<PAGE>
                                                                    EXHIBIT 10.1


                       THIRD AMENDMENT TO CREDIT AGREEMENT


         This Third Amendment to Credit Agreement (this "THIRD AMENDMENT") is
executed as of March 19, 2004 (the "EFFECTIVE DATE"), by and among Encore
Acquisition Company, a Delaware corporation ("BORROWER"), Encore Operating,
L.P., a Texas limited partnership ("OPERATING"), Fleet National Bank, a national
banking association, as Administrative Agent ("ADMINISTRATIVE AGENT"), and the
financial institutions a party hereto as Banks ("EXECUTING BANKS").

                                   WITNESSETH:

         WHEREAS, Borrower, Operating, Administrative Agent, the other Agents
party thereto and Banks are parties to that certain Credit Agreement dated as of
June 25, 2002 (as amended by (a) that certain First Amendment to Credit
Agreement dated as of October 31, 2002, and (b) that certain Second Amendment to
Credit Agreement dated as of October 21, 2003, the "CREDIT AGREEMENT") (unless
otherwise defined herein, all terms used herein with their initial letter
capitalized shall have the meaning given such terms in the Credit Agreement);
and

         WHEREAS, pursuant to the Credit Agreement, Banks have made a revolving
credit loan to Borrower; and

         WHEREAS, Borrower and Operating have requested that Banks amend and
waive certain terms of the Credit Agreement in certain respects; and

         WHEREAS, subject to the terms and conditions set forth herein,
Executing Banks have agreed to Borrower's and Operating's requests.

         NOW THEREFORE, for and in consideration of the mutual covenants and
agreements herein contained and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged and confessed,
Borrower, Operating, Administrative Agent and each Executing Bank hereby agree
as follows:

         SECTION 1. AMENDMENTS. In reliance on the representations, warranties,
covenants and agreements contained in this Third Amendment, and subject to the
satisfaction of the conditions precedent set forth in Section 3 hereof, the
Credit Agreement is hereby amended effective as of the Effective Date in the
manner provided in this Section 1.

         1.1. AMENDMENT TO DEFINITIONS. The definitions of "LOAN PAPERS" and
"PERMITTED SUBORDINATE DEBT" contained in Section 1.1 of the Credit Agreement
shall be amended to read in full as follows:

                  "LOAN PAPERS" means this Agreement, the First Amendment, the
         Second Amendment, the Third Amendment, the Notes, the Mortgages, each
         Borrower Pledge Agreement, each Subsidiary Pledge Agreement, each
         Facility Guaranty, and all other certificates, documents or instruments
         delivered in connection with this Agreement, as the foregoing may be
         amended from time to time.



                                       1
<PAGE>



                  "PERMITTED SUBORDINATE DEBT" means, collectively, (a) Debt of
         Borrower resulting from the issue of Borrower's 8.375% Senior
         Subordinated Notes Due 2012 in an aggregate outstanding principal
         balance of $150,000,000 (the "Original Issuance"), and which (1) is
         fully subordinated to the Obligations pursuant to subordination
         provisions which have been previously approved by Required Banks, and
         (2) is not subject to negative covenants or events of default (or other
         provisions which have the same effect as negative covenants or events
         of default) which have not been previously approved by Required Banks,
         and (b) Debt of Borrower resulting from the issue of Borrower's senior
         subordinated unsecured notes in an aggregate outstanding principal
         balance of not greater than $150,000,000 (the "New Issuance"), and
         which (1) is fully subordinated to the Obligations to the same extent
         set forth in the Original Issuance, unless otherwise approved by
         Required Banks, (2) is not subject to negative covenants or events of
         default (or other provisions which have the same effect as negative
         covenants or events of default) which are more restrictive on Borrower
         than those set forth in the Original Issuance, unless otherwise
         approved by Required Banks, and (3) does not have a coupon rate in
         excess of, or maturity date prior to, the coupon rate and maturity
         date, respectively, relative to the Original Issuance.

         SECTION 2. AGREEMENT AND WAIVER. In reliance on the representations,
warranties, covenants and agreements contained in this Third Amendment, and
subject to the satisfaction of the conditions precedent set forth in Section 3
hereof, Executing Banks hereby agree that a Special Mandatory Redemption (as
defined in the New Issuance Documents) will not be a Default or Event of Default
under Section 10.2 or Section 12.1(f) of the Credit Agreement. The waiver herein
granted is a one-time waiver limited in all respects to a Special Mandatory
Redemption pursuant to the terms of the New Issuance Documents. Nothing
contained herein shall obligate any Bank to grant any waiver of, or consent to
the deviation from, any other provision of the Credit Agreement or any other
Loan Paper.

         SECTION 3. CONDITIONS PRECEDENT. The effectiveness of the amendments
contained in Section 1 hereof, and the agreement and waiver contained in Section
2 hereof, is subject to the satisfaction of each of the following conditions
precedent:

         3.1. NO DEFAULT. No Default or Event of Default shall have occurred
which is continuing.

         3.2. ISSUANCE OF PERMITTED SUBORDINATE DEBT. Administrative Agent shall
have received, reviewed and approved (in its reasonable discretion) a true and
correct copy of each material document, instrument and agreement (the "New
Issuance Documents") relating to the New Issuance, together with a certificate
from an Authorized Officer of Borrower certifying that (1) such copies are
accurate and complete and represent the complete understanding and agreement of
the parties thereto, (2) no material right or obligation of any party to any of
the New Issuance Documents has been modified, amended or waived, and (3) the New
Issuance has been consummated in accordance with the terms set forth in the New
Issuance Documents and the proceeds thereof have been received into escrow into
accordance with the terms of the New Issuance Documents.

         3.3. OTHER FEES. Borrower shall have paid to Administrative Agent any
fees payable to Administrative Agent or any Affiliate of Administrative Agent
pursuant to this Third



                                       2
<PAGE>



Amendment and any separate agreement among Borrower, Operating, Administrative
Agent or any Affiliate of Administrative Agent in consideration for providing
services in connection with the credit facilities provided by the Credit
Agreement.

         3.4. OTHER DOCUMENTS. Administrative Agent shall have been provided
with such other documents, instruments and agreements, and Borrower and
Operating shall have taken such actions, as Administrative Agent may reasonably
require in connection with this Third Amendment and the transactions
contemplated hereby.

         SECTION 4. REPRESENTATIONS AND WARRANTIES OF BORROWER AND OPERATING. To
induce Executing Banks and Administrative Agent to enter into this Third
Amendment, Borrower and Operating hereby jointly and severally represent and
warrant to Banks and Administrative Agent as follows:

         4.1. REAFFIRM EXISTING REPRESENTATIONS AND WARRANTIES. Each
representation and warranty of each Credit Party contained in the Credit
Agreement and the other Loan Papers is true and correct on the date hereof and
will be true and correct immediately after giving effect to the amendments set
forth in Section 1 hereof and the agreement and waiver set forth in Section 2
hereof, or, if such representations and warranties are expressly limited to
particular dates, as of such particular dates.

         4.2. DUE AUTHORIZATION: NO CONFLICT. The execution, delivery and
performance by Borrower and Operating of this Third Amendment are within
Borrower's and Operating's corporate and partnership powers (as applicable),
have been duly authorized by all necessary action, require no action by or in
respect of, or filing with, any governmental body, agency or official and do not
violate or constitute a default under any provision of applicable law or any
Material Agreement binding upon Borrower, Operating or any other Credit Party or
result in the creation or imposition of any Lien upon any of the assets of any
Credit Party except Permitted Encumbrances.

         4.3. VALIDITY AND ENFORCEABILITY: EXTENSION OF LIENS. This Third
Amendment constitutes the valid and binding obligation of Borrower and Operating
enforceable in accordance with its terms, except as (i) the enforceability
thereof may be limited by bankruptcy, insolvency or similar laws affecting
creditor's rights generally, and (ii) the availability of equitable remedies may
be limited by equitable principles of general application.

         4.4. NO DEFAULT OR EVENT OF DEFAULT. No Default or Event of Default has
occurred which is continuing.

         SECTION 5. MISCELLANEOUS.

         5.1. REAFFIRMATION OF LOAN PAPERS. Any and all of the terms and
provisions of the Credit Agreement and the Loan Papers shall, except as amended
and modified hereby, remain in full force and effect. The amendments
contemplated hereby shall not limit or impair any Liens securing the
Obligations, each of which are hereby ratified, affirmed and extended to secure
the Obligations as they may be modified pursuant hereto.



                                       3
<PAGE>



         5.2. PARTIES IN INTEREST. All of the terms and provisions of this Third
Amendment shall bind and inure to the benefit of the parties hereto and their
respective successors and assigns.

         5.3. LEGAL EXPENSES. Borrower hereby agrees to pay on demand all
reasonable fees and expenses of counsel to Administrative Agent incurred by
Administrative Agent in connection with the preparation, negotiation and
execution of this Third Amendment and all related documents.

         5.4. COUNTERPARTS. This Third Amendment may be executed in
counterparts, and all parties need not execute the same counterpart; however, no
party shall be bound by this Third Amendment until Borrower, Operating and
Required Banks have executed a counterpart. Facsimiles shall be effective as
originals.

         5.5. COMPLETE AGREEMENT. THIS THIRD AMENDMENT, THE CREDIT AGREEMENT AND
THE OTHER LOAN PAPERS REPRESENT THE FINAL AGREEMENT AMONG THE PARTIES AND MAY
NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR ORAL AGREEMENTS OF
THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN OR AMONG THE
PARTIES.

         5.6. HEADINGS. The headings, captions and arrangements used in this
Third Amendment are, unless specified otherwise, for convenience only and shall
not be deemed to limit, amplify or modify the terms of this Third Amendment, nor
affect the meaning thereof.

         5.7. EFFECTIVENESS. This Third Amendment shall be effective
automatically and without necessity of any further action by Borrower,
Operating, Administrative Agent or Banks when counterparts hereof have been
executed by Borrower, Operating and Required Banks, and all conditions to the
effectiveness hereof set forth herein have been satisfied.

         IN WITNESS WHEREOF, the parties hereto have caused this Third Amendment
to be duly executed by their respective Authorized Officers on the date and year
first above written.


                           [Signature pages to follow]






                                       4
<PAGE>
                                 SIGNATURE PAGE
                                       TO
                       THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO


BORROWER:

ENCORE ACQUISITION COMPANY,
a Delaware corporation

By:    /s/ RANI M. WAINWRIGHT
       -----------------------
Name:  Rani M. Wainwright
       -----------------------
Title: Assistant Treasurer
       -----------------------

OPERATING:

ENCORE OPERATING, L.P.,
a Texas limited partnership

By:    EAP Operating, Inc.,
       a Delaware corporation,
       its sole general partner

       By:    /s/ RANI M. WAINWRIGHT
              -----------------------
       Name:  Rani M. Wainwright
              -----------------------
       Title: Assistant Treasurer
              -----------------------


                                [Signature Page]
<PAGE>
                                 SIGNATURE PAGE
                                       TO
                       THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO


ADMINISTRATIVE AGENT:

FLEET NATIONAL BANK,
a Administrative Agent:

By:    /s/ JEFFERY H. RATHKAMP
       ------------------------
       Jeffery H. Rathkamp,
       Director

BANK:

FLEET NATIONAL BANK,
as a Bank

By:    /s/ JEFFERY H. RATHKAMP
       -------------------------
       Jeffery H. Rathkamp,
       Director




                                [Signature Page]


<PAGE>
                                 SIGNATURE PAGE
                                       TO
                       THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO


BANK:

WACHOVIA BANK, N.A.


By:    /s/ DAVID HUMPHREYS
       -------------------------
Name:  David Humphreys
       -------------------------
Title: Director
       -------------------------



                                [Signature Page]
<PAGE>
                                 SIGNATURE PAGE
                                       TO
                       THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO


BANK:

FORTIS CAPITAL CORP.

By:    /s/ ILLEGIBLE
       ------------------------
Name:  ILLEGIBLE
       ------------------------
Title: ILLEGIBLE
       -----------------------


By:    /s/ ILLEGIBLE
       ------------------------
Name:  ILLEGIBLE
       ------------------------
Title: Senior Vice President
       -----------------------


                                [Signature Page]


<PAGE>
                                 SIGNATURE PAGE
                                       TO
                       THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO


BANK:

BNP PARIBAS

By:    /s/ DAVID DODD
       ------------------------
Name:  David Dodd
       ------------------------
Title: Director
       -----------------------


By:    /s/ POLLY SCHOTT
       ------------------------
Name:  Polly Schott
       ------------------------
Title: Vice President
       -----------------------


                                [Signature Page]


<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO


BANK:

THE FROST NATIONAL BANK

By:    /s/ JOHN S. WARREN
       ------------------------
Name:  John S. Warren
       ------------------------
Title: Senior Vice President
       -----------------------






                                [Signature Page]


<PAGE>


                                 SIGNATURE PAGE
                                       TO
                       THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO


BANK:


CREDIT SUISSE FIRST BOSTON,
CAYMAN ISLANDS BRANCH


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


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


                                [Signature Page]


<PAGE>

                                 SIGNATURE PAGE
                                       TO
                       THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                           ENCORE ACQUISITION COMPANY,
                             ENCORE OPERATING, L.P.,
                  FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO


BANK:

COMERICA BANK

By:    /s/ V. MARK FUQUA
       ------------------------------------
Name:  V. Mark Fuqua
       ------------------------------------
Title: Senior Vice President-Texas Division
       ------------------------------------




                                [Signature Page]



<PAGE>
                                 SIGNATURE PAGE
                                       TO
                      THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                          ENCORE ACQUISITION COMPANY,
                            ENCORE OPERATING, L.P.,
                 FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO



BANK:

UNION BANK OF CALIFORNIA, N.A.

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


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



                                [Signature Page]


<PAGE>


                                 SIGNATURE PAGE
                                       TO
                      THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                          ENCORE ACQUISITION COMPANY,
                            ENCORE OPERATING, L.P.,
                 FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO



BANK:

CREDIT LYONNAIS NEW YORK BRANCH

By: /s/ OLIVIER AUDEMARD
   -------------------------------
Name: Olivier Audemard
     -----------------------------
Title: Senior Vice President
      ----------------------------



                                [Signature Page]

<PAGE>


                                 SIGNATURE PAGE
                                       TO
                      THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                          ENCORE ACQUISITION COMPANY,
                            ENCORE OPERATING, L.P.,
                 FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO



BANK:

COMPASS BANK

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



                                [Signature Page]

<PAGE>


                                 SIGNATURE PAGE
                                       TO
                      THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                          ENCORE ACQUISITION COMPANY,
                            ENCORE OPERATING, L.P.,
                 FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO



BANK:

SUNTRUST BANK

By: /s/ JAMES M. WARREN
   -------------------------------
Name: JAMES M. WARREN
     -----------------------------
Title: DIRECTOR
      ----------------------------



                                [Signature Page]

<PAGE>


                                 SIGNATURE PAGE
                                       TO
                      THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                          ENCORE ACQUISITION COMPANY,
                            ENCORE OPERATING, L.P.,
                 FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO



BANK:

RZB FINANCE LLC

By: /s/ ASTRID WILKE
   -------------------------------
Name: ASTRID WILKE
     -----------------------------
Title: VICE PRESIDENT
      ----------------------------


By: /s/ JUAN M. CSILLAGI
   -------------------------------
Name: JUAN M. CSILLAGI
     -----------------------------
Title: GROUP VICE PRESIDENT
      ----------------------------



                                [Signature Page]


<PAGE>

                                 SIGNATURE PAGE
                                       TO
                      THIRD AMENDMENT TO CREDIT AGREEMENT
                                  BY AND AMONG
                          ENCORE ACQUISITION COMPANY,
                            ENCORE OPERATING, L.P.,
                 FLEET NATIONAL BANK, AS ADMINISTRATIVE AGENT,
                          AND THE BANKS A PARTY THERETO



BANK:

BANK OF SCOTLAND

By: /s/ JOSEPH FRATUS
   -------------------------------
Name: JOSEPH FRATUS
     -----------------------------
Title: FIRST VICE PRESIDENT
      ----------------------------



                                [Signature Page]