EXHIBIT 21


                     R&B FALCON CORPORATION
                        AND SUBSIDIARIES
      SCHEDULE OF CONSOLIDATED SUBSIDIARIES OF THE COMPANY
                    AS OF DECEMBER 31, 1998


     The  following  table  and text sets forth the subsidiaries  of  the
Company and of such subsidiaries:

                                                       State or
                                                   Jurisdiction of
             Name                                   Incorporation
             ----                                   -------------

     R&B Falcon Holdings, Inc.                         Delaware
      [formerly R&B Falcon Drilling (U.S.), Inc.]
     R&B Falcon Drilling                               Delaware
      (International & Deepwater) Inc.
     Cliffs Drilling Company                           Delaware

SUBSIDIARIES OWNED BY R&B FALCON HOLDINGS, INC.

     BSI Drilling & Workover, Inc.                     Louisiana
     Caribe USA, Inc.                                  Louisiana
     Double Eagle Marine, Inc.                         Louisiana
     Eilert-Olsen Investments, Inc.                    Texas
     Falcon Atlantic Ltd.                              Cayman Islands
     Falcon Drilling De Venezuela, Inc.                Delaware
     Falcon Drilling Do Brasil, Ltda.                  Brazil
     Falcon Offshore, Inc.                             Delaware
     Falcon Services Company, Inc.                     Delaware
      (also d/b/a as Falcon Drilling Company)
     Falgout Brothers, Inc.                            Louisiana
     Falgout Marine, Inc.                              Louisiana
     G&B Marine Tugs, Inc.                             Louisiana
     Knots Marine Inc.                                 Louisiana
     Perforaciones Falrig De Venezuela C.A.            Venezuela
     Raptor Exploration Co., Inc.                      Delaware
     R&B Falcon Drilling (S.E.A.) Pte. Ltd.            Singapore
     R&B Falcon Drilling U.S.A. Inc.                   Delaware

SUBSIDIARIES OWNED BY R&B FALCON DRILLING (INTERNATIONAL
     & DEEPWATER) INC.

     Arcade Drilling AS                                Norway
          [R&B Falcon Drilling (International &
          Deepwater) Inc. owns approximately
          74.4% of Arcade Drilling AS]
     R&B Falcon Drilling Co.                           Oklahoma
     RBF Holding Corporation                           Delaware
     RBF Management Services, Inc.                     Delaware
     Reading & Bates Coal Co.                          Nevada
     Reading & Bates Development Co.                   Delaware
     Reading & Bates Petroleum Co.                     Texas

SUBSIDIARIES OWNED BY CLIFFS DRILLING COMPANY

     Cliffs Drilling International, Inc.               Delaware
     Cliffs Oil and Gas Company                        Delaware
     Cliffs Drilling Venezuela, Inc.                   Delaware
     Cliffs Drilling de Venezuela, S.A.                Venezuela
     Cliffs Drilling do Brasil Servicos
       de Petroleo S/C Ltda.                           Brazil
       [Owned 90% by Cliffs Drilling Company
       and 10% by a third party as nominee for
       the benefit of Cliffs Drilling Company]
     Cliffs Drilling Trinidad L.L.C.                   Delaware
     Cliffs Drilling (Barbados) Holdings SRL           Barbados
       [Owned 99.99% by Cliffs Drilling Company
       and .01% by Cliffs Drilling Trinidad L.L.C.]
     Servicios Integrados Petroleros C.C.I., S.A.
       [A joint venture among Cliffs Drilling
       Company (which owns 33 1/3%), Inelectra
       S.A. and Cementaciones Petroleras
       Venezolanas C.A.]

SUBSIDIARIES OWNED BY R&B FALCON DRILLING CO.

     Onshore Services, Inc.                            Texas
     R&B Falcon Borneo Drilling Co., Ltd.              Oklahoma
     R&B Falcon Deepwater Development Inc.             Nevada
     R&B Falcon Drilling Limited                       Oklahoma
     R&B Falcon Exploration Co.                        Oklahoma
     R&B Falcon Enterprises Co.                        Texas
     R&B Falcon, Inc.                                  Oklahoma
     R&B Falcon International Energy
          Services B.V.                                Netherlands
     R&B Falcon (Ireland) Limited                      Ireland
     R&B Falcon Offshore, Limited                      Oklahoma
     R&B Falcon (U.K.) Limited                         England
     RBF Deepwater Exploration Inc.                    Nevada
     RBF Deepwater Exploration II Inc.                 Nevada
     RBF Deepwater Exploration III Inc.                Nevada
     RBF Drilling Co.                                  Oklahoma
     RBF Drilling Services, Inc.                       Oklahoma
     RBF Exploration Co.                               Nevada
     RBF Offshore, Inc.                                Nevada
     RBF Rig Corporation                               Oklahoma
     Rig Logistics, Inc.                               Nevada
     
          R&B Falcon Drilling Co. and R&B Falcon
          Enterprises Co. together own 100% of
          Reading & Bates-Demaga Perfuracoes Ltda.,
          a civil society with shares of limited
          responsibility organized under the laws
          of the Federative Republic of Brazil
     
SUBSIDIARIES OWNED BY READING & BATES DEVELOPMENT CO.

     RB Gabon Inc.                                     Oklahoma
     RB International Ltd.                             Cayman Islands
     RB Mediterranean Ltd.                             Cayman Islands
     Total Offshore Production Systems                 Texas

          Reading & Bates Development owns
          75% of Total Offshore Production
          Systems, a joint venture organized
          under the laws of the State of
          Texas

SUBSIDIARIES OWNED BY READING & BATES COAL CO.

     Appalachian Permit Co.                            Kentucky
     Bismarck Coal Inc.                                Kentucky
     Caymen Coal Inc.                                  West Virginia
     
SUBSIDIARIES OWNED BY RBF HOLDING CORPORATION

     RBF Subsidiary Corporation                        Delaware
     
SUBSIDIARIES OWNED BY R&B FALCON BORNEO DRILLING
     CO., LTD.

     R&B Falcon Borneo Drilling Co., Ltd.
     owns 49.99% of R&B Falcon (M) Sdn.
     Berhad, incorporated in Malaysia
     
SUBSIDIARIES OWNED BY R&B FALCON ENTERPRISES CO.
     
     Shore Services, Inc.                              Texas
          
     R&B Falcon Drilling Co. and R&B Falcon
     Enterprises Co. together own 100% of
     Reading & Bates-Demaga Perfuracoes Ltda.,
     a civil society with shares of limited
     responsibility organized under the laws
     of the Federative Republic of Brazil

SUBSIDIARIES OWNED BY R&B FALCON EXPLORATION CO.

     R&B Falcon (A) Pty Ltd                            Australia

SUBSIDIARIES OWNED BY R&B FALCON INTERNATIONAL
     ENERGY SERVICES B.V.

     R&B Falcon B.V.                                   Netherlands
     
SUBSIDIARIES OWNED BY R&B FALCON (U.K.) LIMITED

     R&B Falcon (Caledonia) Limited                    England

SUBSIDIARY OWNED BY RBF DEEPWATER EXPLORATION INC.

     RBF Deepwater Exploration Inc. owns 50%
     of Deepwater Drilling L.L.C., a limited
     liability company organized under the
     laws of the State of Delaware

SUBSIDIARY OWNED BY RBF DEEPWATER EXPLORATION II INC.

     RBF Deepwater Exploration II Inc. owns
     60% of Deepwater Drilling L.L.C., a
     limited liability company organized
     under the laws of the State of Delaware
     
SUBSIDIARIES OWNED BY RBF DRILLING SERVICES, INC.

     RBF Drilling Services, Inc. owns 60%
     of NRB Drilling Services Limited
     incorporated in Nigeria

     RBF Drilling Services, Inc. and Onshore
     Services, Inc. together own 100% of
     RBF (Nigeria) Limited, a company limited
     by shares and organized under the laws
     of the Federal Republic of Nigeria
          
SUBSIDIARIES OWNED BY BISMARCK COAL INC.

     Certicoals, Inc.                                  West Virginia

SUBSIDIARIES OWNED BY RB INTERNATIONAL LTD.

     RB Anton Ltd.                                     Cayman Islands
     RB Astrid Ltd.                                    Cayman Islands

SUBSIDIARIES OWNED BY CLIFFS DRILLING INTERNATIONAL, INC.
     
     Cliffs Drilling de Mexico, S.A. de C.V.           Mexico
     Cliffs Central Drilling International
       [A joint venture among Cliffs Drilling
       International, Inc. (which owns 50%) and
       Perfordora Central, S.A. de C.V.]
     Cliffs Neddrill Central Turnkey International
       [A joint venture among Cliffs Drilling
       International, Inc. (which owns 33 1/3%),
       Neddrill Turnkey Drilling B.V. and
       Perforadora Central, S.A. de C.V.]


SUBSIDIARIES OWNED BY CLIFFS DRILLING (BARBADOS) HOLDINGS SRL

     Cliffs Drilling (Barbados) SRL                    Barbados
           [Owned 99.99% by Cliffs Drilling
           (Barbados)Holdings SRL and .01%
           by Cliffs Drilling Trinidad L.L.C.]

SUBSIDIARIES OWNED BY CLIFFS DRILLING (BARBADOS) SRL

     Cliffs Drilling Trinidad Offshore Limited         Trinidad