, deliver and perform its obligations under this Agreement
and the Warrants; the execution, delivery and performance by the Issuer of this
Agreement and the Warrants have been duly authorized by all necessary action
(including all Shareholder action) on the part of the Issuer; this Agreement has
been, and the Warrants if issued, will be duly executed and delivered by the
Issuer and constitute the legal, valid and binding obligations of the Issuer,
enforceable against the Issuer in accordance with their respective terms; the
Warrant Stock initially covered by the Warrants will be duly and validly
authorized and reserved for issuance and shall, when paid for, issued and
delivered in accordance with the Warrants, be duly and validly issued, fully
paid and nonassessable and free and clear of any Liens; and none of the Warrant
Stock issued pursuant to the terms hereof will be in violation of any preemptive
rights of any Shareholder.

            3.04 Approvals. Except in connection with the registration of the
Warrant Stock pursuant to Section 7, no authorizations, approvals or consents
of, and no filings or registrations with, any Governmental Authority or any
other



                                Warrant Agreement


<PAGE>   18



                                       13



Person are necessary for the execution, delivery or performance by the Issuer of
this Agreement or the Warrants or for the validity or enforceability thereof.
Any such action required to be taken as a condition to the execution and
delivery of this Agreement, or the execution, issuance and delivery of the
Warrants, has been duly taken by all such Governmental Authorities or other
Persons, as the case may be.

            3.05 Investment Company Act. The Issuer is not an "investment
company", or a company "controlled by" an "investment company", within the
meaning of the Investment Company Act of 1940, as amended.

            3.06 Public Utility Holding Company Act. The Issuer is not a
"holding company", or an "affiliate" of a "holding company" or a "subsidiary
company" of a "holding company", within the meaning of the Public Utility
Holding Company Act of 1935, as amended.

            3.07  Capitalization.

            (a) On the date hereof, the total number of shares of Common Stock
that the Issuer has authority to issue is 40,000,000 of which 25,614,000 are
outstanding. As of the date hereof, the Issuer does not have outstanding any
Convertible Securities or Options exercisable or convertible into or
exchangeable for any interests or other equity rights of the Issuer, nor does it
have outstanding any agreements providing for the issuance (contingent or
otherwise) of, or any calls, commitments or claims of any character relating to,
any interests or equity rights of the Issuer or Convertible Securities
exercisable or convertible into or exchangeable for any interests or equity
rights of the Issuer other than 500,000 shares of Common Stock which are
issuable pursuant to Option Plans.

            (b) Other than the Other Equity Documents and this Agreement, there
is not in effect on the date hereof any agreement by the Issuer pursuant to
which any holders of securities of the Issuer have a right to cause the Issuer
to register such securities under the Securities Act or any agree-



                                Warrant Agreement


<PAGE>   19



                                       14



ment to which the Issuer or (to its knowledge) any of its Shareholders is a
party relating to the voting, transfer or sale of such securities.

            (c) There is not in effect on the date hereof any agreement by the
Issuer which (i) restricts the transferability of the Warrants and/or the
Warrant Stock, except as provided in Sections 4 and 5, (ii) restricts the
transferability of the right of any Holder in this Agreement to any transferee
of all or a portion of the Holder's Warrants and/or Warrant Stock, or (iii)
requires any consent or other approval of any Person to the exercise of the
Warrants by the Holder or the issuance of Warrant Stock upon such exercise.

            3.08  Private Offering.

            Assuming the truth and accuracy of each Investor's representations
and warranties contained in Section 2.03, the issuance and sale of the Warrants
to each such Investor hereunder are exempt from the registration and prospectus
delivery requirements of the Securities Act.

            3.09 Litigation. There is no action, suit, proceeding or
investigation pending or, to the best of the Issuer's knowledge after due
inquiry, threatened against the Issuer or any of its Subsidiaries before any
Governmental Authority seeking to enjoin the transactions contemplated by this
Agreement or the Warrants.

            3.10 SEC Documents; Financial Statements. The Issuer has filed in a
timely manner all documents that the Issuer was required to file with the
Commission under Sections 13, 14(a) and 15(d) of the Exchange Act, since its
initial public offering. As of their respective filing dates, all documents
filed by the Issuer with the Commission ("SEC Documents") complied in all
material respects with the requirements of the Exchange Act or the Securities
Act, as applicable. None of the SEC Documents as of their respective dates
contained any untrue statement of a material fact or omitted to state a material
fact required to be stated therein or necessary to make the statements made
therein,


                                Warrant Agreement


<PAGE>   20



                                       15


in light of the circumstances under which they were made, not misleading. The
financial statements of the Issuer included in the SEC Documents filed during
1997 (the "Financial Statements") comply as to form in all material respects
with applicable accounting requirements and with the published rules and
regulations of the Commission with respect thereto. The Financial Statements
have been prepared in accordance with GAAP and fairly present the consolidated
financial position of the Issuer and its Subsidiaries at the dates thereof and
the consolidated results of their operations and consolidated cash flows for the
periods then ended (subject, in the case of unaudited statements, to normal,
recurring adjustments).

            SECTION 4.  Restrictions on Transferability.

            4.01 Transfers Generally. Except as otherwise provided in Section 5
and subject to the Issuer's consent, which shall not be unreasonably withheld
(as measured by the Stockholders Agreement), the Restricted Securities shall be
transferable only upon the conditions specified in this Section 4 and in Section
7, which conditions are intended to insure compliance with the provisions of the
Securities Act and applicable state securities laws in respect of the transfer
of any Restricted Securities.

            4.02 Transfers of Restricted Securities Pursuant to Registration
Statements, Rule 144 and Rule 144A. The Restricted Securities may be offered or
sold by the Holder thereof pursuant to (a) an effective registration statement
under the Securities Act, (b) to the extent applicable, Rule 144 or Rule 144A or
(c) any other legally available means of transfer.

            4.03 Notice of Certain Transfers. If any Holder of any Restricted
Security desires to transfer such Restricted Security other than pursuant to an
effective registration statement, Rule 144 under the Securities Act, an
applicable exemption from the Securities Act or in accordance with Section
5.01(a) hereof, such Holder shall deliver to the Issuer at least 7 Business
Days' prior written notice with respect to the proposed transfer, together with
an opinion (at such Holder's



                                Warrant Agreement


<PAGE>   21



                                       16



expense) of Milbank, Tweed, Hadley & McCloy, or such other counsel reasonably
satisfactory to the Issuer, to the effect that an exemption from registration
under the Securities Act is available and specifying the applicable exemption.

                  4.04 Restrictive Legends. Unless and until otherwise permitted
by this Section 4, the certificate for the Warrants issued under this Agreement,
each certificate for any Warrants issued to any subsequent transferee of any
such certificate, each certificate for any Warrant Stock issued upon exercise of
any Warrant and each certificate for any Warrant Stock issued to any subsequent
transferee of any such certificate, shall be stamped or otherwise imprinted with
a legend in substantially the following form:

           "THE TRANSFER OF THE SECURITIES REPRESENTED BY THIS CERTIFICATE IS
         SUBJECT TO THE CONDITIONS SPECIFIED IN THAT CERTAIN WARRANT AGREEMENT
         DATED AS OF DECEMBER 3, 1997 (THE "WARRANT AGREEMENT"), AMONG
         RUTHERFORD-MORAN OIL CORPORATION, A DELAWARE COMPANY (THE "ISSUER"),
         AND THE CHASE MANHATTAN BANK AND BANQUE PARIBAS, AS THE WARRANT
         AGREEMENT MAY BE MODIFIED AND SUPPLEMENTED AND IN EFFECT FROM TIME TO
         TIME, AND NO TRANSFER OF THE SECURITIES REPRESENTED BY THIS CERTIFICATE
         SHALL BE VALID OR EFFECTIVE UNTIL SUCH CONDITIONS HAVE BEEN FULFILLED.
         A COPY OF THE FORM OF THE WARRANT AGREEMENT IS ON FILE AND MAY BE
         INSPECTED AT THE PRINCIPAL EXECUTIVE OFFICE OF THE ISSUER. THE HOLDER
         OF THIS CERTIFICATE, BY ACCEPTANCE OF THIS CERTIFICATE, AGREES TO BE
         BOUND BY THE PROVISIONS OF THE WARRANT AGREEMENT."

                  4.04 Termination of Restrictions. All of the restrictions
imposed by this Section 4 upon the transferability of the Restricted Securities
shall cease and terminate as to any particular Restricted Security when such
Restricted Security shall have been effectively registered under the Securities
Act and applicable state securities laws and sold by the Holder thereof in
accordance with such registration or sold under and pursuant to Rule 144 or is
eligible to be sold under and pursuant to paragraph (k) of Rule 144. Whenever
the restrictions imposed by this



                                Warrant Agreement


<PAGE>   22



                                       17



Section 4 shall terminate as to any Restricted Security as hereinabove provided,
the Holder thereof shall be entitled to receive from the Issuer, without
expense, a new certificate evidencing such Restricted Security not bearing the
restrictive legend otherwise required to be borne by a certificate evidencing
such Restricted Security.

                  SECTION 5.  Dispositions of Securities.

                  5.01 Disposition of Securities. Subject to compliance with all
of the provisions of Section 4 hereof, any Holder shall have the right to
transfer any Restricted Securities to any Person.

                  (a)   Subject to compliance with the provisions of Section 4
hereof, except with respect to the requirement for an opinion of counsel to the
Holder, which shall not be required under this Section 5.01(a), any Holder shall
have the right to transfer any Restricted Securities:

                  (i)   to any Person who at the time owns (directly or
         indirectly) at least a majority of the voting capital stock or other
         equity interests of such Holder;

                  (ii)  to any Person at least a majority of whose voting
         capital stock shall at the time be owned (directly or indirectly) by
         such Holder or by any Person who owns (directly or indirectly) at least
         a majority of the voting capital stock or other equity interests of
         such Holder; or

                  (iii) to another Investor.

                  (b)   If, in the reasonable judgment of a Holder, a transfer 
is required to be effected by such Holder because of a Regulatory Problem, the
Issuer shall use reasonable efforts to assist such Holder in disposing of its
Warrants and Warrant Stock, subject to and in accordance with the terms of this
Agreement and applicable law, to any prospective purchaser which is a financial
institution or other institutional investor



                                Warrant Agreement


<PAGE>   23



                                       18



approved by the Issuer (which approval shall not be unreasonably withheld or
delayed) of the Warrants or Warrant Stock owned by such Holder as such purchaser
may reasonably request (provided that, the Issuer shall not be required to make
available to such purchaser any documents or information if doing so would, in
the reasonable judgment of counsel to the Issuer, compromise any attorney-client
privilege existing with respect thereto) or to a direct or indirect competitor
of the Issuer.

                  (c) In the event of any underwritten public offering of
Restricted Securities in which a Holder which is subject to the provisions of
Regulation Y is participating, the Issuer shall use its reasonable efforts to
assist the underwriter in ensuring that any Warrant Stock issued by the Issuer
and sold by such Holder are widely disseminated.

                  5.02 Transfer Restriction. Notwithstanding anything in this
Agreement or the Warrants to the contrary, no Holder subject to the provisions
of Regulation Y shall transfer any Warrants or shares of Warrant Stock issued by
the Issuer and held by it, if, as a result of such transfer or the right to
effect such transfer, such Holder would be deemed under Regulation Y to have the
power to exercise, directly or indirectly, a controlling influence over the
management or policies of, or otherwise control, the Issuer (and, for purposes
of this restriction, a reasoned opinion of counsel to such Holder delivered to
such Holder (which is based on facts and circumstances deemed appropriate by
such counsel) to the effect that such Holder does not have the power to exercise
such a controlling influence or otherwise control the Issuer shall be
conclusive).

                  5.03 Repurchase of Common Stock. The Issuer shall give 5
Business Days prior written notice to each Investor before purchasing,
redeeming, retiring or otherwise acquiring any shares of Common Stock of the
Issuer in excess of 200,000 shares of Common Stock in any calendar year.

                  5.04 Transfer and Exchange. The Warrants may be exchanged for
other Warrants upon presentation to the Issuer, together with a written notice
specifying the denominations in



                                Warrant Agreement


<PAGE>   24



                                       19



which new Warrants are to be issued, signed by the Holder of such Warrant. The
Issuer shall execute and deliver a new Warrant or Warrants to such Holder in
exchange for the Warrant or Warrants to be divided or combined in accordance
with such notice. The Issuer shall pay all expenses, taxes (other than any
transfer taxes) and other charges payable in connection with the preparation,
issuance and delivery of the Warrants, including any transfer or exchange
thereof.

                  The Issuer shall maintain with its transfer agent or at its
office, books for the registration and transfer of the Warrants.

                  SECTION 6. Adjustment of Stock Unit. The number of shares of
Common Stock comprising a Stock Unit shall be subject to adjustment from time to
time as set forth in this Section 6. The Issuer shall not create any class of
Common Stock ("Other Common Stock") which carries any rights to dividends or
assets differing in any respect from the rights of the Common Stock on the date
hereof without adjusting the number of shares of Common Stock comprising a Stock
Unit in accordance with Section 6.02 hereof (if such Other Common Stock is not
converted into Common Stock or Section 6.03 hereof (if such Other Common Stock
is converted into Common Stock).

                  6.01 Stock Dividends, Subdivisions and Combinations. If at any
time the Issuer shall:

                  (a) declare or pay a dividend payable in Additional Common
         Stock, or

                  (b) subdivide its outstanding shares of Common Stock into a
         larger number of shares of Common Stock, or

                  (c) combine its outstanding shares of Common Stock into a
         smaller number of shares of Common Stock,

then the number of shares of Common Stock comprising a Stock Unit immediately
after the occurrence of any such event shall be adjusted to equal the number of
shares of Common Stock which a



                                Warrant Agreement


<PAGE>   25



                                       20



record holder of the number of shares of Common Stock comprising a Stock Unit
immediately prior to the happening of such event would own or be entitled to
receive after the happening of such event.

                  6.02 Issuance of Additional Common Stock. If at any time the
Issuer shall (except as hereinafter provided) issue or sell any Additional
Common Stock in exchange for consideration in an amount per share of Additional
Common Stock less than the Current Market Price at the time the Additional
Common Stock is issued, then the number of shares of Common Stock thereafter
comprising a Stock Unit shall be adjusted to that number determined by
multiplying the number of shares of Common Stock comprising a Stock Unit
immediately prior to such adjustment by a fraction (a) the numerator of which
shall be the number of shares of Common Stock outstanding immediately prior to
the issuance of such Additional Common Stock plus the number of such shares of
Additional Common Stock so issued, and (b) the denominator of which shall be the
number of shares of Common Stock outstanding immediately prior to the issuance
of such shares of Additional Common Stock plus the number of shares of Common
Stock which the aggregate consideration for the total number of such shares of
Additional Common Stock so issued would purchase at the Current Market Price.
For purposes of this Section 6.02, for all issuances of shares of Additional
Common Stock except for those shares issued in connection with an acquisition of
assets or stock, a tender or exchange offer, a merger or other business
combination or in a public offering, the date as of which the Current Market
Price shall be computed shall be the earlier of (i) the date on which the Issuer
shall enter into a firm contract for the issuance of such Additional Common
Stock and (ii) the date of actual issuance of such Additional Common Stock.
Subject to Section 6.05 hereof, no further adjustment of the number of shares of
Common Stock comprising a Stock Unit shall be made under this Section 6.02 upon
the issuance of any shares of Additional Common Stock:

                  (a) for which an adjustment is provided under Section 6.01
         hereof;




                                Warrant Agreement


<PAGE>   26



                                       21



                  (b) which are issued pursuant to the exercise of any Options
         or the conversion, exchange or exercise of any Convertible Securities,
         if any such adjustment shall previously have been made upon the
         issuance of such Options or Convertible Securities (or upon the
         issuance of any Option therefor) pursuant to Section 6.03 or 6.04
         hereof; or

                  (c) as a distribution or a dividend which is distributed or
         declared and paid in accordance with Section 6.08 hereof.

                  6.03 Issuance of Options. If at any time (other than pursuant
to an Option Plan except with respect to options issued to (i) Patrick
Rutherford or John Moran, (ii) any of their Affiliates or (iii) any of their
immediate family members) the Issuer shall issue or sell, or shall fix a record
date for the determination of holders of any class of securities entitled to
receive, any Options, whether or not the rights to purchase thereunder are
immediately exercisable, and the consideration received by the Issuer in payment
for such Options (determined in accordance with Section 6.06(a) hereof) shall be
less than the Current Market Price in effect on the date of and immediately
prior to such issuance, sale or fixing of a record date, then the number of
shares of Common Stock thereafter comprising a Stock Unit shall be adjusted as
provided in Section 6.02 hereof on the basis that (a) the maximum number of
shares of Additional Common Stock issuable pursuant to all such Options shall be
deemed to have been issued as of (and, accordingly, the date as of which the
Current Market Price shall be computed shall be) the computation date specified
in the next succeeding sentence of this Section 6.03, and (b) the aggregate
consideration for such maximum number of shares of Additional Common Stock shall
be (subject to Section 6.05 hereof) the consideration received by the Issuer for
the issuance or sale of such shares of Additional Common Stock pursuant to the
terms of such Options or pursuant to the terms of such Convertible Securities.
For purposes of this Section 6.03, the computation date for clause (a) above
shall be the earlier of (i) the date on which the Issuer shall take a record of
the holders of its Common Stock for the purpose of entitling them to receive any
such Options, (ii) the date on



                                Warrant Agreement


<PAGE>   27



                                       22



which the Issuer shall enter into a firm contract for the issuance or sale of
such Options and (iii) the date on which the Issuer shall issue or sell such
Options. No further adjustment of the number of shares of Common Stock
comprising a Stock Unit shall be made under this Section 6.03 upon the issuance
or sale of any Options to subscribe for or purchase any shares of Additional
Common Stock or any Convertible Securities or upon the subsequent issue or sale
of shares of such Additional Common Stock upon the exercise of such Options, if
any such adjustment shall previously have been made upon the issuance or sale of
such Option or upon the setting of a record date therefor, or upon any deemed
issuance or sale of such shares of Additional Common Stock, as a distribution or
a dividend which is distributed or declared and paid in accordance with Section
6.08 hereof. Notwithstanding the foregoing, any issuance of an Option which is
issued together with a debt security of the Issuer, as a unit, shall be treated
for the purpose of this Section 6 as the issuance of a Convertible Security.

                      6.04 Issuance of Convertible Securities. If at any time
  the Issuer shall issue or sell any Convertible Securities, whether or not the
  rights to exchange or convert thereunder are immediately exercisable, and the
  consideration received by the Issuer in payment for such Convertible
  Securities shall be less than the Convertible Security Value thereof, then the
  number of shares of Common Stock thereafter comprising a Stock Unit shall be
  increased to a number of shares of Common Stock having a value immediately
  following the computation date (as established below) equal to the value of
  the number of shares comprising such Stock Unit immediately before such
  increase. For this purpose, the value before the increase will be the Current
  Market Price of the Common Stock (determined as at the date immediately
  preceding such increase) divided by the number of shares of Common Stock
  outstanding on a fully diluted basis, and the value immediately following the
  computation date shall be the foregoing value, except that the numerator shall
  be the Current Market Price plus the cash amount paid to the Issuer for such
  Convertible Securities less the Convertible Security Value of such Convertible
  Securities on issuance and the denominator shall be increased by the number of
  shares of Additional Common Stock


                                Warrant Agreement


<PAGE>   28



                                       23


issuable on exercise of such Convertible Securities. For purposes of this
Section 6.04, the computation date shall be the earliest of (i) the date on
which the Issuer shall take a record of the holders of its Common Stock for the
purpose of entitling them to receive any such Convertible Securities, (ii) the
date on which the Issuer shall enter into a firm contract for the issuance or
sale of such Convertible Securities and (iii) the date of actual issuance or
sale of such Convertible Securities. No further adjustment of the number of
shares of Common Stock comprising a Stock Unit shall be made under this Section
6.04 upon the issuance or sale of any Convertible Securities or the conversion
or exchange of such Convertible Securities into shares of Additional Common
Stock:

                  (A) which are issued or sold pursuant to the exercise of any
         Option therefor, if any such adjustment shall previously have been made
         upon the issuance or sale of an Option relating to such Convertible
         Securities pursuant to Section 6.03 hereof; or

                  (B) if any such adjustment in respect thereof shall previously
         have been made upon the setting of a record date therefor, or upon any
         deemed issuance or sale of such Convertible Securities; or

                  (C) as a distribution or a dividend which is distributed or
         declared and paid in accordance with Section 6.08 hereof.

                  6.05 Superseding Adjustment of Stock Unit. If, at any time
after any adjustment of the number of shares of Common Stock comprising a Stock
Unit shall have been made pursuant to Section 6.03 or 6.04 hereof as a result of
the issuance of Options or Convertible Securities, or after any new adjustment
of the number of shares of Common Stock comprising a Stock Unit shall have been
made pursuant to this Section 6.05, (a) such Options or the right of conversion,
exchange or exercise of such Convertible Securities shall expire, and all or a
portion of such Options or the right of conversion, exchange or exercise with
respect to all or a portion of such Convertible Securities, as


                                Warrant Agreement


<PAGE>   29



                                       24



the case may be, shall not have been exercised or treated as having been
exercised or otherwise canceled or acquired by the Issuer in connection with any
settlement (including, without limitation, any cash settlement) of such Options
or the rights of conversion, or exchange or exercise of such convertible
Securities, or (b) there has been any change (whether by the passage of time or
otherwise) in the number of shares issuable upon exercise, conversion or
exchange of such Options or Convertible Securities (including as a result of the
operation of antidilution provisions applicable thereto), or (c) the
consideration per share, for which shares of Additional Common Stock are
issuable pursuant to such Options or the terms of any Convertible Securities, or
the maturity of any such Convertible Security, shall be changed (whether by the
passage of time or otherwise) then such previous adjustment shall be rescinded
and annulled and the shares of Additional Common Stock which were deemed to have
been issued by virtue of the computation made in connection with the adjustment
so rescinded and annulled shall no longer be deemed to have been issued by
virtue of such computation. Thereupon, a recomputation shall be made of the
effect of such Options or Convertible Securities on the basis of:

                  (i)   treating the number of shares of Additional Common 
         Stock, if any, theretofore actually issued or sold pursuant to the
         previous exercise of such Options or such right of conversion or
         exchange, as having been issued or sold on the date or dates of such
         issuance as determined for purposes of such previous adjustment and for
         the consideration actually received therefor;

                  (ii)  treating the maximum number of shares of Additional
         Common Stock (A) issuable pursuant to all Options which then remain
         outstanding and (B) necessary to effect the conversion or exchange of
         all Convertible Securities which then remain outstanding, as having
         been issued (subject, however, to further adjustment under this Section
         6.05); and

               (iii)    making the computations called for in Section 6.04
         hereof on the basis of the revised terms of such Convertible


                                Warrant Agreement


<PAGE>   30



                                       25



         Securities as if the securities being subject to recomputation were
         newly issued as of the relevant recomputation date and, if and to the
         extent called for by the foregoing provisions of this Section 6 on the
         basis aforesaid, a new adjustment of the number of shares of Common
         Stock comprising a Stock Unit shall be made, and such new adjustment
         shall supersede the previous adjustment so rescinded and annulled.

                  6.06 Other Provisions Applicable to Adjustments Under this
Section 6. The following provisions shall be applicable to the making of
adjustments of the number of shares of Common Stock comprising a Stock Unit
hereinbefore provided for in this Section 6, irrespective of the accounting
treatment of any consideration described below:

                  (a)  Computation of Consideration. To the extent that any
         shares of Additional Common Stock, any Options or any Convertible
         Securities shall be issued for cash consideration, the consideration
         received by the Issuer therefor shall be deemed to be the amount of
         cash received by the Issuer therefor, or, if such shares of Additional
         Common Stock, Options or Convertible Securities are offered by the
         Issuer for subscription, the subscription price, or, if such shares of
         Additional Common Stock, Options or Convertible Securities are sold to
         underwriters or dealers for public offering without a subscription
         offering, the initial public offering price. To the extent that such
         issuance or sale shall be for consideration other than cash, then the
         amount of such consideration shall be deemed to be the fair market
         value of such consideration at the time of such issuance, as reasonably
         determined by the Board. The consideration for any shares of Additional
         Common Stock issuable pursuant to any Option to subscribe for or
         purchase the same shall be the consideration received or receivable by
         the Issuer for the sale or issuance of such Option plus the additional
         consideration payable to the Issuer upon the exercise thereof in full.
         The consideration for any shares of Additional Common Stock issuable
         pursuant to the terms of any Convertible Securities shall be the
         consideration paid


                                Warrant Agreement


<PAGE>   31



                                       26


or payable to the Issuer in respect of the subscription for, sale or issuance of
such Convertible Securities plus the additional consideration payable to the
Issuer upon the conversion or exchange thereof in full. In case of the issuance
at any time of any shares of Additional Common Stock in payment or satisfaction
of any dividend upon any class of stock other than Common Stock, the Issuer
shall be deemed to have received for such shares of Additional Common Stock
consideration equal to the amount of such dividend so paid or satisfied.

           (b) When Adjustments to be Made. The adjustments required by this
Section 6 shall be made whenever and as often as any specified event requiring
an adjustment shall occur except that any adjustment of the number of shares of
Common Stock comprising a Stock Unit that would otherwise be required may be
postponed (except in the case of a subdivision or combination of shares of the
Common Stock, as provided for in Section 6.01 hereof) up to but not beyond the
date of exercise if such adjustment either by itself or with other adjustments
not previously made adds or subtracts less than 1% of the aggregate Exercise
Price for all Warrants then outstanding. Any adjustment representing a change of
less than such minimum percent (except as aforesaid) shall be carried forward
and made as soon as such adjustment, together with other adjustments required by
this Section 6 and not previously made, would result in a minimum adjustment on
the date of exercise. For the purpose of any adjustment, any specified event
shall be deemed to have occurred at the close of business on the date of its
occurrence.

           (c) Fractional Interests. In computing adjustments under this Section
6, fractional interests in Common Stock shall be taken into account to the
nearest one-hundredth of a share.

           (d) When Adjustment Not Required. (i) If the Issuer shall take a
record of the holders of its Common Stock for the purpose of entitling them to
receive a dividend or


                                Warrant Agreement


<PAGE>   32



                                       27


         distribution or subscription or purchase rights and shall, thereafter
         and before the distribution thereof to Shareholders, legally abandon
         its plan to pay or deliver such dividend, distribution, subscription or
         purchase rights, then no adjustment shall be required by reason of the
         taking of such record and any such adjustment previously made in
         respect thereof shall be rescinded and annulled, and no adjustment in
         the number of shares of Common Stock thereafter comprising a Stock Unit
         under Section 6.02, 6.03 or 6.04 hereof shall be made in respect of the
         Warrants held by such Holder. (ii) No adjustment shall be made
         hereunder in respect of the issuance of Common Stock pursuant to an
         Option Plan or options representing the right to acquire Common Stock
         pursuant to an Option Plan.

                  6.07 Merger, Consolidation or Disposition of Assets. If the
Issuer shall merge or consolidate with another corporation, or shall sell,
transfer or otherwise dispose of all or substantially all of its assets to
another corporation and pursuant to the terms of such merger, consolidation or
disposition of assets, cash, shares of common stock or other securities of the
successor or acquiring corporation, or property of any nature is to be received
by or distributed to the holders of Common Stock of the Issuer, then each holder
of Warrants which are by their terms then exercisable shall, at such holder's
election, have the right to receive (whether or not such holder exercises such
Warrants) the amount it would have been entitled to receive if such holder had
exercised such Warrants immediately prior to the occurrence of such merger,
consolidation or disposition of assets, net of the exercise price of such
Warrants, and shall thereupon be deemed to have exercised such Warrants. In case
of any such merger, consolidation or disposition of assets in which the
foregoing election is not made, the successor or acquiring corporation (and any
affiliate thereof issuing securities) shall expressly assume the due and
punctual observance and performance of each and every covenant and condition of
this Warrant to be performed and observed by the Issuer and all of the
obligations and liabilities hereunder, subject to such modifications as may be
deemed appropriate (as determined by resolution of the Board and reasonably
acceptable


                                Warrant Agreement


<PAGE>   33



                                       28



to the holders of a majority in interest of the Warrants) in order to provide
for adjustments of Stock Units which shall be as nearly equivalent as
practicable to the adjustments provided for in this Section but which shall
provide for the issuance of the common stock of the Person being issued to the
holders of Common Stock of the Issuer pursuant to such merger, consolidation or
disposition. In the event the election is not made pursuant to the first
sentence of this Section 6.07, the Issuer shall have the right, exercisable
within 30 days following such merger, to purchase in cash all (but not less than
all) of the outstanding Warrants at a price equal to the amount such Holder
would have been entitled to receive if such holder had exercised such Warrants
immediately prior to the occurrence of such merger, consolidation or disposition
of assets, net of the exercise price of such Warrants. The foregoing provisions
shall similarly apply to successive mergers, consolidations and dispositions of
assets.

                  6.08 Distributions upon Declaration of Dividend or Other
Distribution. So long as any Warrants remain outstanding, the Issuer shall pay,
upon the declaration and payment of any dividend or distribution (whether such
dividend or distribution is in the form of cash, debt securities, equity
securities or other property) on any class of Common Stock, to each Holder the
dividend or distribution that such Holder would be otherwise entitled to receive
had such Holder exercised the Warrants held by it in full immediately prior to
the taking of record of those holders of Common Stock entitled to any such
dividend or distribution, provided that, this provision shall apply only to
dividends or distributions in respect of the Common Stock other than ordinary,
periodic cash dividends paid out of earned surplus of the Issuer. If such
dividend or distribution is in the form of a voting equity security, such Holder
will be entitled to receive, at its option, in its stead non-voting equity
securities otherwise identical to and convertible at such Holder's option into
the equity securities to which such Holder is otherwise entitled thereunder and
continuing benefiting from antidilution provisions similar to those herein. This
provision shall not apply to stock dividends of shares of Additional Common
Stock, or to a reclassification or recapitalization, provided that the



                                Warrant Agreement


<PAGE>   34



                                       29



Issuer adjusts the number of shares of Common Stock comprising a Stock Unit
pursuant to Section 6.01 hereof.

                  6.09 Dilution in Case of Other Securities. In case any Other
Securities shall be issued or sold or shall become subject to issue or sale upon
the conversion or exchange of any stock (or Other Securities) of the Issuer (or
any issuer of Other Securities or any other Person referred to in Section 6.08
hereof) or to subscription, purchase or other acquisition pursuant to any
rights, options, warrants to subscribe for, purchase or otherwise acquire either
shares of Additional Common Stock or securities directly or indirectly
convertible into or exchangeable for shares of Additional Common Stock, issued
or granted by the Issuer (or any such other issuer or Person) for a
consideration such as to dilute, on a basis consistent with the standards
established in the other provisions of Section 6 hereof, the purchase rights
granted by the Warrants, then, and in each such case, the computations,
adjustments and readjustments provided for in said Section 6 with respect to the
Stock Units shall be made as nearly as possible in the manner so provided and
applied to determine the amount of Other Securities from time to time receivable
upon the exercise of the Warrants, so as to protect the Holders against the
effect of such dilution.

                  6.10 Notice of Adjustments. Whenever the number of shares of
Warrant Stock comprising a Stock Unit shall be adjusted pursuant to this
Agreement, the Issuer shall forthwith obtain a certificate signed by the
Issuer's chief financial officer, setting forth, in reasonable detail, the event
requiring the adjustment and the method by which such adjustment was calculated
and specifying the number of shares of Warrant Stock comprising a Stock Unit
(whether or not any Warrants have been issued hereunder or whether or not any
Warrants are then exercisable), after giving effect to such adjustment or
change. The Issuer shall promptly cause a signed copy of such certificate to be
delivered to each holder of Warrants. The Issuer shall keep at its office copies
of all such certificates and cause the same to be available for inspection at
said office during normal business hours by any holder of Warrants or any
prospective purchaser of Warrants designated by the registered holder hereof.



                                Warrant Agreement


<PAGE>   35



                                       30



                  6.11 Notice of Certain Corporate Action. If the Issuer shall
propose (i) to pay any dividend to the holders of its Common Stock or to make
any other distribution to the holders of its Common Stock; (ii) to offer to the
holders of its Common Stock rights to subscribe for or to purchase any
additional shares of Common Stock (or options or rights with respect thereto);
(iii) to effect any reclassification of its Common Stock; (iv) to otherwise
issue any Common Stock or other securities; (v) to effect any capital
reorganization; (vi) to effect any consolidation, merger or sale, transfer or
other disposition of all or substantially all of its assets; or (vii) to effect
the liquidation, dissolution or winding up of the Issuer, then, in each such
case, the Issuer shall give to each holder of Warrants a notice of such proposed
action, which shall specify the date on which a record is to be taken for the
purposes of such dividend, distribution or rights offer, or the date on which
such reclassification, issuance, reorganization, consolidation, merger, sale,
transfer, disposition, liquidation, dissolution or winding up is to take place
and the date of participation therein by the holders of Common Stock, if any
such date is to be fixed, and shall also set forth such facts with respect
thereto as shall be reasonably necessary to indicate the effect of such action
on the Common Stock, and the number of shares of Warrant Stock which will
comprise a Stock Unit (whether or not any Warrants have been issued hereunder or
whether or not any Warrants are then exercisable) after giving effect to any
adjustment which will be required as a result of such action. Such notice shall
be so given in the case of any action covered by clause (i) or (ii) above at
least 15 days prior to the record date for determining holders of the Common
Stock for purposes of such action, and in the case of any other such action, at
least 15 days prior to the date of the taking of such proposed action or the
date of participation therein by the holders of Common Stock, whichever shall be
the earlier.

                  SECTION 7.  Registration.

                  7.01 Notice. (a) (i) Upon receipt of notice (a "Demand
Notice") from a Holder of any Warrants or shares of



                                Warrant Agreement


<PAGE>   36



                                       31



Warrant Stock given at any time after the issuance of the Warrants requesting
that the Issuer effect the registration of the shares of Warrant Stock held by
such holder, or (ii) whenever the Issuer otherwise proposes to effect the
registration of all or any part of the Common Stock under the Securities Act,
other than pursuant to a Registration Statement on Form S-8 or Form S-4 or any
successor form, the Issuer shall promptly, and in any event at least 30 days
prior to the effective date of the proposed registration statement, give written
notice of such proposed registration to all holders of Warrants or shares of
Warrant Stock. Each holder of any Warrants or shares of Warrant Stock that
wishes to register its shares of Warrant Stock (each, a "Seller") shall, within
15 days after receipt of such notice from the Issuer, deliver to the Issuer a
notice (a "Seller Notice") stating that such Seller wishes to participate in
such offering and setting forth the number of shares of Warrant Stock that such
Seller desires to include in such offering. The Issuer thereupon shall, subject
to Section 7.01(b) as expeditiously as practicable, use its best efforts to
effect the registration under the Securities Act of such shares of Warrant Stock
(any such registration effected or undertaken pursuant to a Demand Notice being
herein referred to as a "Demand Registration"); provided, however, that the
Issuer shall not be required to effect a Demand Registration pursuant to a
Demand Notice from any holder of Warrants or shares of Warrant Stock unless the
holders of 50% in interest (on an aggregate basis) of the then outstanding
Warrants and shares of Warrant Stock notify the Issuer of their wish to
participate in an offering pursuant to such registration; and, provided,
further, that the Issuer shall not be required to effect more than one Demand
Registration. In the event that (i) the amount of securities proposed to be sold
by Sellers pursuant to a Demand Notice shall be reduced pursuant to this Section
7.02(a) to an amount which is less than 85% of the amount of securities
originally proposed to be sold by Sellers, or (ii) any Demand Notice shall be
withdrawn by the holder or holders originally giving such Demand Notice at any
time prior to the filing by the Issuer of a preliminary registration statement
in connection with such Demand Notice, then, in such event, no right to a Demand
Registration shall be deemed to have been exercised or forfeited and such Demand
Notice


                                Warrant Agreement


<PAGE>   37



                                       32


shall not operate to eliminate the Issuer's obligation to effect a Demand
Registration pursuant to a Demand Notice.

                  (b) Deferral of Filing. The Issuer may defer the filing (but
not the preparation) of a registration statement required by Section 7.01(a)
until a date not later than 90 days after the date of the Demand Notice if (i)
at the time the Issuer receives the Demand Notice, the Issuer or any of its
Subsidiaries is engaged in confidential negotiations or other confidential
business activities, disclosure of which would be required in such registration
statement (but would not be required if such registration statement were not
filed), and the Board determines in good faith that such disclosure would be
materially detrimental to the Issuer and its shareholders or would have a
material adverse effect on any such confidential negotiations or other
confidential business activities or (ii) prior to receiving the Demand Notice,
the Board had determined to effect a registered underwritten public offering of
the Issuer's securities and the Issuer had taken substantial steps (including,
but not limited to, selecting a managing underwriter for such offering) and is
proceeding with reasonable diligence to effect such offering. A deferral of the
filing of a registration statement pursuant to this Section 7.01(b) shall be
lifted, and the requested registration statement shall be filed forthwith, if
the negotiations or other activities are disclosed or terminated. In order to
defer the filing of a registration statement pursuant to this Section 7.01(b),
the Issuer shall promptly (but in any event within 10 days), upon determining to
seek such deferral, deliver to each Seller a certificate signed by an executive
officer of the Issuer setting forth a statement of the reason for such deferral
and an approximation of the anticipated delay, which information the Sellers
shall treat as confidential. Within 20 days after receiving such certificate,
Sellers holding a majority in interest of the Warrant Stock for which
registration was previously requested may withdraw such request by giving notice
to the Issuer; if withdrawn, the Demand Notice shall be deemed not to have been
made for all purposes of this Agreement. The Issuer may not invoke its right to
defer the filing of a registration statement under this Section 7.01(b) more
than once in any twelve month period.


                                Warrant Agreement


<PAGE>   38



                                       33



                      7.02 Proration.

                      (a) In the case of a Demand Registration, if the
  underwriter (or, if the offering is not underwritten, an independent financial
  advisor to the Sellers) determines that marketing factors require a limitation
  on the number of securities to be offered and sold, there shall be included in
  such registration only that number of securities that the underwriter, or
  financial advisor, as the case may be, believes will not jeopardize the
  success of the offering. Any reduction in the number of securities to be so
  offered shall first be pro-rata among all Persons (other than the Issuer)
  proposing to sell securities pursuant to such offering who are not Sellers,
  based on the number of securities originally proposed to be sold by each of
  them, and then, if necessary, pro-rata among all Sellers based on the number
  of securities originally proposed to be sold by each of them.

                      (b) In the case of a registration to be effected pursuant
  to Section 7.01(a) (ii) hereof, if the underwriter (or, if the offering is not
  underwritten, an independent financial advisor to the Issuer) determines that
  marketing factors require a limitation on the number of securities to be
  offered and sold in the offering, including securities requested to be offered
  and sold by Sellers, there shall be included in the offering only that number
  of securities that the underwriter, or financial advisor, as the case may be,
  believes will not jeopardize the success of the offering. Any reduction in the
  number of securities to be so offered shall be pro-rata among the Sellers and
  all other Persons (other than the Issuer or securityholders who are exercising
  "demand" registration rights), proposing to sell securities pursuant to such
  offering, based on the number of securities originally proposed to be sold by
  each such person.

  Nothing contained herein shall be construed to limit in any way the Issuer' s
  right, in its sole discretion, to withdraw any registration statement (other
  than a registration statement filed pursuant to a Demand Notice) before such
  registration statement




                                Warrant Agreement


<PAGE>   39



                                       34



becomes effective, or to postpone the offering of securities contemplated by any
such registration statement.


                  7.03 Registration Procedures. If and whenever the Issuer is
required by the provisions of Section 7.01(a) (i) hereof or, with respect to
subsections (i), (ii), (iii), (vi), (vii), (viii), (ix), (x), (xi) and (xii) of
this Section 7.03, by the provisions of Section 7.01(a) (i) or (ii) hereof, to
use its best efforts to effect the registration of any of its securities under
the Securities Act, the Issuer shall, as expeditiously as possible,

                  (i)   prepare and file with the Commission a registration
         statement with respect to such securities and use its best efforts to
         cause such registration statement to become and remain effective for a
         period of not less than 90 days, to permit the sale of such securities
         in accordance with the plan of distribution chosen by the Seller or
         Sellers and the underwriter;

                  (ii)  prepare and file with the Commission such amendments and
         supplements to such registration statement and the prospectus used in
         connection therewith as may be necessary to keep such registration
         statement effective and to comply with the provisions of the Securities
         Act with respect to the sale or other disposition of all securities
         covered by such registration statement;

                  (iii) furnish to each Seller such numbers of copies of a
         prospectus, including a preliminary prospectus, in conformity with the
         requirements of the Securities Act, and such other documents, as such
         Seller may reasonably request in order to facilitate the public sale or
         other disposition of the securities owned by such Seller;

                  (iv)  use its best efforts to register or qualify the
         securities covered by such registration statement under such other
         securities or blue sky laws of such jurisdictions within the United
         States as each Seller shall reasonably request, and do such other
         reasonable acts and things as may



                                Warrant Agreement


<PAGE>   40



                                       35


be requested of it to enable such Seller to consummate the public sale or other
disposition in such jurisdictions of the securities owned by such Seller, except
that the Issuer shall not for any such purpose be required to qualify to do
business as a foreign corporation in any jurisdiction wherein it is not so
qualified;

           (v)  use its best efforts to cause the securities covered by such
registration statement to be registered with or approved by such other
governmental agencies or authorities in the United States or any state thereof
as may be necessary and as would be customary for the offering of securities by
companies engaged in the oil and gas business to enable the Seller or Sellers
thereof to consummate the disposition of such securities;

           (vi) notify each Seller of any securities covered by such
registration statement, at any time when a prospectus relating thereto is
required to be delivered under the Securities Act, of the Issuer's becoming
aware that the prospectus included in such registration statement, as then in
effect, includes an untrue statement of a material fact or omits to state any
material fact required to be stated therein or necessary to make the statements
therein not misleading in the light of the circumstances then existing (upon
receipt of which each Seller agrees to forthwith cease making offers and sales
of such securities pursuant to such prospectus and to deliver to the Issuer any
copies of such prospectus then in the possession of such Seller), and at the
request of any such Seller promptly prepare and furnish to such Seller a
reasonable number of copies of a prospectus supplemented or amended so that, as
thereafter delivered to the purchasers of such securities, such prospectus shall
not include an untrue statement of a material fact or omit to state a material
fact required to be stated therein or necessary to make the statements therein
not misleading in the light of the circumstances then existing;

         (vii)  make available to its security holders, as soon as reasonably
practicable, an earnings statement covering


                                Warrant Agreement


<PAGE>   41



                                       36



the period of at least twelve months, but not more than eighteen months,
beginning with one of the first three months after the effective date of the
registration statement, which earnings statement shall satisfy the provisions of
Section 11(a) of the Securities Act;

         (viii) otherwise use its best efforts to comply with all applicable
rules and regulations of the Commission;

         (ix) use its best efforts to list such securities on any securities
exchange on which the Common Stock of the Issuer is then listed, or, if not so
listed, on a national securities exchange, if the listing of such securities is
then permitted under the rules of such exchange;

         (x) provide a transfer agent and registrar for all the securities
covered by such registration statement not later than the effective date of such
registration statement;

         (xi) enter into such agreements (including an underwriting agreement in
customary form containing without limitation customary indemnity and
contribution provisions for the benefit of the underwriter or underwriters and
the Seller or Sellers) and take such other actions as the Seller or Sellers
shall reasonably request in order to expedite or facilitate the disposition of
such securities;

         (xii) make available for inspection by any Seller of securities covered
by such registration statement, the lead underwriter participating in any
disposition to be effected pursuant to such registration statement and by any
attorney, accountant or other agent retained by any such Seller or such
underwriter, all pertinent financial and other records, pertinent corporate
documents and properties of the Issuer, and cause all of the Issuer's officers,
directors and employees to supply all information reasonably requested by any
such Seller, underwriter, attorney, accountant or agent in connection with such
registration statement (provided that the Sellers shall use reasonable efforts
to retain




                                Warrant Agreement


<PAGE>   42



                                       37



         common attorneys, accountants and agents and to conduct any such
         investigations as a group); and

                  (xiii) permit any Seller of securities covered by such
         registration statement to require the insertion therein of material,
         furnished to the Issuer in writing with respect to the Seller or the
         plan of distribution (or any other matter that counsel for such Seller
         has advised the Seller in writing is required to be included therein to
         avoid an untrue statement of a material fact or the omission of a
         material fact required to be stated therein or necessary to make the
         statements therein not misleading), which in the reasonable judgment of
         such Seller should be included.

If any such registration or comparable statement refers to any Seller by name or
otherwise as the holder of any securities of the Issuer, then such Seller shall
have the right to require (A) the insertion therein of language, in form and
substance satisfactory to such Seller, to the effect that the holding by such
Seller of such securities is not to be construed as a recommendation by such
Seller of the investment quality of the Issuer's securities covered thereby and
that such holding does not imply that such Seller will assist in meeting any
future financial requirements of the Issuer, or (B) in the event that such
reference to such Seller by name or otherwise is not required by the Securities
Act, the deletion of the reference to such Seller.

                  The Issuer may require each Seller of securities to, and each
such Seller, as a condition to including Securities in such registration, shall,
furnish the Issuer with such information and affidavits regarding such Seller
and the distribution of such securities as the Issuer may from time to time
reasonably request in writing in connection with such registration. No Seller
may participate in any underwritten registration hereunder unless such Seller
(a) agrees to sell such Seller's securities on the basis provided in any
underwriting arrangements approved by the Persons entitled hereunder to approve
such arrangements and (b) completes and executes all questionnaires, powers of
attorney, indemnities, underwriting


                                Warrant Agreement


<PAGE>   43



                                       38



agreements and other documents reasonably required under the terms of such
underwriting arrangements and these registration rights.

                  Each Seller of securities agrees that upon receipt of any
notice from the Issuer of the happening of any event of the kind described in
Section 7.03(vi), such Seller will forthwith discontinue such Seller's
disposition of securities pursuant to the registration statement relating to
such securities until such Seller's receipt of the copies of the supplemented or
amended prospectus contemplated by Section 7.03 (vi) and, if so directed by the
Issuer, will deliver to the Issuer (at the Issuer's expense) all copies, other
than permanent file copies, then in such Seller's possession of any prospectus
relating to such securities at the time of receipt of such notice.

                  7.04 Holdback on Sales. The Issuer and the Holders hereby
agree not to effect any public sale or distribution of any securities similar to
those registered in accordance with Section 7.03 hereof during the 14 day period
prior to, and during the 30 day period beginning on, the effective date of any
registration statement (except as part of such registration statement).

                  7.05 Expenses. All reasonable expenses incurred in complying
with this Section 7, including, without limitation, all registration and filing
fees, printing expenses, fees and disbursements of counsel for the Issuer, the
reasonable fees and disbursements of one counsel for the Seller or the Sellers
(to be chosen by the Seller or the Sellers holding a majority of the securities
to be included by Sellers in a registration statement), expenses of any special
audits incident to or required by any such registration and expenses of
complying with the securities or blue sky laws of any jurisdictions, shall be
paid by the Issuer; provided, that in no event shall the Issuer be required to
pay any underwriting discounts, commissions or fees attributable to the sale of
Warrant Shares by a Seller hereunder.





                                Warrant Agreement


<PAGE>   44



                                       39

                  7.06  Indemnification.

                  (a)   In the event of any registration of any of its 
securities under the Securities Act pursuant to this Section, the Issuer shall,
and hereby agrees to, indemnify and hold harmless each Seller of such
securities, its directors and officers, and each other person, if any, who
controls such Seller within the meaning of Section 15 of the Securities Act,
against any losses, claims, damages, liabilities or expenses ("Losses") to which
such Seller or any such director, officer or person may become subject under the
Securities Act or any other statute or at common law, insofar as such Losses (or
actions in respect thereof) arise out of or are based upon any alleged untrue
statement of any material fact contained in any registration statement under
which such securities were registered under the Securities Act, any preliminary
prospectus or final prospectus with respect thereto, or any amendment or
supplement thereto, or any alleged omission to state therein a material fact
required to be stated therein or necessary to make the statements therein not
misleading, and shall reimburse such Seller or such director, officer or
controlling person for any legal or any other expenses reasonably incurred by
such Seller or such director, officer or controlling person in connection with
investigating or defending any such Loss; provided, however, that the Issuer
shall not be liable in any such case to the extent that any such Loss arises out
of or is based upon any alleged untrue statement or alleged omission made in
such registration statement, preliminary prospectus, prospectus, or amendment or
supplement in reliance upon and in conformity with written information furnished
to the Issuer for inclusion therein by such Seller; provided further, however
that with respect to any untrue statement or omission or alleged untrue
statement or omission made in any preliminary prospectus, the indemnity
agreement contained in this paragraph shall not apply to the extent that any
such Loss results from the fact that a current copy of the prospectus was not
sent or given to the person asserting any such Loss at or prior to the written
confirmation of the sale of the securities concerned to such person if the
Issuer had prior thereto given such Seller the notice referred to in Section
7.03 (vi) hereof and provided to such Seller a supplemented or amended
prospectus as contemplated by Section 7.03(vi), and such current copy of the
prospectus would have cured the defect giving rise to such Loss. Such


                                Warrant Agreement


<PAGE>   45



                                       40



indemnity shall remain in full force and effect regardless of any investigation
made by or on behalf of such Seller or such director, officer or controlling
person, and shall survive the transfer of such securities by such Seller.

                  (b) Each Seller of securities which are included in a
registration statement hereunder, as a condition to including securities in such
registration statement, shall indemnify and hold harmless the Issuer, its
directors and officers and each other Person, if any, who controls the Issuer
within the meaning of Section 15 of the Securities Act, against any Losses to
which the Issuer or any such director, officer or person may become subject
under the Securities Act or otherwise, insofar as such Losses (or actions in
respect thereof) arise out of or are based upon any untrue statement or alleged
untrue statement of any material fact contained in such registration statement,
any preliminary prospectus, final prospectus or summary prospectus contained
therein, or any amendment or supplement thereto, or any omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein (in the case of a prospectus, in the
light of the circumstances under which they were made) not misleading, if such
untrue statement or alleged untrue statement or omission or alleged omission was
made in reliance upon and in conformity with written information furnished to
the Issuer by such Seller specifically for use in the preparation thereof;
provided, however, that the obligation to provide indemnification pursuant to
this Section 7.06(b) shall be several, and not joint and several, among such
Sellers on the basis of the number of securities included by each in such
registration statement and the aggregate amount which may be recovered from any
holder of securities pursuant to the indemnification provided for in this
Section 7.06(b) in connection with any sale of securities shall be limited to
the total proceeds received by such holder from the sale of such securities.
Such indemnity shall remain in full force and effect regardless of any
investigation made by or on behalf of the Issuer or any such other Person and
shall survive the transfer of such securities by such Seller.




                                Warrant Agreement


<PAGE>   46



                                       41


                  (c) Promptly after receipt by any Person under this Section of
notice of the commencement of any action, such Person (an "Indemnified Party")
shall, if a claim in respect thereof is to be made against any other Person (an
"Indemnifying Party") for indemnity under this Section, notify the Indemnifying
Party in writing of the commencement thereof; but the omission so to notify the
Indemnifying Party shall not relieve it from any liability which it may have to
any Indemnified Party, except to the extent that the Indemnifying Party is
prejudiced thereby. The Indemnifying Party may, upon being notified of such
action, assume the defense thereof, with counsel satisfactory to such
Indemnified Party, and, after such assumption, the Indemnifying Party shall not
be liable to such Indemnified Party under this Section for any legal expenses of
other counsel or any other expenses, in each case subsequently incurred by such
Indemnified Party, in connection with the defense thereof; provided, however,
that the Indemnifying Party may not assume the defense of the action, and shall
remain liable to the Indemnified Party for its legal expenses of counsel and
other expenses, in the event that the Indemnified Party determines that a
conflict of interest may exist between the Indemnified Party and the
Indemnifying Party.

                  (d) If the indemnification provided for in this Section is
unenforceable although available, or insufficient to hold harmless an
Indemnified Party hereunder for any Losses (or actions in respect thereof) in
respect of which the provisions of Section 7.06(a) or (b) would otherwise apply
by their terms, then the Indemnifying Party shall contribute to the amount paid
or payable by such Indemnified Party as a result of such Losses (or actions in
respect thereof) in such proportion as is appropriate to reflect the relative
fault of the Indemnifying Party on the one hand and the Indemnified Party on the
other hand in connection with the statements or omissions which resulted in such
Losses (or actions in respect thereof), as well as any other relevant equitable
considerations. The relative fault shall be determined by reference to, among
other things, whether the untrue or alleged untrue statement of a material fact
relates to information supplied by the Indemnifying Party on the one hand or
such Indemnified Party on the other hand and the parties' relative intent,
knowledge, access to information and opportunity


                                Warrant Agreement


<PAGE>   47



                                       42



to correct or prevent such statement or omission. The parties agree that it
would not be just and equitable if contribution pursuant to this subsection were
determined by pro rata allocation or by any other method of allocation which
does not take account of the equitable considerations referred to in this
subsection. The amount paid or payable as a result of the Losses (or actions in
respect thereof) referred to above in this subsection shall be deemed to include
any legal or other expenses reasonably incurred by such Indemnified Party in
connection with investigating or defending any such action or claim. No person
guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of
the Securities Act) shall be entitled to contribution from any person who was
not guilty of such fraudulent misrepresentation.

                  7.07 Option to Purchase Registrable Stock. For a period of 20
calendar days commencing on the date that the Issuer receives a request by the
Sellers to include Warrant Stock in a registration statement pursuant to this
Section 7, the Issuer shall have the right and option, in lieu of including such
Warrant Stock in such registration, to purchase for cash from such Sellers of
the Warrant Stock requested to be included in such registration and to require
such holders to sell, at the Current Market Price, all of such Warrant Stock
proposed to be registered. In order to exercise its option to purchase Warrant
Stock pursuant to this Section 7.07, the Issuer must give written notice to the
Sellers of such exercise (the "Purchase Notice") during such 20-day period. The
closing of any purchase of Warrant Stock pursuant to this Section 7.07 shall
take place at the offices of the Issuer at 11:00 a.m., New York time, on a
Business Day which shall be no earlier than 15 calendar days after the date of
the Purchase Notice. If the Issuer exercises its option to purchase Warrant
Stock under this Section 7.07 in lieu of a registration under Section 7.01, upon
the payment of the purchase price in cash for such Warrant Stock, the Issuer
shall be considered as effecting the registration pursuant to Section 7.01.

                  7.08 No Other Registration Rights. The Issuer shall not grant
any registration rights to any holder of securities of


                                Warrant Agreement


<PAGE>   48



                                       43



the Issuer in respect of such securities if such registration rights would rank
senior to, or otherwise adversely affect, the registration rights granted in
this Section 7. This section 7.08 shall not prohibit the grant of registration
rights to others on a "pari passu" basis with those granted in this Section 7.

                  SECTION 8.  Holders' Rights.

                  8.01 Delivery Expenses. If any Holder surrenders any
certificate for Warrants or Warrant Stock to the Issuer or a transfer agent of
the Issuer for exchange for instruments of other denominations or registered in
another name or names, the Issuer shall cause such new instruments to be issued
and shall pay the cost of delivering to or from the office of such Holder from
or to the Issuer or its transfer agent, duly insured, the surrendered instrument
and any new instruments issued in substitution or replacement for the
surrendered instrument.

                  8.02 Taxes. The Issuer shall pay all taxes (other than
Federal, state or local income taxes) which may be payable in connection with
the execution and delivery of this Agreement or the issuance of the Warrants and
Warrant Stock hereunder or in connection with any modification of this Agreement
or the Warrants and shall hold each Holder harmless without limitation as to
time against any and all liabilities with respect to all such taxes. The
obligations of the Issuer under this Section 8.02 shall survive any redemption,
repurchase or acquisition of Warrants or Warrant Stock by the Issuer, any
termination of this Agreement, and any cancellation or termination of the
Warrants.

                  8.03 Replacement of Instruments. Upon receipt by the Issuer of
evidence reasonably satisfactory to it of the ownership of and the loss, theft,
destruction or mutilation of any certificate or instrument evidencing any
Warrants or Warrant Stock, and

                  (a) in the case of loss, theft or destruction, of indemnity
         reasonably satisfactory to it, or

                  (b) in the case of mutilation, upon surrender or cancellation
         thereof,


                                Warrant Agreement


<PAGE>   49



                                       44



the Issuer, at its expense, shall execute, register and deliver, in lieu
thereof, a new certificate or instrument for (or covering the purchase of) an
equal number of Warrants or Warrant Stock.


                  8.04 Indemnification. The Issuer shall indemnify and hold
harmless each of the Investor and the Holders and each of their respective
directors, officers, employees, shareholders, Affiliates and agents (each, an
"indemnified person") on demand from and against any and all losses, claims,
damages, liabilities (or actions or other proceedings commenced or threatened in
respect thereof) and expenses that arise out of, result from, or in any way
relate to, this Agreement or the Warrants, or in connection with the other
transactions contemplated hereby and thereby, and to reimburse each indemnified
person, upon its demand, for any legal or other expenses incurred in connection
with investigating, defending or participating in the defense of any such loss,
claim, damage, liability, action or other proceeding (whether or not such
indemnified person is a party to any action or proceeding out of which any such
expenses arise), other than any of the foregoing claimed by any indemnified
person to the extent incurred by reason of the gross negligence or willful
misconduct of such indemnified person. No indemnified person shall be
responsible or liable to either the Issuer or any other Person for any damages
which may be alleged as a result of or relating to this Agreement or the
Warrants (other than in connection with a breach of this Agreement), or in
connection with the other transactions contemplated hereby and thereby. Any
claim for indemnity in connection with or relating to a registration of
securities pursuant to Section 7 hereof shall be governed by Section 7.06
hereof, without regard to the provisions of this Section 8.04.

                  SECTION 9. Other Covenants of Issuer. The Issuer agrees with
each Holder that, so long as any of the Warrants and/or Warrant Stock shall be
outstanding:

                  9.01 Financial Statements, Etc. If at any time the Issuer is
not required to file reports pursuant to Sections 13,




                                Warrant Agreement


<PAGE>   50



                                       45



14(a) and 15(d) of the Exchange Act, the Issuer shall deliver the information
specified below to each Holder:

                  (a) within 90 days after the end of each fiscal year of the
         Issuer, its audited consolidated and consolidating balance sheet and
         related statements of operations, stockholders' equity and cash flows
         as of the end of and for such year, setting forth in each case in
         comparative form the figures for the previous fiscal year, together
         with, in the case of such consolidated financial statements, the report
         thereon by the Issuer's independent public accountants of recognized
         national standing (without any qualification or exception as to the
         scope of such audit) to the effect that such consolidated financial
         statements present fairly in all material respects the financial
         condition and results of operations of the Issuer and its consolidated
         Subsidiaries on a consolidated basis in accordance with GAAP
         consistently applied and, in the case of such consolidating financial
         statements, certified by its chief financial officer as presenting
         fairly in all material respects the financial condition and results of
         operations of the Issuer and each of its consolidated subsidiaries in
         accordance with GAAP consistently applied, subject to normal year-end
         audit adjustments and the absence of footnotes;

                  (b) within 45 days after the end of each of the first three
         fiscal quarters of the Issuer's fiscal year, the Issuer's consolidated
         and consolidating balance sheet and related statements of operations,
         stockholders' equity and cash flows as of the end of and for such month
         and the then elapsed portion of the fiscal year, setting forth in each
         case in comparative form the figures for the corresponding period or
         periods of (or, in the case of the balance sheet, as of the end of) the
         previous fiscal year, all certified by its chief financial officer as
         presenting fairly in all material respects the financial condition and
         results of operations of the Issuer and its consolidated Subsidiaries
         on a consolidated basis in accordance with GAAP consistently applied,
         subject to normal year-end audit adjustments and the absence of
         footnotes;


                                Warrant Agreement


<PAGE>   51



                                       46



                  (c) promptly after the same become publicly available, copies
         of all periodic and other reports, proxy statements and other materials
         filed by the Issuer or any Subsidiary with the Commission, or any
         Governmental Authority succeeding to any or all of the functions of
         said Commission, or with any national securities exchange, or
         distributed by the Issuer to its Shareholders generally; and

                  (d) so long as any Investor or any of its respective
         Affiliates, shall hold any Warrant or Warrant Stock, to such Holder or
         Holders only, all other information required to be provided under
         Sections 9.01 of the Loan Agreement as in effect on the date hereof
         (whether or not the same shall remain in effect).

                  9.02 Transactions with Affiliates. Except as expressly
permitted by this Agreement, the Issuer shall not, nor shall it permit any of
its Subsidiaries to, directly or indirectly, sell, lease or otherwise transfer
any property or assets to, or purchase, lease or otherwise acquire any property
or assets from, or otherwise engage in any other transactions with, any of its
Affiliates, except (a) in the ordinary course of business at prices and on terms
and conditions not less favorable to the Issuer or such Subsidiary than could be
obtained on an arm's-length basis from unrelated third parties unless approved
by a majority of the Issuer's non-employee directors, (b) transactions between
or among the Issuer and its wholly owned Subsidiaries not involving any other
Affiliate, (c) any Restricted Payment permitted by Section 9.09 of the Loan
Agreement or (d) any transactions or arrangements existing on the date hereof.

                  9.03 Restrictions on Performance. The Issuer shall not at any
time enter into an agreement or other instrument expressly limiting in any
manner its ability to perform its obligations under this Agreement or the
Warrants, or making such performance or the issuance of Warrant Stock upon the
exercise of any Warrant a default under any such agreement or instrument.




                                Warrant Agreement


<PAGE>   52



                                       47


                      9.04 Rule 144. The Issuer will file the reports required
  to be filed by it under the Securities Act and the Exchange Act so long as the
  Issuer is registered under the Exchange Act. Upon the request of any Holder,
  the Issuer will deliver to such Holder a written statement as to whether it
  has complied with such requirements.

                      SECTION 10.  Miscellaneous.

                      10.01 Office of the Issuer. So long as any of the Warrants
  remains outstanding, the Issuer shall maintain an office in the continental
  United States of America where the Warrants may be presented for exercise,
  transfer, division or combination provided herein and in the Warrants. Such
  office shall be at the address of the Issuer set forth in Section 10.03 hereof
  unless and until the Issuer shall designate and maintain some other office for
  such purposes and give notice thereof to all Holders.

                      10.02 Waiver. No failure on the part of any Investor to
  exercise and no delay in exercising, and no course of dealing with respect to,
  any right, power or privilege under this Agreement or the Warrants shall
  operate as a waiver thereof, nor shall any single or partial exercise of any
  right, power or privilege under this Agreement or the Warrant preclude any
  other or further exercise thereof or the exercise of any other right, power or
  privilege. The remedies provided herein are cumulative and not exclusive of
  any remedies provided by law.

                      10.03   Notices.

                      (a) All notices, requests and other communications
  provided for herein and the Warrants (including any waivers or consents under
  this Agreement and the Warrants) shall be given or made in writing,








                                Warrant Agreement


<PAGE>   53



                                       48



                  (i)      if to the Issuer:

                           Address for Notices:

                           Rutherford-Moran Oil Corporation
                           5 Greenway Plaza, Suite 220
                           Houston, Texas 77046

                           Attention:     Chief Financial Officer
                           Telephone No.: 713-621-7072
                           Fax No.:       713-622-5555


                  (ii)     if to the Investors:

                           The Chase Manhattan Bank
                           270 Park Avenue
                           New York, New York 10017

                           Attention:     Richard Betz
                           Telephone No.: 212-270-6971
                           Fax No.:       212-270-2519


                           and


                           Banque Paribas
                           1200 Smith, Suite 3100
                           Houston, Texas 77002

                           Attention:     Doug Liftman
                           Telephone No.: 713-659-4811
                           Fax No.:       713-659-6915


                  (iii)    if to any other Person who is the registered Holder
                           of any Warrants or Warrant Stock, to the address for
                           such Holder as it appears in the stock or warrant
                           ledger of the Issuer;


or, in the case of any Holder, at such other address as shall be
designated by such party in a notice to the Issuer; or, in the

                                Warrant Agreement


<PAGE>   54



                                       49



case of the Issuer, at such other address as the Issuer may designate in a
notice to the Investor and all other Holders.

                  (b) All such notices, requests and other communications shall
be: (i) personally delivered, sent by courier guaranteeing overnight delivery or
sent by registered or certified mail, return receipt requested, postage prepaid,
in each case given or addressed as aforesaid; and (ii) effective upon receipt.

                  10.04 Expenses, Etc. The Issuer agrees to pay or reimburse
each Investor and the Holders for: (a) all reasonable out-of-pocket costs and
expenses of each such Investors and the Holders (including the reasonable fees
and expenses of Milbank, Tweed, Hadley & McCloy, special New York counsel to the
Investors), in connection with (i) the negotiation, preparation, execution and
delivery of this Agreement and the issuance of Warrants hereunder, and (ii) any
amendment, modification or -waiver of (or consents in respect of ) any of the
terms of this Agreement or the Warrants; and (b) all reasonable costs and
expenses of the Investors and the Holders (including reasonable legal fees and
expenses) in connection with (i) any default by the Issuer hereunder or under
the Warrants or any enforcement proceedings resulting therefrom, and (ii) the
enforcement of this Section 10.04.

                  10.05 Amendments, Etc. Except as otherwise expressly provided
in this Agreement, any provision of this Agreement may be amended or modified
only by an instrument in writing signed by the Issuer and the holders of
two-thirds of the Warrant Stock issued or issuable upon exercise of the
Warrants; provided, however, that (a) the consent of the holders of any Warrant
Stock or Warrants shall not be required with respect to any amendment or waiver
which does not affect the rights or benefits of such class under this Agreement,
and (b) no such amendment or waiver shall, without the written consent of all
holders of such Warrant Stock and Warrants at the time outstanding, amend this
Section 10.05.





                                Warrant Agreement


<PAGE>   55



                                       50



                  10.06 Successors and Assigns. This Agreement shall be binding
upon and inure to the benefit of the parties hereto and their respective
successors and permitted assigns.

                  10.07 Survival. All representations and warranties made by the
Issuer herein or in any certificate or other instrument delivered by it or on
its behalf under this Agreement shall be considered to have been relied upon by
each of the Investors and shall survive the issuance of the Warrants or the
Warrant Stock regardless of any investigation made by or on behalf of the
Investors. All statements in any such certificate or other instrument so
delivered shall constitute representations and warranties by the Issuer
hereunder. All representations and warranties made by the Investors herein shall
be considered to have been relied upon by the Issuer and shall survive the
issuance to the Investors of the Warrants or the Warrant Stock regardless of any
investigation made by the Issuer or on its behalf.

                  10.08 Specific Performance. Damages in the event of breach of
this Agreement by an Investor, a Holder or the Issuer would be difficult, if not
impossible, to ascertain, and it is therefore agreed that each Investor, Holder
and the Issuer, in addition to and without limiting any other remedy or right it
may have, will have the right to an injunction or other equitable relief in any
court of competent jurisdiction, enjoining any such breach, and enforcing
specifically the terms and provisions hereof, and each Investor, Holder and the
Issuer hereby waives any and all defenses it may have on the ground of lack of
jurisdiction or competence of the court to grant such an injunction or other
equitable relief. The existence of this right will not preclude the Investors,
Holders or the Issuer from pursuing any other rights and remedies at law or in
equity which the Investors, Holders or the Issuer may have.

                  10.09 Captions. The captions and section headings appearing
herein are included solely for convenience of reference and are not intended to
affect the interpretation of any provision of this Agreement.




                                Warrant Agreement


<PAGE>   56



                                       51


                  10.10 Counterparts. This Agreement may be executed in any
number of counterparts, all of which taken together shall constitute one and the
same instrument and any of the parties hereto may execute this Agreement by
signing any such counterpart signature page or counterpart.

                  10.11 Governing Law. This Agreement shall be governed by, and
construed in accordance with, the law of the State of New York without giving
effect to the conflicts of law principles thereof, except to the extent that New
York conflicts of laws principles would apply the Delaware General Corporation
Law to matters relating to corporations organized thereunder.

                  10.12 Severability. In the event that any one or more of the
provisions contained herein, or the application thereof in any circumstance, is
held invalid, illegal or unenforceable, the validity, legality and
enforceability of any such provision in every other respect and of the remaining
provisions contained herein shall not be affected or impaired thereby.

                  10.13 Entire Agreement. This Agreement supersedes all prior
discussions and agreements between the parties with respect to the subject
matter hereof, and together with the Warrants contains the sole and entire
agreement between the parties hereto with respect to the subject matter hereof.






                                Warrant Agreement


<PAGE>   57



                                       52


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


                                       RUTHERFORD-MORAN OIL CORPORATION



                                       By
                                         --------------------------------------
                                         Name:
                                         Title:


                                       THE CHASE MANHATTAN BANK



                                       By
                                         --------------------------------------
                                         Name:
                                         Title:


                                       BANQUE PARIBAS



                                       By
                                         --------------------------------------
                                         Name:
                                         Title:




                                Warrant Agreement


<PAGE>   58



                                                                      Schedule I


                                Equity Interests

                           (on a fully diluted basis)


                            NUMBER OF                          PERCENTAGE
                            SHARES OF                          (ON A FULLY
NAME                        COMMON STOCK                       DILUTED BASIS)
----                        -------------                      --------------












TOTAL




*     Includes Options
**    Warrant













<PAGE>   59




                                   Schedule I











<PAGE>   60


                                                                   Annex 1
                                                                     to
                                                               Warrant Agreement


                                [Form of Warrant]

                                     WARRANT


THE TRANSFER OF THE SECURITIES REPRESENTED BY THIS CERTIFICATE IS SUBJECT TO THE
CONDITIONS SPECIFIED IN THAT CERTAIN WARRANT AGREEMENT DATED AS OF DECEMBER 3,
1997 (THE "WARRANT AGREEMENT"), BETWEEN RUTHERFORD-MORAN OIL CORPORATION, A
DELAWARE COMPANY (THE "ISSUER") AND THE CHASE MANHATTAN BANK AND BANQUE PARIBAS
AS THE WARRANT AGREEMENT MAY BE MODIFIED AND SUPPLEMENTED AND IN EFFECT FROM
TIME TO TIME, AND NO TRANSFER OF THE SECURITIES REPRESENTED BY THIS CERTIFICATE
SHALL BE VALID OR EFFECTIVE UNTIL SUCH CONDITIONS HAVE BEEN FULFILLED. A COPY OF
THE FORM OF THE WARRANT AGREEMENT IS ON FILE AND MAY BE INSPECTED AT THE
PRINCIPAL EXECUTIVE OFFICE OF THE ISSUER. THE HOLDER OF THIS CERTIFICATE, BY
ACCEPTANCE OF THIS CERTIFICATE, AGREES TO BE BOUND BY THE PROVISIONS OF THE
WARRANT AGREEMENT.

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS, AND
ACCORDINGLY, SUCH SECURITIES MAY NOT BE TRANSFERRED, SOLD OR OTHERWISE DISPOSED
OF EXCEPT IN COMPLIANCE WITH THE REGISTRATION OR QUALIFICATION PROVISIONS OF
APPLICABLE FEDERAL AND STATE SECURITIES LAWS OR APPLICABLE EXEMPTIONS THEREFROM.

No. of Stock Units Covered Hereby: __                       Warrant No. ________

                                     WARRANT

                          to Purchase Common -Stock of

                        RUTHERFORD-MORAN OIL CORPORATION

                  THIS IS TO CERTIFY THAT [INSERT NAME OF HOLDER], or its
registered assigns (the "Holder"), is entitled to purchase in whole or in part
from time to time from RUTHERFORD-MORAN OIL CORPORATION, a Delaware company (the
"Issuer"), at any time on and after the date hereof, but not later than 5:00
p.m., New York


                                     Warrant


<PAGE>   61



                                        2


time, on June 30, 2005 (the "Expiration Date"), ____ Stock Units (as hereinafter
defined and subject to adjustment as provided herein) at a purchase price of
$21.00 per share of Common Stock (the "Exercise Price"), subject to the terms
and conditions hereinbelow provided. "Stock Unit" shall mean one share of Common
Stock, as such Common Stock is constituted on the date hereof, and thereafter
shall mean such number of shares (including any fractional shares) of Common
Stock and other securities, cash or other property as shall result from the
adjustments specified in Section 6 of the Warrant Agreement. "Common Stock"
shall mean the Common Stock of the Issuer, par value $.01 per share, or any
other common stock or other securities receivable thereon, or into which the
Common Stock is convertible or exchangeable, as a result of any
recapitalization, reclassification, merger or consolidation of, or deposition of
assets by, the Issuer. All capitalized terms unless otherwise defined herein
shall have the meanings set forth in the Warrant Agreement.

           On and after the date hereof and until 5:00 p.m., New York time, on
the Expiration Date, the Holder may exercise this Warrant, on one or more
occasions, on any Business Day, in whole or in part, by delivering to the
Issuer,

           (a)    a written notice of the Holder's election to exercise this
                  Warrant, which notice shall specify the number of Stock Units
                  to be purchased (the "Exercise Notice");

           (b)    payment of the aggregate Exercise Price for the number of
                  Stock Units as to which this Warrant is being exercised
                  (payable as set forth below); and

           (c)    this Warrant.

                  The Exercise Price shall be payable (a) in cash or by
certified or official bank check payable to the order of the Issuer or by wire
transfer of immediately available funds to the account of the Issuer or (b) by
delivery of this Warrant Certificate to the Issuer for cancellation in
accordance with the following formula: in exchange for each share of Common
Stock issuable on exercise of each Warrant represented by this Warrant
Certificate that is being exercised, the holder shall receive such number of
shares of Common Stock as is equal to (a) (i) the

                                     Warrant


<PAGE>   62



                                        3


product of (x) the number of shares of Common Stock comprising a Stock Unit at
the time of such conversion and (y) the Current Market Price per share of Common
Stock at the time of such conversion minus the Exercise Price per share of
Common Stock at such time, divided by (b) the Current Market Price per share of
Common Stock at the time of conversion, all as provided in the Warrant
Agreement. Such Exercise Notice may be substantially in the form of Annex A
hereto. Upon receipt thereof, the Issuer shall, as promptly as practicable and
in any event within 5 Business Days thereafter, execute or cause to be executed
and deliver or cause to be delivered to the Holder a certificate or certificates
representing the aggregate number of Warrant Stock and other securities issuable
upon such exercise and any other property to which such Holder is entitled.

                  The certificate or certificates for Warrant Stock so delivered
shall be in such denominations as may be specified in the Exercise Notice and
shall be registered in the name of the Holder or such other name or names as
shall be designated in such Exercise Notice. Such certificate or certificates
shall be deemed to have been issued and the Holder or any other Person so
designated to be named therein shall be deemed to have become a holder of record
of Warrant Stock, including, to the extent permitted by law, the right to vote
Warrant Stock or to consent or to receive notice as a Shareholder, as of the
date on which the last of the Exercise Notice, payment of the Exercise Price and
this Warrant is received by the Issuer as aforesaid, and all taxes required to
be paid by the Holder, if any, pursuant to the Warrant Agreement, prior to the
issuance of Warrants Units have been paid. If this Warrant shall have been
exercised only in part, the Issuer shall, at the time of delivery of the
certificate or certificates representing Warrant Stock and other securities,
execute and deliver to the Holder a new Warrant evidencing the rights of the
Holder to purchase the unpurchased Stock Units called for by this Warrant, which
new Warrant shall in all other respects be identical with this Warrant, or, at
the request of the Holder, appropriate notation may be made on this Warrant and
the same returned to the Holder.

                  The Issuer shall not be required to issue a fractional amount
of Warrant Stock upon exercise of this Warrant. As to any fraction of a Warrant
Stock which the Holder would otherwise be entitled to purchase upon such
exercise, the Issuer shall pay a


                                     Warrant


<PAGE>   63



                                        4


cash adjustment in respect of such final fraction in an amount equal to the same
fraction of the Current Market Price per share of Warrant Stock on the date of
exercise.

                  THIS WARRANT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE
WITH THE LAWS OF THE STATE OF NEW YORK.









                                     Warrant


<PAGE>   64



                                        5



                  IN WITNESS WHEREOF, the Issuer has duly executed this Warrant.


Dated:          , 1998
      ----------

                                  RUTHERFORD-MORAN OIL CORPORATION



                                  By 
                                     ----------------------------------
                                      Name:
                                      Title:


Attest:



---------------------------------
Secretary









                                     Warrant


<PAGE>   65


                                                                         Annex A
                                                                           to
                                                                         Warrant

                                FORM OF EXERCISE

               (To be executed by the registered holder hereof)

                  The undersigned registered owner of this Warrant irrevocably
exercises this Warrant for the purchase of [the number of] [ ] Stock Units of
RUTHERFORD-MORAN OIL CORPORATION, a Delaware company, and herewith makes payment
there for, all at the price and on the terms and conditions specified in this
Warrant, and requests that certificates for the shares of Common Stock be issued
in accordance with the instructions given below, and, if such Stock Units shall
not include all of the Stock Units to which the Holder is entitled under this
Warrant, that a new Warrant of like tenor and date for the unpurchased balance
of the Stock Units issuable hereunder be delivered to the undersigned.


Dated: 
      ---------------------    

                                       -----------------------------------------
                                       (Signature of Registered Holder)


Instructions for issuance and 
registration of Common Stock:


---------------------------------------
Name of Registered Holder
(please print)


Social Security or Other Identifying
Number: 
       ------------------------------


Please deliver certificate to the following address:


---------------------------------------
             Street


---------------------------------------
      City, State and Zip Code


                                     Warrant


<PAGE>   66



                                                                         Annex 2
                                                                              to
                                                               Warrant Agreement


                               FORM OF ASSIGNMENT


               (To be executed by the registered holder hereof)


                  FOR VALUE RECEIVED the undersigned registered owner of this
Warrant hereby sells, assigns and transfers unto the assignee named below all
the rights of the undersigned under this Warrant with respect to the number of
shares of Warrant Stock covered thereby set forth hereinbelow unto:


                                                                       Number of
Shares
Name of Assignee                Address                                of Common
Stock            ---------------------------------------------------------------



Dated:
      ------------------------    



                                    -------------------------------------------
                                    Signature of Registered Holder



                                    -------------------------------------------
                                    Name of Registered Holder
                                    (Please Print)


Witness:



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






                                     Warrant


<PAGE>   67

                                                                      Annex 3 to
                                                               Warrant Agreement


           Investor                            Number of Warrants
           --------                            ------------------

           The Chase Manhattan Bank                 133,333*


           Banque Paribas                            66,667*












* If The Chase Manhattan Bank ("Chase") has taken an assignment of any of Banque
Paribas's Commitment under the Credit Agreement, the additional number of
Warrants to be issued to Chase shall equal the amount of the Commitment assigned
by Banque Paribas to Chase divided by $150,000,000 multiplied by 200,000 and the
number of Warrants to be issued to Banque Paribas shall be reduced by the
additional Warrants to be issued to Chase; provided the foregoing shall not
reduce the 133,333 Warrants to be issued to Chase.



                                     Warrant