<PAGE>   1


                                                                    EXHIBIT 21.1

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<S>                                                 <C>
Arcair Stoody Europe S.A. (Belgium)                  Maxweld Braze
Europa Building                                      9 First Street
Chorley North Industrial Park                        Boksburg North
Drumhead Road                                        Boksburg
Chorley Lancashire PR6 7BX England                   South Africa
                                                     Stand #471 B14
C&G Systems, Inc.
1401 Glenlake                                        MECO Holding Company
Itaska,IL 60143                                      101 South Hanley Road, Suite 600
                                                     St Louis, MO 63105
C&G Systems Holding, Inc.
101 South Hanley Road, Suite 600                     Modern Engineering Company, Inc.
St. Louis, MO 63105                                  Unit 65, US Highway I-55 South
                                                     Gallman, MS 39077
Canadian Cylinder Company
101 South Hanley Road, Suite 600                     O.C.I.M. S.r.l.
St. Louis, MO 63105                                  Via Benaco, 3
                                                     20098 S. Giuliano Milanese (MI)
Comet Property Holdings Limited                      Italy
Jagobiao, Mandaue City
Cebu, Philippines                                    Palco Trading Company
                                                     P.O. Box 34-35
Comweld Group Pty Ltd.                               Dubal, UAE
85 Chifley Drive
Preston Victoria 3072                                Philippine Welding Equipment, Inc.
Australia                                            Jagobiao, Mandaue City
                                                     Cebu, Philippines
Comweld Malaysia Sdn. Bhd.
Lot 151, Rawang Integrated Industrial Park           PT CATU Tehnik Arya Unggul (Indonesia)
Jalan Batu Arang                                     JL. Compaka Purih Raya A-3
48000 Rawang                                         Jakarta 10510 Indonesia
Selangor Darul Ehsan
West Malaysia                                        PT Comweld Indonesia
                                                     85 Chifley Drive
Comweld (Philippines) Inc.                           Preston Victoria 3072 Australia
85 Chifley Drive
Preston Victoria 3072 Australia                      Quetack Pty Ltd.
                                                     85 Chifley Drive
Coyne Natural Gas System, Inc.                       Preston Victoria 3072 Australia
101 South Hanley Road, Suite 600
St. Louis, MO 63105                                  Quetala Pty Ltd.
                                                     85 Chifley Drive
Duxtech Pty Ltd.                                     Preston Victoria 3072 Australia
85 Chifley Drive
Preston Victoria 3072 Australia                      Quetala Unit Trust
                                                     85 Chifley Drive
GENSET SpA                                           Preston Victoria 3072 Australia
Thermadyne Italia S.P.A. fka PALCO, Italia S.P.A.
Via Stazione 5                                       Soltec S.A.
Villanova d'Ardenghi                                 Piloto Lazo #9 Cennillo
Pavia 27030 Italy                                    Santiago 7278654 Chile

Marison Cylinder Company                             Stoody Company
101 South Hanley Road, Suite 600                     5557 Nashville Road
St. Louis, MO 63105                                  Bowling Green, KY 42101

                                                     TAG Realty
                                                     101 South Hanley Road, Suite 600
                                                     St. Louis, MO 63105


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<PAGE>   2
<TABLE>
<S>                                                  <C>
TEC.MO. S.r.l.                                       Thermadyne Holding Corp.
Via Rio Fabbiani, 8                                  101 S. Hanley Road, Suite 600
40067 Rastignano (BO)                                St Louis, MO 63105
Italy
                                                     Thermadyne Industries, Inc.
THC Italia SRL                                       101 South Hanley Road, Suite 600
Via Stazione, 5                                      St. Louis, MO 63105
Villanove d'Ardenghi
Pavia 27030 Italy                                    Thermadyne Industries Limited (UK)
                                                     Europa Building
Thermadyne Asia/Pacific PTE Ltd.                     Chorley North Industrial Park
101 South Hanley Road, Suite 600                     Chorley Lancashire PR6 7BX England
St. Louis, MO 63105
                                                     Thermadyne International Corp.
Thermadyne Asia SDN BHD (Malaysia)                   2070 Wyecroft Road
Lot 151, Rawang Integrated Industrial Park           Oakville, Ontario L6L 5V6
Jalan Batu Arang
48000 Rawang                                         Thermadyne Hong Kong Limited
Selangor Darul Ehsan                                 Lot 789 DD 216 No. 7 Hillock
West Malaysia                                        95 Chuk Young Road, Sha Ha
                                                     Sai Kung, New Territories, Hong Kong, China
Thermadyne Australia Pty Ltd.
80 Chifley Drive                                     Thermadyne Japan Ltd.
Preston Victoria 3072 Australia                      10-20, Koyanagi-cho
                                                     Ibaraki City Osaka 567 Japan
Thermadyne Brazil Holdings, Ltd.
101 South Hanley Road, Suite 600                     Thermadyne Korea, Ltd.
St. Louis, MO 63105                                  5th Floor Seohwa Building
                                                     Yeoksam-Dong 839-8.9
Thermadyne Capital Corp.                             Kangnam-Ku Seoul Korea
101 South Hanley Road, Suite 600
St. Louis, MO 63105                                  Thermadyne Mfg. LLC
                                                     101 South Hanley Road, Suite 600
Thermadyne Chile Holdings, Ltd.                      St. Louis, MO 63105
101 South Hanley Road, Suite 600
St. Louis, MO 63105                                  Thermadyne Receivables, Inc.
                                                     101 South Hanley Road, Suite 600
Thermadyne Cylinder Co.                              St. Louis, MO 63105
101 South Hanley Road, Suite 600
St. Louis, MO 63105                                  Thermadyne South Africa (Pty) Limited
                                                     Dba Unique Welding Alloys
Thermadyne de Mexico S.A. de C.V.                    9 First Street
Francisco del Paso y Troncoso 869                    Boksburg North
Co. Los Reyes CP 08620                               Boksburg
Mexico City, Mexico                                  South Africa
                                                     Stand #471 B14
Thermadyne do Brasil Ltda
Rua Thorquato Tasso 636                              Thermadyne South Africa (Pty) Limited
Sao Paulo 03100 Brasil                               Dba Unique Welding Alloys
                                                     82A Zehdeling Street
Thermadyne Foreign Sales Corporation (Barbados)      Rustenburg
c/o Price Waterhouse Corporate Services              South Africa
Price Waterhouse Centre                              Stand #Portion ERF9S2
Collymore Road, St. Michael, Barbados
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<PAGE>   3

<TABLE>
<S>                                                     <C>
     Thermadyne South America Holdings, Ltd.            Thermadyne (Thailand) Co. Ltd.
     101 South Hanley Road, Suite 600                   29/9 Moo 14, Bagna-Trad Road, Km.6
     St. Louis, MO 63105                                Samutprakarn 10540

     Thermadyue Victor Ltd.
     Avenida Brazil 13629
     Rio de Janeiro RJ 21012--351
     Brazil

     Thermadyne Welding Products Canada, Ltd.
     2070 Wyecroft Road
     Oakville, Ontario L6L 5V6

     Thermal Dynamics Corp.
     Industrial Part #2
     West Lebanon, NH 03784

     Thermal Arc, Inc.
     2200 Corporate Drive
     Troy, OH 45373

     Thermal Arc Phils, Inc. (Philippines)
     Pelbel Building 2019 Shaw Boulevard
     Pasig City Manila Philippines

     Tweco de Mexico SA de CV
     Jesus Siqueiros 652
     Col. Alvaro Obregon
     Hermosillo Sonora 83170

     TWECO Products, Inc.
     4200 West Harry
     Wichita, KS 67209

     Victor Coyne International, Inc.
     2800 Old Airport
     Denton, TX 76202

     Victor Equipment Company
     2800 Old Airport Road
     Denton, TX 76205

     Victor Equipment de Mexico, S.A. de C.V.
     Jesus Siqueiros #652
     Colonia Alvaro Obregon
     Hermosillo, Sonora, Mexico, CP 83170

     Victor Gas Systems, Inc.
     2536 South 59th Street
     Philadelphia, PA 19143

     Wichita Warehouse Corp.
     4200 West Harry
     Wichita, KS 67209
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