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                                                                    EXHIBIT
                                                                            ----

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                                ESCROW AGREEMENT


                                      among


                        RUTHERFORD-MORAN OIL CORPORATION

                                       and


                            THE CHASE MANHATTAN BANK


                                       and



                    CHASE BANK OF TEXAS, NATIONAL ASSOCIATION


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


                         Dated as of September 28, 1998


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







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                                ESCROW AGREEMENT


                  Escrow Agreement (the "Agreement"), dated as of September 28,
1998, among Rutherford-Moran Oil Corporation, a Delaware corporation (the
"Company"), The Chase Manhattan Bank, a New York banking corporation ("Chase"),
and Chase Bank of Texas, National Association, as escrow agent (the "Escrow
Agent").


                                    RECITALS

                  WHEREAS, the Company, Chase as Administrative Agent, and the
lenders party thereto (the "Lenders") have entered into a Second Amended and
Restated Credit Agreement dated as of September 28, 1998 (the "Credit
Agreement") pursuant to which the Lenders have agreed to lend the Company up to
$200,000,000, subject to the terms and conditions set forth in the Credit
Agreement.

                  WHEREAS, pursuant to Section 7.1(k) of the Credit Agreement,
it is a condition to each Lender's obligation to make loans under the Credit
Agreement that: (i) this Escrow Agreement shall have been executed and delivered
by each of the parties hereto, (ii) the Company shall have executed the Warrant
Agreement (as defined below) and (iii) the Company shall have executed and
delivered to the Escrow Agent fully executed and authenticated Warrants to be
held pursuant to this Agreement.

                  WHEREAS, pursuant to Section 7.1(k) of the Credit Agreement,
the Company has agreed to authorize, execute and deliver Warrants to the Escrow
Agent on the date hereof.


                                    AGREEMENT

                  NOW, THEREFORE, the parties hereto agree as follows:

                           1.       Definitions. Capitalized terms used
herein without definition have the meanings assigned to them in the Credit
Agreement, or if not defined therein, in the Warrant Agreement. The terms set
forth below have the following meanings:

                  "Authorized Officer" shall mean, (x) with respect to the
Company, the President or chief financial officer and (y) with respect to Chase,
any vice president or more senior officer.

                  "Deferral Certificate" shall mean a certificate from an
Authorized Officer of each of the Company and Chase to the effect that a
Purchase and Sale Agreement has been executed.

                  "Distribution Date" shall have the meaning assigned to such
term in Section 3(a) hereof.



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                  "Termination Certificate" shall mean a certificate from an
Authorized Officer of each of the Company and Chase to the effect that the
closing has occurred pursuant to the Purchase and Sale Agreement.

                  "Warrant" and "Warrants" shall mean the warrants issued by the
Company pursuant to the Warrant Agreement, evidencing rights to purchase up to
an aggregate of 2,561,400 Stock Units (which represents 10% 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.

                  "Warrant Agreement" shall mean the Warrant Agreement dated as
of September 28, 1998 among the Company and Chase, as the same may be amended
and modified in accordance with its terms.


                           2.       Delivery of Escrow Securities.

                           (a)      On the date hereof, the Company shall
deliver, or cause to be delivered to the Escrow Agent (i) an original of the
Warrant Agreement, executed by the Company and Chase, and (ii) three duly
authorized and executed Warrants, registered in the name of Chase, or in such
other names as directed by Chase, pursuant to Section 2.02 of the Warrant
Agreement, representing Warrants to purchase 2,305,260 Stock Units (as such
amount of shares may be adjusted from time to time in accordance with the
Warrant Agreement), representing 9% of the Common Stock of the Company on a
fully-diluted basis as contemplated by the Warrant Agreement.

                           (b)      The Warrants delivered to the Escrow Agent
pursuant to this Escrow Agreement shall be held in escrow and released therefrom
on the terms and conditions set forth herein.

                           Receipt of the Warrant Agreement and Warrants shall
be confirmed by the Escrow Agent as soon as practical by account statement, and
any discrepancies in any such account statement shall be noted by the Company
and Chase to the Escrow Agent within 30 calendar days after receipt thereof.

                           3.       Release of Warrants.

                           (a)      Unless the Escrow Agent has received a
Termination Certificate or a Deferral Certificate prior to such date, Warrants
shall be released from escrow and delivered to or at the direction of Chase, at
the address specified in Section 10 below (or such other address as Chase shall
specify in writing), without any action or notice by Chase or the Company to the
Escrow Agent, in the following amounts and on the following dates (each such
date, a "Distribution Date"):



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                           (i)      11.1111%, rounded to the nearest dollar,
                                    (representing 256,140 Stock Units as of the
                                    date hereof) of the Warrants originally
                                    delivered to the Escrow Agent, on November
                                    2, 1998;

                          (ii)      33.3333%, rounded to the nearest dollar,
                                    (representing 768,420 Stock Units as of the
                                    date hereof) of the Warrants originally
                                    delivered to the Escrow Agent, on November
                                    30, 1998; provided that if Chase receives
                                    any Warrants on November 30, 1998, and a
                                    Deferral Certificate is received by the
                                    Escrow Agent on such date or if a closing
                                    under the Purchase and Sale Agreement occurs
                                    on or prior to such date, Chase shall return
                                    any Warrants received on November 30, 1998
                                    from the Escrow Agent pursuant to this
                                    Escrow Agreement to the Escrow Agent; and

                         (iii)      all of the remaining Warrants held by the
                                    Escrow Agent, on December 31, 1998.

                           (b)      If the Escrow Agent receives a Deferral
Certificate at any time that it is holding any of the Warrants in escrow, it
shall not distribute any Warrants to Chase or any other Person until December
31, 1998; provided that if the Escrow Agent has not received a Deferral
Certificate the Business Day prior to a Distribution Date, the Escrow Agent
shall release the Warrants scheduled to be released from Escrow on such
Distribution Date. If the Escrow Agent has not received a Termination
Certificate prior to December 31, 1998, on December 31, 1998, the Escrow Agent
shall deliver all Warrants held by it to Chase at the address specified in
Section 10 below (or at such other address as Chase shall specify in writing);
provided that if Chase receives any Warrants on December 31, 1998 and a closing
under the Purchase and Sale Agreement occurs on or has occurred prior to such
date, Chase shall return any Warrants received on December 31, 1998 from the
Escrow Agent pursuant to this Escrow Agreement to the Company.

                           (c)      If at any time prior to December 31, 1998,
the Escrow Agent receives a Termination Certificate, the Escrow Agent shall
promptly deliver to the Company all Warrants at such time held by the Escrow
Agent.

                           (d)      The Company will provide, or cause to be
provided, to the Escrow Agent all such information as the Escrow Agent may from
time to time reasonably request.

                           (e)      Upon release of all of the Warrants from
escrow and the termination of this Escrow Agreement, the Escrow Agent shall
destroy the Warrant Agreement.

                  4.       Responsibility of the Escrow Agent. The Company and
Chase appoint and designate the Escrow Agent as escrow agent for the purposes
set forth herein, and the Escrow Agent owes no duty to any other person or
entity by reason of this Escrow Agreement. The Escrow Agent accepts the duties
expressly set forth in this Escrow Agreement and undertakes to perform only such
duties relating thereto as are specifically set forth herein. The



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parties hereto agree that the following terms and conditions shall govern and
control with respect to the rights, duties, liabilities and immunities of the
Escrow Agent hereunder.

                  (a)      The duties and obligations of the Escrow Agent shall
be determined solely by the express provisions of this Escrow Agreement, and no
implied covenants, duties or obligations (including, without limitation, any
duty to solicit the delivery of any Warrants) shall be read into this Escrow
Agreement against the Escrow Agent, nor shall it have, or be deemed to have, any
duties or responsibilities under the provisions of any other agreements
(including without limitation the Warrant Agreement) between the other parties
hereto or any other Person.

                  (b)      The Escrow Agent shall not be liable for any error of
judgment, or any action taken, suffered or omitted by it in good faith, or
mistake of fact or law, or for anything it may do or refrain from doing in
connection herewith or therewith, except its own gross negligence or willful
misconduct.

                  (c)      The Escrow Agent may rely and shall be authorized and
protected in acting or refraining from acting in good faith in reliance upon any
written instruction, communication, notice, request, resolution, direction,
certificate, statement, approval, appraisal, promissory note, share or warrant
certificate or other paper or document, not only as to its due execution and the
validity and effectiveness of its provision, but also as to the truth of any
information therein contained, which it in good faith believes to be genuine and
to have been presented by the proper party.

                  (d)      The Escrow Agent may consult with counsel, auditors
and other experts of its own choice and any opinion or advice of counsel or of
such auditors or other experts shall be full and complete authorization and
protection with respect to any action taken or suffered or omitted by the Escrow
Agent hereunder in good faith and in accordance with such opinion or advice of
counsel or of such auditors or other experts within the area of their respective
expertise.

                  (e)      The Escrow Agent may execute any of its powers or
responsibilities hereunder and exercise any rights hereunder either directly or
by or through its agents or attorneys.

                  (f)      The Escrow Agent shall not be responsible for and
shall not be under a duty to examine or pass upon, the validity, binding effect,
execution or sufficiency of this Escrow Agreement, the Warrants or of any
agreement amendatory or supplemental hereto or thereto or the absence or
presence of any liens or encumbrances on the property held in escrow hereunder.

                  (g)      The Escrow Agent shall be under no duty to prepare,
conduct or monitor any filing, recording or registration, re-filing,
re-recording or re-registration of this Escrow Agreement or of any agreement
amendatory hereof or of any instrument or assignment, conveyance or further
assurance, or to pay any taxes, fees or charges in connection therewith, or to
give any notice with respect thereto or to pay, inquire into or prepare, conduct
or monitor the payment of, or be under any duty in respect of or arising out of,
any tax or assessment or other governmental charge which may be levied or
assessed on the property held in escrow hereunder



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or any part thereof or any confiscation of such property. No property held in
escrow by the Escrow Agent hereunder shall be subject to any set-off,
counterclaim, recoupment or other right which the Escrow Agent may have against
any of the parties hereto (except with respect to any payments to be made to the
Escrow Agent hereunder) or against any other Person for any reason whatsoever.

                  (h)      If any controversy arises between the parties hereto
or with any third person with respect to the subject matter of the escrow
described herein, the Escrow Agent shall not be required to determine the
outcome of same or take any action in the premises, but may await the settlement
of any such controversy by final appropriate legal proceedings or otherwise as
the Escrow Agent may require, notwithstanding instructions to the contrary, and
in such event the Escrow Agent shall not be liable for interest or damages,
except that the Escrow Agent shall not deliver the Securities held in escrow
hereunder in any manner other than in accordance with Section 3 hereof, except
in accordance with a final unappealable order of a court of competent
jurisdiction.

                  (i)      If the Escrow Agent shall be uncertain as to its
duties or rights hereunder or shall receive instructions, claims or demands from
any party hereto which, in its opinion, conflict with any of the provisions of
this Escrow Agreement, it shall be entitled to refrain from taking any action
and its sole obligation shall be to keep safely all property held in escrow
until it shall be redirected otherwise in writing by all of the other parties
hereto or by a final order or judgment of a court of competent jurisdiction.

                  (j)      Without limiting and in furtherance of the foregoing,
the Escrow Agent shall not be liable or responsible for any of the provisions of
the Warrants except for those expressly referred to herein.

                  (k)      The Escrow Agent shall be responsible for holding and
disbursing the Warrants and Warrant Agreement pursuant to this Escrow Agreement;
provided, however, that in no event shall the Escrow Agent be liable for any
lost profits, lost savings or other special, exemplary, consequential or
incidental damages in excess of the Escrow Agent's fees hereunder (other than
due to the Escrow Agent's gross negligence or willful misconduct) and provided
further, that the Escrow Agent shall have no liability for any loss arising from
any cause beyond its control, including, but not limited to, the following: (a)
acts of God, force majeure, including, without limitation, war (whether or not
declared or existing), revolution, insurrection, riot, civil commotion,
accident, fire, explosion, stoppage of labor, strikes and other differences with
employees; (b) the act, failure or neglect of any of the Company and Chase or
any agent or correspondent or any other person selected by the Escrow Agent; (c)
any delay, error, omission or default of any mail, courier, telegraph, cable or
wireless agency or operator; or (d) the acts or edicts of any government or
governmental agency or other group or entity exercising governmental powers.

                  5.       Qualifications. The Escrow Agent shall at all times
be Chase Bank of Texas, National Association, or a bank, trust company or
corporation in good standing organized and doing business under the laws of the
United States of America or a State of the United



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States, and having combined capital and surplus of not less than one hundred
million dollars ($100,000,000). If the Escrow Agent shall at any time cease to
have the foregoing qualifications, the Escrow Agent shall resign within 30 days
thereafter, such resignation to become effective as provided in Section 6
hereof.

                  6.       Removal and Resignation. The Escrow Agent and any
successor Escrow Agent may at any time be removed at the written direction of
the Company and Chase. The Escrow Agent or any successor Escrow Agent may at any
time resign and be discharged of its obligations hereunder by giving written
notice to the Company and Chase specifying the date upon which it desires that
such resignation shall take effect. Such removal or resignation shall take
effect on the date specified in the notice of removal or resignation, which date
shall not be earlier than 30 days after the giving of the notice of removal or
resignation unless previously a successor Escrow Agent shall have been appointed
pursuant to Section 7 hereof and shall have accepted such appointment, in which
event such removal or resignation shall take effect immediately upon the
acceptance by such successor Escrow Agent. The Company agrees to take prompt
steps to have a successor Escrow Agent appointed in the manner hereinafter
provided.

                  7.       Appointment of Successor Agent. If at any time the
Escrow Agent shall resign or be removed or otherwise become incapable of acting
or if at any time a vacancy shall occur in the office of the Escrow Agent for
any other cause, a successor Escrow Agent (duly qualified as provided in Section
5 above) shall be appointed by the Company with the consent of Chase by an
instrument in writing delivered to the Escrow Agent within the time specified
below. Upon delivery of said instrument to and acceptance of said instrument by
the successor Escrow Agent, the resignation or removal of the Escrow Agent shall
become effective and such successor Escrow Agent shall become vested with all
the rights, powers, duties and obligations of its predecessor hereunder. If no
successor Escrow Agent shall have been appointed at the effective date of
resignation or within 30 days of a notice of removal, the Escrow Agent or any
other party hereto may petition a court of competent jurisdiction for the
appointment of a successor.

                  8.       Compensation, Reimbursement and Indemnification of
Escrow Agent. The Escrow Agent shall be entitled to compensation from the
Company in accordance with the Escrow Agent's fee schedule in effect from time
to time including reimbursement from the Company for all reasonable expenses,
disbursements, advances and liabilities incurred or made by the Escrow Agent
hereunder (including the reasonable compensation, expenses and disbursements of
the Escrow Agent's agents and counsel).

                  The Company agrees to indemnify the Escrow Agent for, and to
hold it harmless from and against, any loss, liability, claims, actions, damages
or expenses (including reasonable expenses and disbursements of its agents and
counsel) incurred without gross negligence or bad faith on the part of the
Escrow Agent arising out of or in connection with its entering into this Escrow
Agreement and carrying out its duties hereunder, including the costs and
expenses of defending itself against any claim or liability in the premises.



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                  9.       Termination. This Escrow Agreement shall terminate on
the later of (x) the receipt by the Escrow Agent of a Termination Certificate
and the delivery by the Escrow Agent to the Company of any Warrants at such time
held by the Escrow Agent and (y) the date on or following December 31, 1998 on
which the Escrow Agent has delivered to or at the direction of Chase all
Warrants at such time held by the Escrow Agent. The indemnity provision in
Section 8 hereof shall survive the termination of this Escrow Agreement.

                  10.      Notices. Except as otherwise expressly provided
herein, all demands, notices, consents, requests and other documents authorized
or required to be given to any party to this Escrow Agreement shall be given in
writing and either personally served on an officer of such party or mailed by
registered or certified first class mail, postage prepaid or sent by telecopy,

                  (i)  if to the Company:
                           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 Chase:
                           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

                  (iii)    if to the Escrow Agent
                           Chase Bank of Texas, National Association
                           600 Travis Street, Suite 1150
                           Houston, Texas  77002-8086
                           Attention: May Ng
                           Telephone No.: 713-216-6467
                           Fax No.: 713-216-6927


or, at such other address or telecopy number as shall be designated by such
party in a notice to the other parties hereto.

                  (b)      All such notices, requests and other communications
shall be effective upon receipt.



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                  11.      Amendments, Etc. Except as otherwise expressly
provided in this Agreement, any provision of this Escrow Agreement may be
amended or modified only by an instrument in writing signed by each of the
parties

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


                  13.      Governing Law. THIS ESCROW 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.


                  14.      Waiver of Jury Trial. EACH OF THE COMPANY, CHASE AND
THE ESCROW AGENT HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY
APPLICABLE LAW, ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING
ARISING OUT OF OR RELATING TO THIS ESCROW AGREEMENT OR THE TRANSACTIONS
CONTEMPLATED HEREBY.

                  15.      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.

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

                  17.      Counterparts. This Escrow Agreement may be executed
in any number of counterparts, each of which shall be an original, but such
counterparts shall together constitute but one and the same instrument.

                  18.      No Waiver. No course of dealing, nor any delay on the
part of any party hereto in exercising any rights hereunder, or any failure to
exercise the same, shall operate as a waiver of such or any other rights.

                  19.      Descriptive Headings. The descriptive headings of the
several sections of this Escrow Agreement are inserted for convenience only and
do not constitute a part of this Escrow Agreement.



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                  IN WITNESS WHEREOF, the parties hereto have caused this Escrow
Agreement to be duly executed by their respective authorized officers, as of the
date first above written.

                                       RUTHERFORD-MORAN OIL CORPORATION

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

                                       THE CHASE MANHATTAN BANK


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

                                       CHASE BANK OF TEXAS, NATIONAL ASSOCIATION
                                       as Escrow Agent


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