Exhibit 10.88

                                Supplement No. 2
                                       to
                         FIRST PREFERRED FLEET MORTGAGE


  SUPPLEMENT NO. 2 dated  December 20, 1995 ("Supplement No. 2"), by READING
  &  BATES OFFSHORE,  LIMITED, an  Oklahoma  corporation with  its principal
  place  of  business  at  901   Threadneedle,  Houston,  Texas  77079  (the
  "Mortgagor")  to  THE CIT  GROUP/EQUIPMENT  FINANCING, INC.,  a  New  York
  corporation with an office at 1211 Avenue of the Americas, New York, N.Y.,
  10036 (the "Mortgagee").

                              W I T N E S S E T H:

        WHEREAS, the Mortgagor  has executed and delivered to  the Mortgagee
  the First  Preferred Fleet  Mortgage dated  May 25,  1995, as amended  and
  supplemented  by  Supplement  No.  1 dated  July  13,  1995,  (said  First
  Preferred Fleet Mortgage, as amended and supplemented, being herein called
  the "Mortgage" and the terms herein, unless otherwise defined, being  used
  as defined in the Mortgage); and

        WHEREAS, by the Mortgage  the Mortgagor  mortgaged to the  Mortgagee
  the U.S.  flag drilling  rigs  F.G. McCLINTOCK,  Official No.  562059  and
  GEORGE  H. GALLOWAY, Official No.  651646 (as more  fully described in the
  Mortgage),  to secure, among other things, payment of  all amounts due and
  owing under the Loan Agreement dated as of May 25, 1995 and the Note dated
  May 25, 1995; and

        WHEREAS, the Mortgage was recorded on May 25, 1995  at 11:18 a.m. at
  the United States Coast Guard Vessel Documentation  Office at the Port  of
  Houston, Texas, in Book B-95/5, page 491; and

        WHEREAS, Supplement No. 1 was recorded on July 14, 1995 at 1:00 p.m.
  at the United States  Coast Guard Vessel Documentation  Office at the Port
  of Houston, Texas, in Book 95/7, page 136; and

        WHEREAS, pursuant to  Amendment No. 1 to Loan Agreement dated  as of
  December __, 1995 ("Amendment No. 1") the Mortgagee has  agreed to lend an
  additional USD 5,000,000 to the Mortgagee and such additional amount is to
  be secured by the Mortgage and evidenced by the Note; and

        WHEREAS,  the Note  has  been  amended by  Endorsement No.  1  dated
  December __, 1995 ("Endorsement No. 1"); and

        WHEREAS,  the execution and  delivery of this Supplement  No. 2 have
  been duly authorized and all conditions and requirements necessary to make
  this  instrument  a  valid  and  binding  agreement  and  to  effect   the
  modifications  of  the  Mortgage  provided  herein  and  to  continue  the
  Mortgage,  as supplemented  and amended  by  this Supplement  No. 2,  as a
  valid, binding and  legal first preferred fleet mortgage for  the security
  of all amounts due under the Loan  Agreement and the Note, have been  duly
  performed and complied with:

        NOW, THEREFORE, THIS SUPPLEMENT WITNESSETH:

                                 ARTICLE FIRST

        SECTION 1.  The form of Loan Agreement as Annex I to the Mortgage is
  hereby amended by adding to it Amendment No. 1 in the form of Exhibit A to
  this Supplement No. 2. 

        SECTION 2.  The form of Note as Exhibit A to Annex I of the Mortgage
  is hereby amended by adding to it Endorsement No. 1 in the form of Exhibit
  B to this Supplement No. 2.

        SECTION 3.  For the  purpose of recording the  Mortgage, as the same
  is  hereby supplemented,  as required by  46 U.S. Code Ch.  313, the total
  amount  is  increased  to  Thirty  Million  United  States   Dollars  (USD
  30,000,000)  plus interest,  costs, expenses  and performance  of mortgage
  covenants; the discharge amount is the same as the total amount; and there
  is no separate discharge amount.

                                 ARTICLE SECOND

        SECTION 1.  All of the  covenants and agreements on the part  of the
  Mortgagor which are set forth in,  and all the rights,  privileges, powers
  and immunities of the Mortgagee which are provided for in the Mortgage are
  incorporated herein and  shall apply to the Vessels hereby  and heretofore
  subjected to  the lien of  the Mortgage and otherwise with  the same force
  and effect as though set forth at length in this supplement.

        SECTION 2.  This  instrument is executed as and  shall constitute an
  instrument  supplemental  to  the  Mortgage,  and shall  be  construed  in
  connection with and as part of the Mortgage.

        SECTION 3.  Except  as  modified   and  expressly  amended  by  this
  Supplement No. 2 and any other supplement, the Mortgage is in all respects
  ratified  and  confirmed and  all  the  terms,  provisions  and conditions
  thereof shall be and remain in full force and effect.

        SECTION 4.  This Supplement No.  2 may be executed in any  number of
  counterparts,  and each  of such  counterparts shall  for all  purposes be
  deemed to be an original.

        IN  WITNESS WHEREOF,  this Supplement  No. 2  has been  executed and
  delivered the day and year first above written.


                          READING AND BATES OFFSHORE, LIMITED


                          By:_________________________________
                             Name:____________________________
                             Title:___________________________


                          THE CIT GROUP/EQUIPMENT FINANCING, INC.


                          By:_________________________________
                             Name:____________________________
                             Title:___________________________ 



  STATE OF TEXAS          )
                          ) ss.:
  COUNTY OF HARRIS        )


        On  this  ___  day  of  December, 1995,  before  me  personally came
  __________________, to me known, who,  being by me duly  sworn, did depose
  and say that his address is 901 Threadneedle, Houston,  Texas  77079; that
  he is _______________ of Reading & Bates Offshore, Limited the corporation
  described  in and  which executed  the foregoing  instrument; and  that he
  signed his name thereto pursuant to authority granted to  him by the Board
  of Directors of said corporation.



                          ______________________________________
                          (Notary Public) 




  STATE OF TEXAS          )
                          ) ss.:
  COUNTY OF DALLAS        )


        On  this  ___  day  of  December, 1995,  before  me  personally came
  __________________, to me known, who,  being by me duly  sworn, did depose
  and  say that  his address  is Two  Lincoln Center,  Suite  200, 5420  LBJ
  Freeway,  Dallas, Texas  75240;  that  he is  _______________ of  The  CIT
  Group/Equipment Financing,  Inc., the corporation described  in and  which
  executed the  foregoing instrument;  and that he signed  his name  thereto
  pursuant to  authority granted to  him by  the Board of  Directors of said
  corporation.



                          ______________________________________
                          (Notary Public)