<PAGE>   1
                        CERTIFICATE OF SECOND AMENDMENT
                                       TO
                       CERTIFICATE OF LIMITED PARTNERSHIP
                                       OF
                      MEWBOURNE ENERGY PARTNERS 97-A, L.P.


         The Certificate of Second Amendment to Certificate of Limited
Partnership of MEWBOURNE ENERGY PARTNERS 97-A, L.P. (the "Partnership") is
being executed and filed by the undersigned general partners under the Delaware
Revised Uniform Limited Partnership Act.

                                  ARTICLE ONE

         In order to reflect the assignment and withdrawal by certain general
   partners of their General Partner Interest in the Partnership and the
   substitution of their respective transferees as a substituted General Partner
   in the Partnership, Exhibit A to the Certificate of Limited Partnership of
   the Partnership, as previously amended by that certain Certificate of
   Amendment to Certificate of Limited Partnership dated November 7, 1997, is
   hereby deleted and such Exhibit A is hereby restated as set forth in Exhibit
   A hereto.


                                  ARTICLE TWO

   Article Four of the Certificate of Limited Partnership of the Partnership is
hereby amended in its entirety to read as follows:

         The name and business address of the managing general partner of the
   Partnership is Mewbourne Development Corporation, 3901 S. Broadway, Tyler,
   Texas 75701.  The names of the investor general partners admitted to the
   Partnership are set forth on Exhibit A hereto.  The business address of the
   investor general partners is 3901 S.  Broadway, Tyler, Texas 75701.

   IN WITNESS WHEREOF, the undersigned, the Managing Partner by and
through a duly authorized officer thereof acting for itself and as
attorney-in-fact for each of the General Partners set forth on Exhibit A has
executed this Certificate of Amendment to Certificate of Limited Partnership on
this 23rd day of December, 1997.

                        MEWBOURNE DEVELOPMENT CORPORATION,
                        acting for itself and as attorney-in-fact for each of 
                        the General Partners as set forth on Exhibit A


                        By:     /s/ J. Roe Buckley                            
                           ---------------------------------------------------
                                J. Roe Buckley, Treasurer
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                                   EXHIBIT A
                            GENERAL PARTNER INTEREST

                         MEWBOURNE ENERGY PARTNERS 97-A



Billy J. & Val Joyce Adams

John R. Amrien, M.D.

Howard L. Baker Jr. Trust
Albert D. Ballance

Dale W. & Lillian R. Beebee

L. Walter, Jr. & Joan B. Benjamin

Doris M. Bishop
Herman & Anne K. Blackman

Blackman Family Trust
James E. & Virginia M. Blackman, Trustees

Frederick W. Bode

Thomas C. Bode
Michael F. & Mary Ann Bond

Mark J. Bowman

William L. & Nancy H. Brach

Ivor E. & Delores Bridge
Anne J. Britt

Brook Family Trust
Arthur H. & Mary P. Brook, Trustees

Eric B. & Ann G. Brown

Esther L. Bucher
Greg & Molly Bunton

J. Millard & Diane Burr

Esther Calcaterra Trust
Esther Calcaterra, Trustee
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Carroll E. Caldwell Trust
Carroll E. Caldwell, Trustee

Mary M. Caldwell Trust
Mary M. Caldwell, Trustee

John E. Cameron, Jr.
L. Robert Castorr

Miriam M. Chang & Arthur W. Donoho

Philip W. Chao

Marcella H. Cleary Trust
Marcella H. Cleary, Trustee
John T. & Mary J. Coffey

Donald W. Cohen

Linda S. Cohen

Conrad Family Trust
William D. & Eloise D. Conrad, Trustees
Clare Crawford-Mason

R. Russell Darby

Greg D. Davis

Del-Kijaico, Inc.
Anthony J. & Rosina Disalvo

Carlo J. Disalvo Trust
Carlo J. Disalvo, Trustee

Timothy R. & Nancy L. Dorlac

Donald J. Dorr
Mary Lou Doyle

The Engle Trust
Charles V. & Marjorie C. Engle, Trustees

Sigo Falk
Louis E. Fettig Rev. Trust
Louis E. Fettig, Trustee

Dr. George Figacz Trust
Dr. George Figacz, Trustee
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Robert S. Fishman Trust
Richard C. Freedman & Michele Fishman, Trustees

Mary M. Flauaus Rev. Living Trust
Mary M. Wurtz, Trustee

Francus Family Ltd. Partnership
Cyril Francus General Partner
Norman G. Frank

Stephen J. Fukayama

Edward Gilbert

Dorothy I. Goggio Trust
Dorothy I. Goggio, Trustee
Leonard & Margaret Goggio

Lawrence S. & Jolande E. Goldberg

Vivian F. Goode

Anne R. Gregg Rev. Trust
Anne R. Gregg, Trustee
Walter E. Gregg Rev. Trust
Walter E. Gregg, Trustee

Alice Griffey Rev. Living Trust
Alice Griffey, Trustee

David L. & Diane M. Grubbs

Joan M. Gruebner Trust
Herman W. Gruebner, Trustee
George E. & Judy Guttschalk

Farzana S. Habib

Don E. & Gloria F. Hamrick

Timothy A. Harrison Revocable Trust
Timothy A. Harrison, Trustee
Donald G. Heth Revocable Trust
Donald G. Heth, Trustee

Elaine M. & Phillip Heverin

Floyd & Alice Ho
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Larue A. & Amy M. Hoffman Family Trust
Amy M. Hoffman, Trustee

Holbrook Family Trust
Joseph C. & Martha S. Holbrook, Trustees

Rett & Jeanne Humke
Larry S. & Beverly Humphries

Barbara G. Johnson

Larry A. Jones

Jodi P. & Jessica L. Kane
David K. Kennedy

Kevin P. Kertz

Rose Mary Kinder Rev. Living Trust

William L. Kraus III
Dennis L. Krause

Richard D. Lind Trust
Richard D. Lind, Trustee

Edward G. Lippitt

Albert L., Jr. & Barbara A. Lock
Susan M. Longust Trust

Rose Lorie Trust
Richard A. Bishop, Trustee

Robert B. & Susan G. McKimens

C. Robert Meloni
John G. Mergner, Sr.

Ralph W. Minard Trust
Ralph W. Minard, Trustee

Nancy Thompson Minnich
Lois A. Minto Rev. Living Trust
Lois A. Minto, Trustee

C. W. Moore

Robert E. Mortensen
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Mothershead Family Trust
Theodore & Beaty Mothershead, Trustees

John C. & Mildred Estes New

Robert E. O'Neill

Linda J. Ochenrider

Loretta A. Perry

Danial L. & Robbie L. Rose-Poel

Patricia H. Polinsky

Charles H. Powers

Katherine Rallo Trust
Katherine Rallo, Trustee

Rita A. Relyea

The Richards Family Trust
Jeanette A. Richards, Trustee

David P. Robinson

Marilyn D. Rodell Trust
Marilyn D. Rodell, Trustee

Fred L. Romantine

Lance D. & Carmen E. Samuelson

Thomas P. & Rachel M. Schneider

Judy L. Schreiber & Loren R. Mosher

David R. & Jan Schroeder

James Burton Shaw

Tina R. Sigman Trust

John T. Skehan

James C. Smith, Jr. Trust
James C. Smith, Jr., Trustee

R. Curtis, Jr.  & Anne V. Steele

Ronald W. & Mary Jane Steele

Carol H. Straus

Mary A. Suchan Rev. Living Trust
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Gladyce Sumida

Jesse L. & Charlene A. Szwargulski Trust
Jesse L. & Charlene A. Szwargulski, Trustees

George S. & Susan D. Templeton
Thompson Revocable Living Trust
Cary J. & Linda L. Thompson, Trustees

The Thompson Family Trust
Virgil R. Thompson, Trustee

Gary R. Todd

Thomas M. & Barbara A. Tuggle
Ka Khy Tze

Barbara Waldman

Wamhoff Revocable Trust
Robert E. & Diane F. Wamhoff, Trustees

Weiland Family Trust
Barbara Waldman, Trustee
Gary S. & Patricia J. Wilson

Dennis P. Yarnell

Maria A. Zettler Trust
Maria A. Zettler, Trustee
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                                   EXHIBIT B

                            LIMITED PARTNER INTEREST

                         MEWBOURNE ENERGY PARTNERS 97-A


Elizabeth C. O. Bellaver

William F. Ferguson, Jr.

Helen F. Grim

John E. Gusto Trust
John E. Gusto, Trustee

C. Russell & Anita D. Johnson

Johnson Loving Trust
Susan G. Johnson, Trustee

Thomas Michael & Anne L. Knasel

Wilfred Mendez

Charles W. Rannells, III

Marian M. Reagan

Josephine L. Smith

Josephine L. Smith Trust B
Josephine L. Smith, Trustee

Russell F. & Laurie A. Warren