<PAGE>   1
 
                                                                      EXHIBIT 21
 
                        SUBSIDIARIES OF PENNZOIL COMPANY
                           (AS OF DECEMBER 31, 1997)
 
<TABLE>
<CAPTION>
                                                                 PZL          PARENT
                                                                 ---          ------
<S>                                                            <C>           <C>
Pennzoil Receivables Company (Delaware).....................     100%
Jiffy Lube International, Inc. (Nevada).....................     100%
     American Oil Change Corporation (Delaware).............                   100%
     Heritage Merchandising Co., Inc. (Virginia)............                   100%
     Jiffy Lube International of Maryland, Inc.
      (Maryland)............................................                   100%
Pennzoil Exploration and Production Company (Delaware)......     100%
     Cachuma Gas Processing Company (Delaware)..............                   100%
     Canyon Reef Carriers, Inc. (Texas).....................                   100%
     Capitan Oil Pipeline Company (Delaware)................                   100%
     Pennzoil Energy Marketing Company (Delaware)...........                   100%
     Pennzoil Gas Marketing Company (Delaware)..............                   100%
     Pennzoil International Company (Delaware)..............                   100%
          Pennzoil Beni Suef, Inc. (British Virgin
            Islands)........................................                   100%
          Pennzoil Caspian Corporation (British Virgin
            Islands)........................................                   100%
          Pennzoil Caspian Development Corporation (British
            Virgin Islands).................................                   100%
          Pennzoil Egypt, Inc. (Delaware)...................                   100%
          Pennzoil Exploration Australia, Inc. (British
            Virgin Islands).................................                   100%
          Pennzoil Qatar, Inc. (Delaware)...................                   100%
          Pennzoil Red Sea, Inc. (British Virgin Islands)...                   100%
          Pennzoil Sinai, Inc. (British Virgin Islands).....                   100%
          Pennzoil Suez, Inc. (British Virgin Islands)......                   100%
          Pennzoil Venezuela Corporation, S.A. (British
            Virgin Islands).................................                   100%
     Pennzoil Petroleum Pipeline Company (Delaware).........                   100%
     Pennzoil Petroleums Ltd. (Delaware)....................                   100%
     Sisquoc Gas Pipeline Company (Delaware)................                   100%
Pennzoil Products Company (Nevada)..........................     100%
     Atlas Processing Company (Delaware)....................                   100%
          Excel Paralubes (Texas General Partnership).......                    50%
     Pennzoil Deutschland GmbH Mineralolvertrieb
      (Germany).............................................                   100%
     Pennzoil Products Australia Company (Nevada)...........                   100%
     Pennzoil Products Europe GmbH (Germany)................                    99%
     Pennzoil Products Europe South Company (Nevada)........                   100%
     Pennzoil Wax Partner Company (Nevada)..................                   100%
          Bareco Asia Pacific Pte. Ltd. (Singapore).........                    50%
          Bareco Products (South Carolina General
            Partnership)....................................                    50%
               Bareco International Sales Corporation
                 (Virgin Islands)...........................                   100%
     Penreco (Texas General Partnership)....................                    50%(1)
     UMW Pennzoil Distributors SDN. BHD. (Malaysia).........                    50%
Richland Development Corporation (Nevada)...................     100%
     Inco Real Estate Company (Nevada)......................                   100%
     Savannah Company Limited (Bermuda).....................                   100%
     Vermejo Park Corporation (Delaware)....................                   100%
          Vermejo Minerals Corporation (Delaware)...........                   100%
</TABLE>
 
---------------
(1) Since formation of the partnership in October 1997, Pennzoil's share of
    Penreco's earnings was approximately 62%. The profit sharing ratio in future
    periods will be adjusted based on the partner's completion of certain
    contract provisions.