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                                                                     EXHIBIT 4.5


                      FIRST AMENDMENT TO WARRANT AGREEMENT
                        AND APPOINTMENT OF WARRANT AGENT


          FIRST AMENDMENT TO WARRANT AGREEMENT AND APPOINTMENT OF WARRANT AGENT
(this "First Amendment"), dated as of March 31, 1997, among BJ SERVICES
COMPANY, a Delaware corporation ("BJ Services"), First Chicago Trust Company of
New York, a New York limited purpose trust company ("First Chicago"), and THE
BANK OF NEW YORK, a New York trust company.

         WHEREAS, BJ Services and First Chicago have heretofore entered into a
Warrant Agreement, dated as of April 13, 1995 (the "Warrant Agreement"),
pursuant to which BJ Services appointed First Chicago and First Chicago agreed
to act, in accordance with the terms and subject to the conditions of the
Warrant Agreement, as agent (the "Warrant Agent") for the issuance, transfer,
exchange and exercise of warrants (the "BJ Warrants") to purchase Common Stock,
par value $0.10 per share, of BJ Services ("BJ Common Stock"); and

         WHEREAS, BJ Services has determined that it is advisable to remove
First Chicago as Warrant Agent and to appoint The Bank of New York as successor
Warrant Agent under the Warrant Agreement; and

         WHEREAS, BJ Services has heretofore provided notice of the removal of
First Chicago as Warrant Agent to First Chicago, to the transfer agent of the
BJ Common Stock and to the holders of the BJ Warrants, in each case in
accordance with the requirements of Section 20 of the Warrant Agreement; and

         WHEREAS, BJ Services, First Chicago and The Bank of New York are
entering into this First Amendment in order to confirm the removal of First
Chicago as Warrant Agent, the appointment of The Bank of New York as successor
Warrant Agent, and the acceptance  by The Bank of New York of such appointment
and of its powers, rights, duties and responsibilities as Warrant Agent as
provided for in the Warrant Agreement;

         NOW, THEREFORE, in consideration of the foregoing premises, and other
good and valuable consideration, the parties hereto agree as follows:


                                   ARTICLE I
                                  APPOINTMENT

         1.1     BJ Services hereby removes First Chicago as Warrant Agent
under the Warrant Agreement, effective at the Effective Time (as defined in
Section 1.2).
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         1.2     BJ Services hereby appoints The Bank of New York as Warrant
Agent under the Warrant Agreement, and The Bank of New York hereby accepts such
appointment, all in accordance with the terms and subject to the conditions of
the Warrant Agreement, and effective as of 5:00 p.m., New York time, on March
31, 1997 (the "Effective Time").


                                   ARTICLE II
                                   AMENDMENTS

         As of the Effective Time, the Warrant Agreement is hereby amended as
follows:

         2.1     First Chicago shall hereby cease to be a party to the Warrant
Agreement.

         2.2     Each reference to the Warrant Agent in the Warrant Agreement
and, as applicable, each exhibit thereto is hereby amended to be a reference to
The Bank of New York.

         2.3     The reference to the "Stockholder Rights Agreement, dated as
of January 12, 1994, as amended, between BJ and First Chicago Trust Company of
New York, as amended (the "Rights Agreement")" in Section 10(e) of the Warrant
Agreement is hereby deleted, and the following is inserted in place thereof:
"Amended and Restated Rights Agreement, dated as of September 26, 1996, as
amended, between BJ and The Bank of New York (as the same may be further
amended from time to time, the "Rights Agreement")."

         2.4     Section 24(b) of the Warrant Agreement is hereby amended to
read as follows:

         "(b)  If to the Warrant Agent, to:

                 The Bank of New York
                 101 Barclay Street (12W)
                 New York, New York  10286

                 Attention: Tenders and Exchange Administration"

         2.5     The form of Warrant Certificate attached as Exhibit 1 to the
Warrant Agreement shall be deleted and replaced in its entirety with the
amended Exhibit 1 that is attached as Annex A to this First Amendment.





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                                  ARTICLE III
                                 MISCELLANEOUS

         3.1     Terms used in this First Amendment without definition shall
have the meanings ascribed to such terms in the Warrant Agreement.

         3.2     This First Amendment may be executed in one or more
counterparts, and by the different parties hereto in separate counterparts,
each of which when executed shall be deemed to be an original but all of which
taken together shall constitute one and the same agreement.

         3.3     Except as expressly amended and modified by the terms of this
First Amendment, the terms and provisions of the Warrant Agreement shall remain
in full force and effect.

         3.4     This First Amendment shall be governed by, and construed in
accordance with, the laws of the State of New York, without giving effect to
the conflicts of laws principles thereof.

                                   * * * * *





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         IN WITNESS WHEREOF, the parties hereto have caused this First
Amendment to be duly executed as of the day first written above by their
respective officers thereunto duly authorized, to be effective as of the
Effective Time.

                                  BJ SERVICES COMPANY


                                  By: /s/  Margaret B. Shannon             
                                     --------------------------------------
                                      Margaret B. Shannon, Vice President

                                  FIRST CHICAGO TRUST COMPANY
                                  OF NEW YORK


                                  By: /s/  Kevin Laurita                   
                                     --------------------------------------
                                      Kevin Laurita, Assistant Vice President

                                  THE BANK OF NEW YORK


                                  By: /s/  John I. Sivertsen               
                                     --------------------------------------
                                      John I. Sivertsen, Vice President