<PAGE>
 
                                                                    EXHIBIT 4.19



                            INTERCREDITOR AGREEMENT

                                     among

                          United Meridian Corporation,

                           UMC Petroleum Corporation,
                             Norfolk Holdings Inc.,
                           UMC Resources Canada Ltd.,
                        UMIC Cote d'Ivoire Corporation,
                       UMC Equatorial Guinea Corporation,

                           The Chase Manhattan Bank,
                 as Administrative Agent and Collateral Agent,

                   Morgan Guaranty Trust Company of New York,
                             as Syndication Agent,

                           NationsBank of Texas, N.A.
                                      and
                               Societe Generale,
                            as Documentation Agents,

                                Banque Paribas,
                            Wells Fargo Bank, N.A.,
                                      and
                            Colorado National Bank,
                                 as Co-Agents,

                      The Chase Manhattan Bank of Canada,
                               as Canadian Agent,

                                      and

                 The Lenders Now or Hereafter Signatory Hereto


                                 March 18, 1997
<PAGE>
 
                               TABLE OF CONTENTS
                               -----------------

                                  Article I 
                                  Definitions

     Section 1.01  Definitions............................................   2
     Section 1.02  Incorporation of U.S. Credit Agreement Definitions.....   3

                                  Article II 
                            Application of Proceeds

     Section 2.01    Election to Pursue Remedies..........................   3
     Section 2.02    Duty of the Collateral Agent.........................   4
     Section 2.03    Application of Proceeds..............................   5
     Section 2.04    Payments by Collateral Agent.........................   5
     Section 2.05    Notices under Related Documents......................   5
     Section 2.06    Amendments...........................................   5
     Section 2.07    Pro Rata Treatment...................................   6
     Section 2.08    Voting Procedure.....................................   6
     Section 2.09    Triggering Event.....................................   6
     Section 2.10    Bankruptcy Preferences...............................   6
     Section 2.11    Property of Obligors.................................   6
     Section 2.12    Marshalling..........................................   7
     Section 2.13    Lender Dealings; Good Faith..........................   7

                                 Article III 
                          Calculation of Indebtedness

     Section 3.01    Notice of Amount of Indebtedness.....................   7
     Section 3.02    Escrow Account.......................................   7
     Section 3.03    Handling of Escrow Account...........................   8
     Section 3.04    Currency Conversion..................................   8

                                  Article IV 
                             The Collateral Agent

     Section 4.01    Appointment of Collateral Agent......................   8
     Section 4.02    Nature of Duties of Collateral Agent.................   9
     Section 4.03    Lack of Reliance on the Collateral Agent.............   9
     Section 4.04    Certain Rights of the Collateral Agent...............  10
     Section 4.05    Reliance by Collateral Agent.........................  10
     Section 4.06    Collateral Agent's Reimbursements and Indemnification  10
     Section 4.07    The Collateral Agent in its Individual Capacity......  11
     Section 4.08    Creditors as Owners..................................  11
 
                                       i
<PAGE>
 
     Section 4.09    Successor Collateral Agent...........................  11
     Section 4.10    Employment of Collateral Agent and Counsel...........  11
     Section 4.11    Independent Action...................................  12

                                  ARTICLE V 
                                 Miscellaneous

     Section 5.01    Authority............................................  12
     Section 5.02    Termination..........................................  12
     Section 5.03    Notices, etc.........................................  12
     Section 5.04    Payment of Expenses, Indemnities, etc................  12
     Section 5.05    Applicable Law.......................................  12
     Section 5.06    Entire Agreement.....................................  13
     Section 5.07    Execution in Counterparts............................  13
     Section 5.08    Amendment of Defined Instruments.....................  13
     Section 5.09    References and Titles................................  13
     Section 5.10    Severability.........................................  13
     Section 5.11    Authority............................................  13
     Section 5.12    Conflict with Loan Documents.........................  13
     Section 5.13    Limitation by Law....................................  13
     Section 5.14    Benefit of Agreement; Limitation on Assignment.......  13

                                      ii
<PAGE>
 
                            INTERCREDITOR AGREEMENT
                            -----------------------

     THIS INTERCREDITOR AGREEMENT dated as of March 18, 1997 (this "Agreement"),
is among: United Meridian Corporation, a corporation duly organized and validly
existing under the laws of the state of Delaware ("United Meridian"); UMC
Petroleum Corporation, a corporation duly organized and validly existing under
the laws of the state of Delaware (the "Company"); Norfolk Holdings Inc., a
corporation duly organized and validly existing under the laws of the state of
Delaware  ("Norfolk"); UMC Resources Canada Ltd., a company continued under the
laws of the Province of British Columbia ("UMC Canada"); UMIC Cote d'Ivoire
Corporation, a corporation duly organized and validly existing under the laws of
the state of Delaware ("UMC-CI-11"); UMC Equatorial Guinea Corporation, a
corporation duly organized and validly existing under the laws of the state of
Delaware ("UMC-EG-B"); each of the other Persons now or hereafter signatory
hereto as an Obligor; each of the financial institutions that is now or
hereafter a signatory hereto (individually, a "U.S. Lender" and, collectively,
the "U.S. Lenders"); The Chase Manhattan Bank, as administrative agent for the
U.S. Lenders (in such capacity, the "Administrative Agent") and as Collateral
Agent for the Lender Group, Morgan Guaranty Trust Company of New York, as
syndication agent for the U.S. Lenders (in such capacity, the "Syndication
Agent"), NationsBank of Texas, N.A. and Societe Generale, as documentation
agents for the U.S. Lenders (in such capacity, the "Documentation Agents"), and
Banque Paribas, Wells Fargo Bank, N.A., and Colorado National Bank, as co-agents
for the U.S. Lenders (in such capacity, the "Co-Agents"), The Chase Manhattan
Bank of Canada ("Chase Canada"), as agent for the Canadian Lenders (in such
capacity, the "Canadian Agent"), each of the lenders now or hereafter signatory
to the Canadian Credit Agreement (collectively, the "Canadian Lenders").

                                    Recitals

     A.   On the date of this Intercreditor Agreement, United Meridian, as
guarantor, the Company, the Administrative Agent, the Syndication Agent, the
Documentation Agents, the Co-Agents (the Administrative Agent, the Documentation
Agent and the Co-Agents collectively being the "U.S. Agents"), and the U.S.
Lenders are entering into that certain Global Credit Agreement (as the same is
from time to time supplemented, amended, restated, extended, or increased herein
called the "U.S. Credit Agreement").

     B.   On the date of this Intercreditor Agreement, UMC Canada, the Canadian
Agent, and the Canadian Lenders are entering into that certain Credit Agreement
(as the same is from time to time supplemented, amended, restated, extended, or
increased herein called the "Canadian Credit Agreement").

     C.   To secure, inter alia, the U.S. Indebtedness of the Company under the
U.S. Credit Agreement and the Canadian Indebtedness of UMC Canada under the
Canadian Credit Agreement (collectively, the "Credit Agreements") and the other
obligations of the Obligors under the Security Instruments, the Obligors will
execute and deliver the Security Instruments.

     D.   The U.S. Lenders and the Canadian Lenders (collectively, the
"Lenders") and the U.S. Agents and the Canadian Agent (collectively, the
"Agents"; and the Collateral Agent, the Lenders and

                                       1
<PAGE>
 
the Agents collectively being the "Lender Group") are entering into this
Intercreditor Agreement to establish their relative rights with respect to
payment of their respective Indebtedness owed by the Obligors, to agree as to
the exercise of certain remedies and to appoint The Chase Manhattan Bank as
collateral agent for the purposes of dealing with the Security Instruments and
apportioning payments among the Lenders and for other purposes as set forth
herein.

     E.   The execution and delivery of this Intercreditor Agreement is a
condition to the performance by each Lender of its obligations under the Credit
Agreement to which it is a party.

     F.   NOW, THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged and to induce the U.S. Agents and
the U.S. Lenders to enter into the U.S. Credit Agreement and the Canadian Agent
and the Canadian Lenders to enter into the Canadian Credit Agreement, the
parties hereto hereby agree as follows:

                                   Article I
                                  Definitions

     Section 1.01   Definitions.  The terms defined in the recitals shall have
the meanings assigned to those terms in such recitals, and the following terms
shall have the meanings assigned as follows:

     "Acceptance Exposure" means, at any time, the aggregate face amount of all
Bankers Acceptances outstanding at such time for which UMC Canada has not yet
reimbursed the Canadian Lenders which have accepted such Bankers Acceptance
pursuant to the terms of the Canadian Credit Agreement.

     "Balance" shall have the meaning assigned such term in Section 3.03.

     "Business Day" shall mean any day excluding Saturday, Sunday and any other
day on which banks are required or authorized to close in New York City or
Toronto.

     "Canadian Indebtedness" shall mean the Indebtedness (as defined in the
Canadian Credit Agreement) and shall include the aggregate Acceptance Exposure.

     "Canadian Lender Notes" shall mean the Notes issued to the Canadian Lenders
under the Canadian Credit Agreement.

     "Collateral Agent" shall mean The Chase Manhattan Bank in such capacity,
together with all successors in such capacity under the terms of this
Intercreditor Agreement.

     "Commitments" shall mean the sum of the Aggregate Commitments of the U.S.
Lenders under the U.S. Credit Agreement and the Aggregate Commitments of the
Canadian Lenders under the Canadian Credit Agreement.

     "Contingent Indebtedness" shall have the meaning assigned such term in
Section 3.03.

     "Conversion Ratio" shall have the meaning assigned such term in Section
3.04.

     "Escrow Account" shall have the meaning assigned such term in Section 3.02.

                                       2
<PAGE>
 
     "Group" shall mean the U.S. Lenders, as a group of Lenders, or the Canadian
Lenders, as a group of Lenders, as the case may be.

     "Guarantors" shall mean each Person who now or hereafter guarantees the
U.S. Indebtedness and/or the Canadian Indebtedness.

     "Guaranty Agreements" shall mean the Guaranty Agreements guarantying
payment of the U.S. Indebtedness and the Guaranty Agreements guarantying payment
of the Canadian Indebtedness.

     "Indebtedness" shall mean all U.S. Indebtedness and Canadian Indebtedness,
including, but not limited to, all other sums of money which may be hereafter
paid or advanced by the Agents or the Lenders under the terms and provisions of
this Intercreditor Agreement or the other Security Instruments as such sums of
money relate either to the administration, protection and exercise of remedies
in connection with this Intercreditor Agreement or the Security Instruments, or
to any reimbursement and indemnity provisions contained in this Intercreditor
Agreement and the Security Instruments.

     "Issuing Bank" shall mean, for each of the Letters of Credit, the issuer of
such Letter of Credit.

     "Notes" shall mean the U.S. Lender Notes and the Canadian Lender Notes.

     "Obligors" shall mean the Company, UMC Canada and the Guarantors.

     "Pro Rata Share" shall mean as to each holder of any of the Indebtedness
the percentage that the Indebtedness held by such holder represents of all
Indebtedness.

     "Proceeds" shall mean all cash proceeds and other Property received by the
Collateral Agent or any of the Lenders from or for the account of any Obligor,
from whatever source.

     "Triggering Event" shall have the meaning assigned such term in Section
2.09.

     "U.S. $ Amount" shall have the meaning assigned such term in Section 3.04.

     "U.S. Indebtedness" shall mean the Indebtedness, including but not limited
to, the amount of the LC Exposure which is not at such time a part of the fixed
Indebtedness.

     "U.S. Lender Notes" shall mean the Notes issued to the U.S. Lenders under
the U.S. Credit Agreement.

     Section 1.02   Incorporation of U.S. Credit Agreement Definitions.
Capitalized terms not defined herein shall have the meaning assigned such terms
in the U.S. Credit Agreement.

                                       3
<PAGE>
 
                                 Article II
                            Application of Proceeds

          Section 2.01  Election to Pursue Remedies.

          (a) Upon the occurrence and during the continuance of any Triggering
Event, the Collateral Agent shall, subject to Section 2.02 and Article IV, take
or, as appropriate, direct the appropriate trustee or agent to take any and all
actions provided for in the Security Instruments relating to the pursuit of
remedies, including the foreclosure or disposition of collateral only if such
actions are authorized as provided in this Section 2.01.

          (b) Upon the occurrence and during the continuance of any Triggering
Event, the Lenders shall vote on whether or not to pursue any remedy or remedies
available to them at law or otherwise, including whether or not to foreclose on
or dispose of collateral, if any.  If the Required Lenders at such time vote to
pursue any particular remedy or remedies, including foreclosure or disposition
of collateral, instructions specifying the particular action to be taken from
the Required Lenders shall be delivered to the Collateral Agent.  Upon receipt
by the Collateral Agent of such instructions from the Required Lenders, with
indemnities appropriate for such instructions as provided in Section 4.04, the
Collateral Agent shall immediately commence to take or direct the instructed
actions (and continue to take such actions) relating such remedies.

          (c) Without regard to the occurrence of a Triggering Event, upon the
written instruction of the Required Lenders, with indemnities appropriate for
such instructions as provided in Section 4.04, the Collateral Agent shall (i)
take or direct any action provided for in the Security Instruments (other than
foreclosure or disposition of the collateral) or proceed to enforce, or direct
the enforcement of, consistent with the Security Instruments and applicable law
(other than foreclosure or disposition of the collateral), the rights or powers
provided in the Security Instruments and under applicable law for the benefit of
the Lender Group and shall give such notice or direction or shall take such
action or exercise such right or power hereunder or under any of the Security
Instruments incidental thereto as shall be reasonably specified in such
instructions and consistent with the terms of the Security Instruments and this
Intercreditor Agreement; and/or (ii) execute such instruments or agreements or
take such other action in connection with the Security Instruments as may be
deemed reasonably necessary or appropriate by the Required Lenders and
consistent with the terms of the Security Instruments and this Intercreditor
Agreement.  Such action may include, but is not limited to (x) the giving of any
notice, approval, consent or waiver which may be called for under the Security
Instruments, (y) the requiring of the execution and delivery of additional
Security Instruments, or (z) employing agents or directing trustees in order to
accomplish the actions requested.

          (d) Nothing in this Section 2.01 shall impair the right of a Lender to
exercise its rights of set-off existing at law or under the Credit Agreements,
but in any event, subject to the terms thereof.

          Section 2.02  Duty of the Collateral Agent.

          (a) The Collateral Agent shall not be obligated to follow any
instructions of any one or more of the Lenders if: (i) such instructions
conflict with the provisions of this Intercreditor Agreement or any other
Security Instrument or any law or (ii) the Collateral Agent has not been
adequately indemnified to its satisfaction.  Nothing in this Article II shall
impair the right of the Collateral Agent in its discretion to take any action,
to the extent that the consent of any of the Lenders is not required or to the
extent

                                       4
<PAGE>
 
such action is not prohibited by the terms hereof, which it deems proper and
consistent with the instructions given by the Lenders as provided for herein.
In the absence of written instructions, containing the appropriate indemnities,
from the Lenders or Required Lenders as appropriate for any particular matter,
the Collateral Agent shall have no duty to take or refrain from taking any
action unless such action or inaction is explicitly required by the terms of
this Intercreditor Agreement.

          (b) Beyond its duties expressly provided herein or in any Security
Instrument and its duties to account to the Lender Group and/or the Obligors for
monies and other Property received by it hereunder or under any Security
Instrument, the Collateral Agent shall not have any implied duty to the Lender
Group or any Obligor as to any Property belonging to an Obligor (whether or not
the same constitutes collateral) in its possession or control or in the
possession or control of any of its agents or nominees, or any income thereon or
as to the preservation of rights against prior parties or any other rights
pertaining thereto.

          Section 2.03  Application of Proceeds.

          (a) Upon the occurrence and during the continuance of a Triggering
Event, all Proceeds shall be applied as follows and in accordance with Section
3.03:

          (i) First, to the pro rata payment of costs and expenses reasonably
incurred by the Collateral Agent, the Agents or any other Lender in connection
with any action taken or proceeding brought, including reasonable legal expenses
and attorneys' fees, and of all Taxes (other than Excluded Taxes) or
assessments.

          (ii) Second, any Balance remaining shall be applied to repay the
Indebtedness or held in escrow as specified in Section 3.03.

          (iii)  Finally, the payment of surplus proceeds, if any, to any Person
that may be lawfully entitled to receive the same, including without limitation,
an Obligor, and in the order of priority specified for by any Governmental
Requirement.

          (b) At any time other than after the occurrence and during continuance
of a Triggering Event, payments made to the Lenders may be applied as provided
in the Credit Agreements.

          Section 2.04  Payments by Collateral Agent.  All payments by the
Collateral Agent hereunder shall be delivered to the administrative agents under
the Credit Agreements for distribution in the manner set forth therein.

          Section 2.05  Notices under Related Documents.  The Collateral Agent
shall deliver to each Lender promptly upon receipt thereof, duplicates or copies
of all material notices, requests and other instruments received by the
Collateral Agent under or pursuant to this Intercreditor Agreement or any
Security Instrument, to the extent that the same shall not have been previously
furnished to such Lender pursuant hereto or thereto.  Promptly upon obtaining
such knowledge, each Lender agrees: (a) to deliver to the Collateral Agent, at
the same time it makes delivery to the Obligors, a copy of any notice of
default, notice of intent to accelerate or notice of acceleration with respect
to the Indebtedness subject to this Intercreditor Agreement; (b) to deliver to
the Collateral Agent, at the same time it makes delivery to any other Person, a
copy of any notice of the commencement of any judicial proceeding and a copy of
any other notice with respect to the exercise of remedies with respect to the
Indebtedness subject to

                                       5
<PAGE>
 
this Intercreditor Agreement.  The Collateral Agent agrees to deliver to each
Lender any notice or other communication received by it from any Lender pursuant
to clause (a) or (b) of this Section 2.05.

          Section 2.06  Amendments.  Amendments, modifications, supplements,
waivers, consents and approvals of or in connection with this Intercreditor
Agreement or any other Security Instrument (other than the Credit Agreements)
may be effectuated only upon the written consent of the Required Lenders  (and,
if the rights or duties of the Collateral Agent and the Agents or any Obligors
are affected thereby, by the Collateral Agent and the Agents or the applicable
Obligor, as the case may be).  Amendments, modifications, supplements, waivers,
consents and approvals of or in connection with the Credit Agreements shall be
effectuated only in accordance with the terms contained therein.

          Section 2.07  Pro Rata Treatment.  The Lenders hereby agree among
themselves that (a) prior to the occurrence and continuance of a Triggering
Event, each Lender shall be entitled to receive and retain for its own account
scheduled payments or voluntary prepayments of principal, interest, fees and
premium, if any, all in compliance with the Credit Agreements, and (b) after the
occurrence and during the continuance of a Triggering Event, all Proceeds shall
be applied by the Collateral Agent and shared by Lenders in accordance with the
respective Pro Rata Share held by each of them and in accordance with Section
2.03(a).  In the event that any Lender shall obtain payment after the occurrence
and during the continuance of a Triggering Event, whether in whole or in part,
from any source in respect of its portion of the Indebtedness, including without
limitation payments by reason of the exercise of its right of offset, banker's
lien, general lien or counterclaim, such Lender shall promptly pay to the
Collateral Agent such amount for application in accordance with Section 2.03(a).

          Section 2.08  Voting Procedure.  Notwithstanding anything to the
contrary herein, in the Credit Agreements or in any other Security Instrument,
the Lenders agree that for purposes of any provision hereof or thereof that
requires a vote of the Required Lenders, each Lender shall have the right to
vote independently of the other Lenders in its Group.  When this Intercreditor
Agreement requires a vote of the Required Lenders, the Collateral Agent shall
poll the Lenders in order to determine the vote of the Required Lenders (and
such vote shall be binding upon the Lenders who are not among the Required
Lenders).  The Obligors and the Lender Group may rely on the Collateral Agent
with regard to any such vote without any duty of further inquiry.

          Section 2.09 Triggering Event. The occurrence of any of the following
shall constitute a "Triggering Event":

          (a) The occurrence and continuance of an Event of Default specified in
Sections 10.01(f), (g), and (h) of the U.S. Credit Agreement as it relates to
the Company, any Guarantor or UMC Canada, or

          (b) The Collateral Agent shall have received from either the
Administrative Agent, the Canadian Agent or the Required Lenders, as
appropriate, written advice, which advice shall reference this Section 2.09, (i)
that an Event of Default has occurred and is continuing and (ii) that the unpaid
principal amount of the Notes and all interest accrued and unpaid thereon have
been declared to be then due and payable.

          Section 2.10  Bankruptcy Preferences.  If any payment actually
received by any member of the Lender Group is subsequently invalidated, declared
to be fraudulent or preferential or set aside and is required to be repaid to a
trustee, receiver or any other party under any bankruptcy law, state, provincial

                                       6
<PAGE>
 
or Federal law, common law, or equitable cause, then the Collateral Agent shall
distribute to such Person from the Balance, exclusive of any amount in the
Escrow Account in accordance with Section 3.03, an amount equal to such payment.
If, due to previous disbursements to the Lender Group pursuant to Section
2.03(a), the Balance then held by the Collateral Agent is insufficient for such
purpose, then each other member of the Lender Group shall pay to such Person
upon demand an amount equal to a ratable portion of such payment according to
the aggregate amounts distributed to each member of the Lender Group by the
Collateral Agent.

          Section 2.11  Property of Obligors.  The Lenders agree that all the
provisions of this Intercreditor Agreement shall apply to any and all Properties
and rights of the Obligors or any other Obligor in which the Collateral Agent
(in its capacity as such), any Agent or any Lender at anytime acquires a right
of set-off or Lien, whether pursuant to the Security Instruments, the Credit
Agreements or a judgment, including, without limitation, real property or rights
in, on or over real property, notwithstanding any provision to the contrary in
any mortgage, leasehold mortgage or other document purporting to grant or
perfect any Lien in favor of any Lender, any Agent, or the Collateral Agent.

          Section 2.12  Marshalling.  The Collateral Agent shall not be required
to marshall any present or future security for (including without limitation any
collateral described in any of the Security Instruments), or guaranties of the
Indebtedness or any part or portion thereof, or to resort to such security or
guaranties in any particular order; and all rights in respect of such securities
and guaranties shall be cumulative and in addition to all other rights, however
existing or arising.  To the extent that they lawfully may, each Agent and
Lender hereby agrees that it will not invoke any law relating to the marshalling
of collateral which might cause delay or impede the enforcement of the Lender
Group's rights under the Security Instruments or under any other instrument
evidencing any of the Indebtedness or under which any of the Indebtedness is
outstanding or by which any of the Indebtedness is secured or guaranteed.

          Section 2.13  Lender Dealings; Good Faith.  Nothing contained in this
Intercreditor Agreement shall prevent either Group of Lenders from dealing
directly or negotiating with the other Group for any purpose, including, but not
limited to, the purpose of attempting to reach agreement as to any vote or
proposed vote relating to the Collateral Agent's actions hereunder, whether or
not any Triggering Event or other Default or Event of Default has occurred.
Each U.S. Agent and U.S. Lender covenants and agrees with and for the benefit of
the Canadian Agent and each Canadian Lender, and the Canadian Agent and each
Canadian Lender covenants and agrees with and for the benefit of each U.S. Agent
and U.S. Lender, that it will, in taking any action under this Intercreditor
Agreement or directing the Collateral Agent to exercise any remedy hereunder or
under any other Security Instrument, take such action or make such direction in
good faith and in a commercially reasonable manner and not for the purpose of
hindering, delaying, obstructing or preventing the exercise by the other of its
rights under the Security Instruments.

                                  Article III
                          Calculation of Indebtedness

          Section 3.01  Notice of Amount of Indebtedness.  Upon receipt of any
Proceeds to be distributed pursuant to Section 2.03(a)(ii), the Collateral Agent
shall give the Lenders notice thereof, and each Lender shall within five (5)
Business Days notify the Collateral Agent of the amount of Indebtedness owing to
such Lender.  Such notification shall state the amount of its Indebtedness, how
much is then due and owing, and how much is Contingent Indebtedness.  Each
Lender with Contingent

                                       7
<PAGE>
 
Indebtedness shall describe the status of such Indebtedness.  If requested by
the Collateral Agent, each Lender shall demonstrate that the amounts set forth
in its notice are actually owing to such Lender to the satisfaction of the
Collateral Agent.

          Section 3.02  Escrow Account.  Prior to taking any action to enforce
any Lien or remedy under any Security Instrument, or requesting cash collateral
for the Letters of Credit or Bankers Acceptances, the Collateral Agent shall
open an escrow account (the "Escrow Account") at its banking quarters in New
York, New York (or such other city where any successor may maintain banking
quarters) designated the "United Meridian Collateral Account."

          Section 3.03  Handling of Escrow Account.  Upon each receipt by the
Collateral Agent of Proceeds and after payment therefrom of all items referred
to in Section 2.03(a)(i), remaining Proceeds ("Balance") shall be applied as
provided in this Section 3.03.  If at such time, there exists any Indebtedness
which is contingent in amount, including, without limitation, contingent amounts
of LC Exposure, but not including the Acceptance Exposure (such Indebtedness
being "Contingent Indebtedness"), the Collateral Agent shall (with the
information provided under Section 3.01) determine the amount of all
Indebtedness then outstanding, including, without limitation, Contingent
Indebtedness.  The Balance shall be applied as follows:

          (a) If no Contingent Indebtedness is outstanding, then all such
Balance shall be applied to repay or prepay the amount of the Indebtedness then
outstanding until the Indebtedness shall have been paid in full.

          (b) If there exists Contingent Indebtedness, the Collateral Agent
shall (i) deposit in the Escrow Account a portion of such Balance equal to the
Contingent Indebtedness divided by total Indebtedness (until such time as the
amount on deposit in the Escrow Account equals the maximum amount of the
Contingent Indebtedness), and (ii) apply the remaining Balance to repay or
prepay the amount of the Indebtedness then outstanding until the Indebtedness
shall have been paid in full.  Thereafter, any further remaining Balance shall
be returned or applied as provided in Section 2.03(a)(iii).

          (c) If at any time Contingent Indebtedness or any part thereof becomes
Indebtedness which is no longer contingent, any funds held in the Escrow Account
up to the amount (or pro rata amount based upon the total amount of remaining
Contingent Indebtedness if the Escrow Amount is less than the amount of the
remaining Contingent Indebtedness) of such Indebtedness which has become fixed
(or pro rata amount based upon the total amount of remaining Contingent
Indebtedness) shall be distributed pro rata to the holders of such previously
Contingent Indebtedness.  If all of the fixed Indebtedness has been paid in full
and the Collateral Agent determines that the amount of monies held in the Escrow
Account exceeds the sum of the Contingent Indebtedness outstanding at such time,
such excess shall be returned or applied as provided in Section 2.03(a)(iii).

          Section 3.04  Currency Conversion.  To the extent that calculations
under this Intercreditor Agreement involve U.S. and Canadian currency (or any
other currency), the Collateral Agent shall, at the time of such calculation,
determine all amounts based on U.S. dollars, using a conversion ratio (the
"Conversion Ratio") determined by it in good faith (the "U.S. $ Amount").   The
amount of distributions of a Lender's Pro Rata Share shall be based upon the
U.S. $ Amount, but in the case of a Canadian Lender shall be distributed in and
converted to a Canadian dollar amount calculated by using the Conversion Ratio.

                                       8
<PAGE>
 
                                  Article IV
                             The Collateral Agent

          Section 4.01  Appointment of Collateral Agent.  Each Lender hereby
designates The Chase Manhattan Bank to act as the collateral agent for the
Lenders with respect to the collateral pledge under any of the Security
Instruments, the enforcement of the Liens granted thereunder and the collection
of Proceeds following the disposition of any such collateral.  Each Lender
hereby authorizes the Collateral Agent to designate The Chase Manhattan Bank of
Canada to act as the agent for the Collateral Agent on behalf of the Lenders
with respect to the Canadian assets under the Security Instruments.  Each Lender
hereby authorizes the Collateral Agent to take such action on its behalf under
the provisions of this Intercreditor Agreement and the Security Instruments and
to exercise such powers and to perform such duties hereunder and thereunder as
are specifically delegated to either The Chase Manhattan Bank, as Administrative
Agent, or The Chase Manhattan Bank of Canada, as Canadian Agent, or required of
the Collateral Agent by the terms hereof and such other powers as are reasonably
incidental thereto.  The Collateral Agent may perform any of its duties
hereunder by or through its agents or employees.  The Collateral Agent agrees to
act as Collateral Agent upon the express terms and conditions contained in this
Article IV.

          Section 4.02  Nature of Duties of Collateral Agent.  The Collateral
Agent shall have no duties or responsibilities, except those expressly set forth
in this Intercreditor Agreement or any Security Instrument.  The Collateral
Agent shall have and may exercise such powers hereunder and under the Security
Instruments as are specifically delegated to the Collateral Agent by the terms
hereof or to either The Chase Manhattan Bank, as Administrative Agent, or The
Chase Manhattan Bank of Canada, as Canadian Agent thereunder, together with such
powers as are reasonably incidental thereto.  Neither the Collateral Agent nor
any of its directors, officers, employees or agents shall be liable to the
Lenders for any action taken or omitted by it as such hereunder or under the
Security Instruments, unless caused solely by its or their gross negligence or
willful misconduct.  The duties of the Collateral Agent shall be mechanical and
administrative in nature; and the Collateral Agent shall not have by reason of
this Intercreditor Agreement a fiduciary relationship in respect of any Lender.
Nothing in this Intercreditor Agreement, expressed or implied, is intended to or
shall be so construed as to impose upon the Collateral Agent any Indebtedness in
respect of this Intercreditor Agreement and the other Security Instruments
except as expressly set forth herein.

          Section 4.03  Lack of Reliance on the Collateral Agent.

          (a) Independently and without reliance upon the Collateral Agent or
any other Lender, each Lender, to the extent it deems appropriate, has made (i)
its own independent investigation of the financial condition and affairs of the
Obligors based on such documents and information as it has deemed appropriate in
connection with the taking or not taking of any action in connection herewith,
and (ii) its own appraisal of the credit worthiness of the Obligors.  Each
Lender also acknowledges that it will, independently and without reliance upon
the Collateral Agent or any other Person and based on such documents and
information as it shall deem appropriate at the time, continue to make its own
credit decisions in taking or not taking action under this Intercreditor
Agreement, the Indebtedness or the Security Instruments.  Except as expressly
provided in this Intercreditor Agreement and the other Security Instruments, the
Collateral Agent shall have no duty or responsibility, either initially or on a
continuing basis, to provide any Lender with any credit or other information
concerning the affairs, financial condition or business of the Obligors or any
of United Meridian's Subsidiaries which may come into the possession of the
Collateral Agent or any of its Affiliates whether now in its possession or in

                                       9
<PAGE>
 
its possession at any time or times hereafter; and the Collateral Agent shall
not be required to keep itself informed as to the performance or observance by
any Obligor of this Intercreditor Agreement, any Security Instrument or any
other document referred to or provided for herein or to inspect the Properties
or books of any Obligor.

          (b) The Collateral Agent shall not (i) be responsible to any Lender
for any recitals, statements, information, representations or warranties herein,
in any Security Instrument, or in any document, certificate or other writing
delivered in connection herewith or therewith or for the execution,
effectiveness, genuineness, validity, enforceability, collectability, priority
or sufficiency of this Intercreditor Agreement, the Indebtedness or the Security
Instruments or the financial condition of the Obligors; or (ii) be required to
make any inquiry concerning the performance or observance of any of the terms,
provisions or conditions of this Intercreditor Agreement, the Indebtedness or
the Security Instruments, the financial condition of the Obligors, or the
existence or possible existence of any Default or Event of Default.

          Section 4.04  Certain Rights of the Collateral Agent.  If the
Collateral Agent shall request instructions from the Lenders with respect to any
act or action (including the failure to act) in connection with this
Intercreditor Agreement, the Indebtedness and the Security Instruments, the
Collateral Agent shall be entitled to refrain from such act or taking such
action unless and until the Collateral Agent shall have received instructions
from the Required Lenders pursuant to the terms hereof; and the Collateral Agent
shall not incur liability to any Person by reason of so refraining.  Without
limiting the foregoing, no Lender shall have any right of action whatsoever
against the Collateral Agent as a result of the Collateral Agent acting or
refraining from acting under this Intercreditor Agreement or the Security
Instruments in accordance with the written instructions given in accordance with
this Intercreditor Agreement and such instructions and any action taken or
failure to act pursuant thereto shall be binding on all the Lenders.  Except for
action expressly required of the Collateral Agent pursuant to the terms hereof,
the Collateral Agent shall be fully justified in failing or refusing to take any
action hereunder or under the Security Instruments unless it shall first be
indemnified to its satisfaction by the Obligors or the Lenders against any and
all liability and expense which may be incurred by the Collateral Agent by
reason of taking or continuing to take any such action.  Notwithstanding any
other provision of this Article IV or any indemnity or instructions provided by
any or all of the Lenders, the Collateral Agent shall not be required to take
any action which exposes the Collateral Agent to personal liability or which is
contrary to this Intercreditor Agreement, the Security Instruments or applicable
law.

          Section 4.05  Reliance by Collateral Agent.  The Collateral Agent
shall be entitled to rely, and shall be fully protected in relying, upon any
Note or other instrument evidencing the Indebtedness, writing, resolution,
notice, statement, certificate, telex, teletype or telecopier message,
cablegram, radiogram, order or other documentary, teletransmission or telephone
message believed by it to be genuine and correct and to have been signed, sent
or made by the proper Person.  The Collateral Agent may consult with independent
legal counsel (which shall not be counsel for the Obligors), independent public
accountants and other experts selected by it and shall not be liable for any
action taken or omitted to be taken by it in good faith in accordance with the
advice of such counsel, accountants or experts.

          SECTION 4.06  COLLATERAL AGENT'S REIMBURSEMENTS AND INDEMNIFICATION.
TO THE EXTENT THE COLLATERAL AGENT IS NOT REIMBURSED BY THE COMPANY OR UMC
CANADA, EACH LENDER WILL (WITHOUT DUPLICATION IN THE CASE OF A U.S. LENDER AND
ITS AFFILIATED CANADIAN LENDER) REIMBURSE AND INDEMNIFY THE COLLATERAL AGENT, IN
PROPORTION TO ITS GLOBAL COMMITMENT PERCENTAGE, FOR AND AGAINST ANY AND ALL
INDEMNITY MATTERS WHICH

                                       10
<PAGE>
 
MAY BE IMPOSED ON, INCURRED BY OR ASSERTED AGAINST THE COLLATERAL AGENT IN
PERFORMING ITS DUTIES HEREUNDER OR UNDER ANY SECURITY INSTRUMENT OR OTHERWISE IN
CONNECTION HEREWITH OR THEREWITH, INCLUDING LOSSES OCCURRING FROM THE ORDINARY
AND/OR COMPARATIVE NEGLIGENCE OF THE COLLATERAL AGENT, IN ANY WAY RELATING TO OR
ARISING OUT OF THIS INTERCREDITOR AGREEMENT; PROVIDED THAT NO LENDER SHALL BE
LIABLE FOR ANY PORTION OF SUCH LIABILITIES, INDEBTEDNESS, LOSSES, DAMAGES,
PENALTIES, ACTIONS, JUDGMENTS, SUITS, COSTS, EXPENSES OR DISBURSEMENTS RESULTING
SOLELY FROM THE COLLATERAL AGENT'S GROSS NEGLIGENCE OR WILLFUL MISCONDUCT.

          Section 4.07  The Collateral Agent in its Individual Capacity.    With
respect to its Indebtedness under the Credit Agreements and its Indebtedness,
the Collateral Agent shall have the same rights and powers hereunder as any
other Lender and may exercise the same as though it were not performing the
duties specified herein; and the terms "Lenders", "Required Lenders", or any
similar terms shall, unless the context clearly otherwise indicates, include The
Chase Manhattan Bank (or any successor Collateral Agent), in its individual
capacity as and to the extent it is a holder of any Note or is an Issuing Bank
and not in its capacity as an Agent or as the Collateral Agent.  The Collateral
Agent may accept deposits from, lend money to, and generally engage in any kind
of banking, trust, financial advisory or other business with the Obligors or any
Affiliate of the Obligors as if it were not performing the duties specified
herein, and may accept fees and other consideration from the Obligors for
services in connection with this Intercreditor Agreement and otherwise without
having to account for the same to the Lenders.

          Section 4.08  Creditors as Owners.  The Collateral Agent may deem and
treat each Lender as the owner of such Lender's Indebtedness for all purposes
hereof unless and until the Collateral Agent is notified of a change in Lenders
pursuant to the terms of Section 12.06 of the U.S. Credit Agreement or Section
12.03 of the Canadian Credit Agreement, as applicable.

          Section 4.09  Successor Collateral Agent.

          (a) The Collateral Agent may resign at any time by giving sixty (60)
days prior written notice thereof to the Lender Group, the Company and UMC
Canada and may be removed at any time with cause by the Required Lenders, which
resignation or removal shall be effective upon the appointment of a successor to
the Collateral Agent.  Upon any such resignation or removal, the Required
Lenders shall have the right to appoint a successor Collateral Agent.  If within
thirty (30) days after the retiring Collateral Agent's giving of notice of
resignation or the Required Lenders' removal of the retiring Collateral Agent,
no successor Collateral Agent shall have been so appointed by the Required
Lenders and accepted such appointment, then, the retiring Collateral Agent may,
on behalf of the Lenders, appoint a successor Collateral Agent, which shall be a
bank which maintains an office in the United States of America, or a commercial
bank organized under the laws of the United States of America or of any State
thereof, or any Affiliate of such bank, having a combined capital and surplus of
at least $200,000,000 as of the date of its most recent financial statements.

          (b) Upon the acceptance of any appointment as Collateral Agent
hereunder by a successor Collateral Agent, such successor Collateral Agent shall
thereupon succeed to and become vested with all the rights, powers, privileges
and duties of the retiring Collateral Agent, and the retiring Collateral Agent
shall be discharged from its duties and Indebtedness under this Intercreditor
Agreement.  After any retiring Collateral Agent's resignation or removal
hereunder as Collateral Agent, the provisions of

                                       11
<PAGE>
 
this Intercreditor Agreement shall inure to its benefit as to any actions taken
or omitted to be taken by it while it was Collateral Agent under this
Intercreditor Agreement.

          Section 4.10  Employment of Collateral Agent and Counsel.  The
Collateral Agent may execute any of its duties as Collateral Agent hereunder or
under the Security Instruments by or through employees, agents, and attorneys-
in-fact and shall not be answerable to the Lenders for the default or misconduct
of any such agents or attorneys-in-fact selected by it with reasonable care,
provided that the Collateral Agent shall always be obligated to account for
moneys or securities received by it or its authorized agents. The Collateral
Agent shall be entitled to advice of independent counsel concerning all matters
pertaining to the agency hereby created and its duties hereunder or under the
Security Instruments.

          Section 4.11  Independent Action.  Each Lender agrees that no Lender
or Agent other than the Collateral Agent shall have any right individually to
realize upon the Liens granted by the Security Instruments or to otherwise
enforce or exercise any remedy in respect of the Security Instruments (other
than the right of set-off at law or specified in the Credit Agreements, but in
any event, subject to the terms thereof), it being understood and agreed that
such remedies may be exercised only by the Collateral Agent for the ratable
benefit of the Lender Group.  Each Agent and Lender further agrees that it shall
not individually institute any judicial action pertaining to the Security
Instruments or exercise any other remedy (other than the right of set-off at law
or specified in the Credit Agreements, but in any event, subject to the terms
thereof), pertaining to the Security Instruments, except with the consent of the
Required Lenders.

                                   ARTICLE V
                                 Miscellaneous

          Section 5.01  Authority.  The parties hereto represent and warrant
that they have all requisite power to, and have been duly authorized to, enter
into this Intercreditor Agreement.

          Section 5.02  Termination.  This Intercreditor Agreement shall
terminate upon receipt by the Collateral Agent of evidence satisfactory to it of
(a) the payment (or prepayment) in full of the principal of and the premium, if
any, and interest on all Indebtedness, (b) the termination of the Commitments in
the Credit Agreements, and (c) the termination of the Security Instruments
pursuant to the terms of the Credit Agreements.

          Section 5.03  Notices, etc.  All notices and other communications
hereunder shall be given in writing and shall be given to such Person at its
address or telecopy number as set forth on the signature pages of the Credit
Agreements or such other address or telecopy number such Person may hereafter
specify by notice to the Collateral Agent (who shall promptly notify the
Obligors and the other Lenders).  Each notice or other communication shall be
effective (a) if given by mail, upon receipt, (b) if given by telecopier during
regular business hours, once such telecopy is transmitted to the telecopy number
provided in writing to the Collateral Agent by each Lender and by each Obligor,
respectively, or (c) if given by any other means, upon receipt; provided that
notices to the Collateral Agent are not effective until received.

          SECTION 5.04  PAYMENT OF EXPENSES, INDEMNITIES, ETC.  TO THE FULLEST
EXTENT PERMITTED BY APPLICABLE LAW, THE OBLIGORS SHALL INDEMNIFY THE AGENTS AND
THE LENDERS IN ACCORDANCE WITH THE TERMS OF THE CREDIT AGREEMENTS AND THE
OBLIGORS HEREBY AGREE THAT ALL INDEMNITIES SET FORTH IN THE CREDIT AGREEMENTS
SHALL ALSO RUN IN FAVOR OF THE

                                       12
<PAGE>
 
COLLATERAL AGENT.  IF AND TO THE EXTENT THAT THE INDEBTEDNESS OF THE OBLIGORS
UNDER THIS SECTION 5.04 OR UNDER THE RESPECTIVE INDEMNITY PROVISIONS OF THE
CREDIT AGREEMENTS ARE UNENFORCEABLE FOR ANY REASON, THE OBLIGORS HEREBY AGREE TO
MAKE THE MAXIMUM CONTRIBUTION TO THE PAYMENT AND SATISFACTION OF SUCH
INDEBTEDNESS WHICH IS PERMISSIBLE UNDER APPLICABLE LAW.  THE OBLIGORS'
INDEBTEDNESS UNDER THIS SECTION SHALL SURVIVE ANY TERMINATION OF THIS
INTERCREDITOR AGREEMENT AND THE PAYMENT OF THE INDEBTEDNESS, BUT SHALL TERMINATE
UPON THE TERMINATION OF THE INDEMNITIES CONTAINED IN THE CREDIT AGREEMENTS.

          Section 5.05  Applicable Law.  THIS INTERCREDITOR AGREEMENT
(INCLUDING, BUT NOT LIMITED TO, THE VALIDITY AND ENFORCEABILITY HEREOF AND
THEREOF) SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE
STATE OF NEW YORK.

          Section 5.06  Entire Agreement.  The Notes, this Intercreditor
Agreement and the other Security Instruments embody the entire agreement and
understanding between the Lenders, the Agents and the Obligors and supersede all
prior agreements and understandings between such parties relating to the subject
matter hereof and thereof.  There are no unwritten oral agreements between the
parties.

          Section 5.07  Execution in Counterparts.  This Intercreditor Agreement
may be executed in any number of counterparts, each of which when so executed
shall be deemed to be an original and all of which taken together shall
constitute one and the same agreement.  Any signature page of a counterpart may
be detached therefrom without impairing the legal effect of the signatures
thereon and attached to another counterpart identical in form thereto but having
attached to it one or more additional signature pages signed by other parties.

          Section 5.08   Amendment of Defined Instruments.  Unless the context
otherwise requires or unless otherwise provided herein, the terms defined in
this Intercreditor Agreement which refer to a particular agreement, instrument
or document also refer to and include all renewals, extensions, increases,
modifications, supplements, amendments, and restatements of such agreement,
instrument or document; provided that nothing contained in this section shall be
construed to authorize any such renewal, extension, increases, modification,
supplement, amendment or restatement.

          Section 5.09  References and Titles.  All references in this
Intercreditor Agreement to Schedules, articles, sections, subsections and other
subdivisions refer to the Schedules, articles, sections, subsections and other
subdivisions of this Intercreditor Agreement unless expressly provided
otherwise.  Titles appearing at the beginning of any subdivisions are for
convenience only and do not constitute any part of such subdivisions and shall
be disregarded in construing the language contained in such subdivisions.

          Section 5.10  Severability.  If any term or provision of this
Intercreditor Agreement shall be determined to be illegal or unenforceable, all
other terms and provisions of this Intercreditor Agreement shall nevertheless
remain effective and shall be enforced to the fullest extent permitted by
applicable law.

          Section 5.11  Authority.  The parties hereto represent and warrant
that they have all requisite power to, and have been duly authorized to, enter
into this Agreement.

          Section 5.12  Conflict with Loan Documents.  If there is a conflict
between the terms and provisions contained in the Credit Agreements, the Notes,
any instrument evidencing the Indebtedness or any Security Instrument with the
terms and provisions contained herein, the terms and provisions contained in
this Intercreditor Agreement shall control.

                                       13
<PAGE>
 
          Section 5.13  Limitation by Law.  All rights, remedies and powers
provided herein may be exercised only to the extent that the exercise thereof
does not violate any applicable provision of law; and all the provisions hereof
are intended (a) to be subject to all applicable mandatory provisions of law
which may be controlling and (b) to be limited to the extent necessary so that
they will not render this Intercreditor Agreement or any Security Instrument
invalid under the provisions of any applicable law.

          Section 5.14  Benefit of Agreement; Limitation on Assignment.  The
terms and provisions of this Intercreditor Agreement shall be binding upon and
inure to the benefit of the Agents and each Lender and their respective
successors and assigns.  Except as stated in the last sentence of Section 2.08
hereof, the terms and provisions of this Intercreditor Agreement shall not inure
to the benefit of, nor be relied upon by, the Obligors or their successors or
assigns.  No Lender shall assign, transfer or sell any part of its portion of
the Indebtedness, unless in connection with such assignment, transfer or sale,
such assignee, transferee or purchaser shall first become a party to this
Intercreditor Agreement.

                                       14
<PAGE>
 
          IN WITNESS WHEREOF, the parties have caused their duly authorized
representatives to execute this Intercreditor Agreement as of the date first
above written.

LENDERS AND AGENTS:

                                       THE CHASE MANHATTAN BANK, individually 
                                        and as Administrative Agent


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



                                       MORGAN GUARANTY TRUST COMPANY OF 
                                        NEW YORK, individually and as 
                                        Syndication Agent


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



                                       NATIONSBANK OF TEXAS, N.A., individually
                                        and as Documentation Agent


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



                                       SOCIETE GENERALE, SOUTHWEST AGENCY, 
                                        individually and as Documentation Agent


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

                                       15
<PAGE>
 
                                       BANQUE PARIBAS, individually and as 
                                        Co-Agent


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


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



                                       WELLS FARGO BANK, N.A., individually 
                                        and as Co-Agent


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



                                       COLORADO NATIONAL BANK, individually 
                                        and as Co-Agent


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



                                       THE CHASE MANHATTAN BANK OF CANADA, 
                                        individually and as Canadian Agent


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



                                       SOCIETE GENERALE (CANADA)


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

                                       16
<PAGE>
 
COLLATERAL AGENT:
---------------- 
                                       THE CHASE MANHATTAN BANK, as
                                        Collateral Agent


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

                                       17
<PAGE>
 
The Obligors hereby execute this Intercreditor Agreement to evidence their
agreement that:

     1. The Obligors shall be bound by all of the terms and provisions of this
        Intercreditor Agreement.

     2. The Obligors acknowledge and agree that the terms of this Intercreditor
        Agreement shall control over the terms of the Credit Agreements, the
        Notes, the instruments evidencing the Indebtedness and the Security
        Instruments to the extent of any conflict relating to the relative
        rights of the Agents and the Lenders.

     3. THE INDEMNITY AND REIMBURSEMENT PROVISIONS CONTAINED IN SECTION 5.04
        SHALL APPLY TO ALL MATTERS UNDER THIS INTERCREDITOR AGREEMENT AND THE
        OBLIGORS AGREE TO INDEMNIFY AND REIMBURSE THE COLLATERAL AGENT IN
        ACCORDANCE WITH THE TERMS THEREOF.

     4. Except as stated in the last sentence of Section 2.08 hereof, the terms
        and provisions of this Intercreditor Agreement shall inure solely to the
        benefit of the Agents, each Lender and their respective successors and
        assigns and the terms and provisions of this Intercreditor Agreement
        shall not inure to the benefit of nor be enforceable by the Obligors or
        their successors or assigns. This Intercreditor Agreement may be amended
        as provided herein without the necessity of the Obligors joining in any
        such amendment, provided, that the Obligors shall not be bound by any
        amendment which would have the effect of increasing their Indebtedness
        and indemnities hereunder or materially affecting their rights or duties
        under the Security Instruments unless they shall have consented to such
        amendment.

     5. Each Obligor at its expense will execute, acknowledge and deliver all
        such agreements and instruments and take all such action as the
        Collateral Agent or the Required Lenders from time to time may
        reasonably request in order further to effectuate the purposes of this
        Intercreditor Agreement and to carry out the terms hereof.

                                       18
<PAGE>
 
OBLIGORS:          
--------                                    
                                       UMC PETROLEUM CORPORATION 


                                       By:
                                          --------------------------------
                                          Kevin McMillan
                                          Vice President and Treasurer



                                       UMC RESOURCES CANADA LTD.



                                       By:
                                          --------------------------------
                                          Kevin McMillan
                                          Vice President and Treasurer



                                       UNITED MERIDIAN CORPORATION



                                       By:
                                          --------------------------------
                                          Kevin McMillan
                                          Vice President and Treasurer



                                       NORFOLK HOLDINGS INC.



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


                                       UMIC Cote d'Ivoire Corporation



                                       By:
                                          --------------------------------
                                          Kevin McMillan
                                          Vice President and Treasurer



                                       UMC Equatorial Guinea Corporation



                                       By:
                                          --------------------------------
                                          Kevin McMillan
                                          Vice President and Treasurer

                                       19