<PAGE>   1
 
                                                                    EXHIBIT 21.1
 
                 SUBSIDIARIES OF PENNZOIL-QUAKER STATE COMPANY
                           (AS OF DECEMBER 31, 1998)
 
<TABLE>
<CAPTION>
                                                              PZL   PARENT
                                                              ---   ------
<S>                                                           <C>   <C>
Atlas Processing Company (Delaware).........................  100%
  Excel Paralubes (Texas General Partnership)...............           50%
  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%
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 Deutschland GmbH Mineralolvertrieb (Germany).......  100%
Pennzoil Products Australia Company (Nevada)................  100%
Pennzoil Products Benelux Company (Nevada)..................  100%
Pennzoil Products Company de Mexico (Nevada)................  100%
Pennzoil Products International Company (Mauritius).........  100%
  Pennzoil India Limited (India)............................         96.4%
Pennzoil Products International Holding Company
  (Delaware)................................................  100%
  Pennzoil Products Canada Company (Nova Scotia)............          100%
Pennzoil Products Mediterraneo, S.L. (Spain)................  100%
Pennzoil-Quaker State Asia Pacific Company (Nevada).........  100%
Pennzoil Receivables Company (Delaware).....................  100%
PZ Shareowner Services Company (Delaware)...................  100%
Quaker State Corporation (Delaware).........................  100%
  Lube Acquisition Corporation (Delaware)...................          100%
  QSHK Corporation (Delaware)...............................          100%
  Quaker State, Inc. (Canada)...............................          100%
  Quaker State Investment Corporation (Delaware)............          100%
     Blue Coral, Inc. (Delaware)............................          100%
       Blue Coral-Slick 50, Inc. (Delaware).................          100%
       Petrolon International Limited (Isle of Man).........         99.9%
          Petrolon Europe Limited (Isle of Man).............         99.4%
          Quaker State France S.A. (France).................          100%
          Pennzoil-Quaker State Limited (United Kingdom)....          100%
     Medo Industries, Inc. (New York).......................          100%
     Q Lube, Inc. (Delaware)................................          100%
     The Valley Camp Coal Company (Delaware)................          100%
       Donaldson Mine Company (West Virginia)...............          100%
       Kelley's Creek and Northwestern Railroad Company
        (West Virginia).....................................          100%
       Elm Grove Coal Company (West Virginia)...............          100%
       The Helen Mining Company (Pennsylvania)..............          100%
       Kanawha and Hocking Coal and Coke Company (West
        Virginia)...........................................          100%
       Shrewsbury Coal Company (West Virginia)..............          100%
       Valley Camp of Utah, Inc. (Utah).....................          100%
     Valley Camp, Inc. (Canada).............................          100%
  Rain-X Corporation (Arizona)..............................          100%
  Specialty Oil Company, Inc. (Delaware)....................          100%
     Specialty Environmental Services of Texas, Inc.
      (Texas)...............................................           50%
Savannah Company Limited (Bermuda)..........................  100%
UMW Pennzoil Distributors SDN. BHD. (Malaysia)..............  50%
</TABLE>