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                                                                   EXHIBIT 10.35
                                      
                     ASSIGNMENT AND ASSUMPTION AGREEMENT


                THIS ASSIGNMENT AND ASSUMPTION AGREEMENT (this "Agreement") is
made and entered into this 22nd day of May, 1998, by and between Thermadyne
Holdings Corporation, a Delaware corporation (the "Company"), and DLJ Merchant
Banking II, Inc., a Delaware corporation ("DLJMB").  

                                  RECITALS:

                WHEREAS, the Company and Mercury Acquisition Corporation, a
Delaware corporation and affiliate of DLJMB ("MergerSub"), have executed and
delivered that certain Agreement and Plan of Merger dated as of January 20,
1998 (as amended, the "Merger Agreement");

                WHEREAS, in connection with the consummation of the
transactions contemplated by the Merger Agreement, DLJMB entered into a letter
agreement (the "Engagement Letter") dated January 16, 1998, with Donaldson,
Lufkin & Jenrette Securities Corporation ("DLJSC") pursuant to which, among
other things, DLJSC agreed to provide certain financial advisory services to
the Company; and

                WHEREAS, the transactions contemplated by the Merger Agreement
have been consummated; and 

                WHEREAS, in connection with the consummation of the
transactions contemplated by the Merger Agreement, DLJMB wishes to assign its
rights under the Engagement Letter to the Company and the Company wishes to
assume DLJMB's obligations under the Engagement Letter.

                NOW, THEREFORE, for good and valuable consideration, the
receipt of which is hereby acknowledged, the Company and DLJMB hereby agree as
follows:

                1.       DLJMB hereby transfers and assigns unto the Company
all of the rights and incidents of interest of DLJMB in and under the
Engagement Letter.

                2.      The Company hereby agrees to assume and thereafter pay,
perform, or otherwise discharge, as and when the same shall become due and
payable all of DLJMB's obligations under the Engagement Letter.

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                3.      This Agreement may be executed in one or more
counterparts for the convenience of the parties hereto, all of which together
shall constitute one and the same instrument.

                IN WITNESS WHEREOF, the parties hereto have executed this
Agreement as of the date first above written. 

                                        THERMADYNE HOLDINGS CORPORATION




                                        By: /s/ Stephanie N. Josephson  
                                            -----------------------------------
                                             Stephanie N. Josephson
                                             Vice President, General Counsel
                                               and Corporate Secretary


                                        DLJ MERCHANT BANKING II, INC.




                                        By: /s/ William F. Dawson       
                                            -----------------------------------
                                             William F. Dawson          
                                             Principal