<PAGE>   1

                                                                    EXHIBIT 4.11


                             SUBSCRIPTION AGREEMENT

                                   dated as of

                                December 22, 1999

                                  by and among

                     DLJ MERCHANT BANKING PARTNERS II, L.P.,
                    DLJ MERCHANT BANKING PARTNERS II-A, L.P.,
                         DLJ OFFSHORE PARTNERS II, C.V.,
                         DLJ DIVERSIFIED PARTNERS, L.P.,
                        DLJ DIVERSIFIED PARTNERS-A, L.P.,
                             DLJMB FUNDING II, INC.,
                         DLJ MILLENNIUM PARTNERS, L.P.,
                        DLJ MILLENNIUM PARTNERS-A, L.P.,
                             DLJ EAB PARTNERS, L.P.,
                                DLJ ESC II L.P.,
                              DLJ FIRST ESC, L.P.,


                         THERMADYNE HOLDINGS CORPORATION

                                       and

                               THERMADYNE MFG. LLC

                        relating to the purchase and sale

                                       of

            Junior Subordinated Notes due 2009 of Thermadyne Mfg. LLC

                                       and

                   Warrants to Purchase Shares of Common Stock
                       of Thermadyne Holdings Corporation



<PAGE>   2



                                TABLE OF CONTENTS

                             ----------------------

<TABLE>
<CAPTION>

                                                                                             PAGE
                                                                                             ----

                                             ARTICLE 1
                                            DEFINITIONS

<S>            <C>                                                                           <C>
SECTION 1.01.  Definitions......................................................................1

                                             ARTICLE 2
                                         PURCHASE AND SALE

SECTION 2.01.  Purchase and Sale................................................................5
SECTION 2.02.  Closing..........................................................................5
SECTION 2.03.  Purchase Price Allocation........................................................5

                                             ARTICLE 3
                           REPRESENTATIONS AND WARRANTIES OF THE ISSUERS

SECTION 3.01.  Corporate Existence and Power....................................................6
SECTION 3.02.  Corporate Authorization..........................................................6
SECTION 3.03.  Noncontravention.................................................................6
SECTION 3.04.  Capitalization; Indebtedness.....................................................7
SECTION 3.05.  Subsidiaries.....................................................................8
SECTION 3.06.  Parent 34 Act Reports............................................................8
SECTION 3.07.  Litigation.......................................................................8
SECTION 3.08.  Environmental Matters............................................................8
SECTION 3.09.  Licenses and Permits.............................................................9
SECTION 3.10.  Financial Statements.............................................................9
SECTION 3.11.  Investment Company Act...........................................................9
SECTION 3.12.  Registration Obligations........................................................10
SECTION 3.13.  No Violation of Regulation G, T, U or X.........................................10
SECTION 3.14.  No Ratings Decline..............................................................10
SECTION 3.15.  No Material Change..............................................................10
SECTION 3.16.  No Solicitation.................................................................10
SECTION 3.17.  Labor Matters...................................................................11
SECTION 3.18.  Accounting Controls.............................................................11
SECTION 3.19.  Intellectual Property...........................................................11
SECTION 3.20.  Indenture.......................................................................12
SECTION 3.21.  No Registration.................................................................12
SECTION 3.22.  Certificates....................................................................12
</TABLE>






<PAGE>   3

<TABLE>
<CAPTION>

                                                                                             PAGE
                                                                                             ----

                                             ARTICLE 4
                           REPRESENTATIONS AND WARRANTIES OF THE BUYERS

<S>            <C>                                                                           <C>
SECTION 4.01.  Corporate/Partnership Existence and Power.......................................12
SECTION 4.02.  Corporate/Partnership Authorization.............................................12
SECTION 4.03.  Governmental Authorization......................................................12
SECTION 4.04.  Noncontravention................................................................13
SECTION 4.05.  Purchase for Investment.........................................................13
SECTION 4.06.  Litigation......................................................................13
SECTION 4.07.  Finders' Fees...................................................................13

                                             ARTICLE 5
                                     COVENANTS OF THE PARTIES

SECTION 5.01.  Best Efforts; Further Assurances................................................14
SECTION 5.02.  Certain Filings.................................................................14
SECTION 5.03.  Public Announcements............................................................14

                                             ARTICLE 6
                                       CONDITIONS TO CLOSING

SECTION 6.01.  Conditions to Obligations of each Party.........................................14
SECTION 6.02.  Conditions to Obligation of the Buyers..........................................15
SECTION 6.03.  Conditions to Obligation of the Issuers.........................................16

                                             ARTICLE 7
                                     SURVIVAL; INDEMNIFICATION

SECTION 7.01.  Survival........................................................................17
SECTION 7.02.  Indemnification.................................................................18
SECTION 7.03.  Procedures......................................................................18

                                             ARTICLE 8
                                           MISCELLANEOUS

SECTION 8.01.  Notices.........................................................................19
SECTION 8.02.  Amendments and Waivers..........................................................20
SECTION 8.03.  Expenses........................................................................20
SECTION 8.04.  Successors and Assigns..........................................................20
SECTION 8.05.  Governing Law...................................................................20
SECTION 8.06.  Jurisdiction....................................................................21
SECTION 8.07.  WAIVER OF JURY TRIAL............................................................21
</TABLE>


                                       ii


<PAGE>   4


<TABLE>

<S>            <C>                                                                             <C>
SECTION 8.08.  Counterparts; Third Party Beneficiaries.........................................21
SECTION 8.09.  Appointment of Agent............................................................21
SECTION 8.10.  Entire Agreement................................................................22
SECTION 8.11.  Captions........................................................................22
SECTION 8.12.  Enforcement of Voting Rights....................................................22

                                             EXHIBITS

Exhibit A-- Form of Notes, including attached Form of Indenture
Exhibit B-- Form of Registration Rights Agreement
Exhibit C-- Form of Warrants

                                             SCHEDULE

Schedule 3.05 -- Subsidiaries
</TABLE>



<PAGE>   5



                             SUBSCRIPTION AGREEMENT


         AGREEMENT dated as of December 22, 1999 by and among DLJ Merchant
Banking Partners II, L.P., DLJ Merchant Banking Partners II-A, L.P., DLJ
Offshore Partners II, C.V., DLJ Diversified Partners, L.P., DLJ Diversified
Partners-A, L.P., DLJMB Funding II, Inc., DLJ Millennium Partners, L.P., DLJ
Millennium Partners-A, L.P., DLJ EAB Partners, L.P., DLJ ESC II L.P. and DLJ
First ESC, L.P., (each of the foregoing, a "DLJ BUYER", and collectively, the
"DLJ BUYERS" and sometimes referred to as the "BUYERS"), Thermadyne Holdings
Corporation, a Delaware corporation ("PARENT"), and Thermadyne Mfg. LLC, a
Delaware limited liability company and a wholly-owned subsidiary of Parent (the
"COMPANY").

                              W I T N E S S E T H :

         WHEREAS, the Buyers desire to purchase, and Parent and the Company
desire to issue and sell to the Buyers, the Securities (as defined below), upon
the terms and subject to the conditions hereinafter set forth.

         NOW THEREFORE, the parties hereto agree as follows:

                                    ARTICLE 1
                                   DEFINITIONS

         SECTION 1.01. Definitions. (a) The following terms, as used herein,
have the following meanings:

         "AFFILIATE" means, with respect to any Person, any other Person
directly or indirectly controlling, controlled by, or under common control with
such Person; provided that no securityholder of Parent shall be deemed an
Affiliate of any other securityholder of Parent or any Subsidiary solely by
reason of any investment in Parent. For the purpose of this definition, the term
"control" (including with correlative meanings, the terms "controlling,"
"controlled by" and "under common control with"), as used with respect to any
Person, shall mean the possession, directly or indirectly, of the power to
direct or cause the direction of the management and policies of such Person,
whether through the ownership of voting securities or by contract or otherwise.


<PAGE>   6



         "CLOSING DATE" means the date of the Closing.

         "CODE" means the Internal Revenue Code of 1986, as amended.

         "COMMON STOCK" means the Common Stock, par value $0.01 per share, of
Parent.

         "CREDIT AGREEMENT" means the Credit Agreement dated as of May 22, 1998
among the Company, Comweld Group Pty. Ltd., GenSet S.p.A., Thermadyne Welding
Products Canada Limited, the various financial institutions party thereto from
time to time, DLJ Capital Funding, Inc., as syndication agent, Societe Generale,
as documentation agent and ABN AMRO Bank N.V., as administrative agent, as
amended from time to time, together with the related documents thereto
(including, without limitation, the term loans, revolving loans and swingline
loans thereunder, the letters of credit issued pursuant thereto and any
guarantees and security documents).

         "FEDERAL TAX" means any Tax imposed under Subtitle A of the Code.

         "FINAL DETERMINATION" shall mean (i) any final determination of
liability in respect of a Tax that, under applicable law, is not subject to
further appeal, review or modification through proceedings or otherwise
(including the expiration of a statute of limitations or a period for the filing
of claims for refunds, amended returns or appeals from adverse determinations),
including a "determination" as defined in Section 1313(a) of the Code or
execution of an Internal Revenue Service Form 870AD or (ii) the payment of Tax
by the Buyers, Parent or a Subsidiary, whichever is responsible for payment of
such Tax under applicable law, with respect to any item disallowed or adjusted
by a Taxing Authority, provided that such responsible party determines that no
action should be taken to recoup such payment and the other party agrees.

         "INDENTURE" means the Indenture relating to the Notes, substantially in
the form attached to Exhibit A hereto.

         "LIEN" means, with respect to any property or asset, any mortgage,
lien, pledge, charge, security interest, encumbrance or other adverse claim of
any kind in respect of such property or asset. For the purposes of this
Agreement, a Person shall be deemed to own subject to a Lien any property or
asset which it has acquired or holds subject to the interest of a vendor or
lessor under any conditional sale agreement, capital lease or other title
retention agreement relating to such property or asset.


                                        2
<PAGE>   7


         "MATERIAL ADVERSE EFFECT" means a material adverse effect on the
condition (financial or otherwise), business, assets or results of operations of
Parent and the Subsidiaries, taken as whole.

         "1933 ACT" means the Securities Act of 1933, as amended, and the rules
and regulations promulgated thereunder.

         "1934 ACT" means the Securities Exchange Act of 1934, as amended, and
the rules and regulations promulgated thereunder.

         "NOTES" means the Junior Subordinated Notes of the Company due 2009, a
specimen certificate substantially the form of which is attached hereto as
Exhibit A.

         "PARENT 1934 ACT REPORTS" means the reports filed by Parent in
compliance with the 1934 Act during Parent's most recent fiscal year and, in any
event, Parent's annual report on Form 10-K for the year ended December 31, 1998.

         "PERSON" means an individual, corporation, partnership, limited
liability company, association, trust or other entity or organization, including
a government or political subdivision or an agency or instrumentality thereof.

         "REGISTRATION RIGHTS AGREEMENT" means the Registration Rights
Agreement, substantially in the form attached hereto as Exhibit B.

         "SECURITIES" means, collectively, the Notes and the Warrants.

         "SUBSIDIARY" means any entity of which securities or other ownership
interests having ordinary voting power to elect a majority of the board of
directors or other persons performing similar functions are at the time directly
or indirectly owned by Parent (including, without limitation, the Company).

         "TAX" means (i) any tax, governmental fee or other like assessment or
charge of any kind whatsoever (including, but not limited to, withholding on
amounts paid to or by any Person), together with any interest, penalty, addition
to tax or additional amount imposed by any governmental authority (a "TAXING
AUTHORITY") responsible for the imposition of any such tax (domestic or
foreign), (ii) in the case of Parent or any Subsidiary, liability for the
payment of any amount of the type described in clause (i) as a result of being
or having been before the Closing Date a member of an affiliated, consolidated,
combined or unitary group, or a party to any agreement or arrangement, as a
result of which liability of Parent or any Subsidiary to a Taxing Authority is
determined or taken into account with


                                       3
<PAGE>   8



reference to the liability of any other Person, and (iii) liability of Parent or
any Subsidiary for the payment of any amount as a result of being party to any
Tax Sharing Agreement or with respect to the payment of any amount of the type
described in (i) or (ii) as a result of any existing express or implied
obligation (including, but not limited to, an indemnification obligation).

         "TAX SHARING AGREEMENTS" means all existing agreements or arrangements
(whether or not written) binding Parent or any Subsidiary that provide for the
allocation, apportionment, sharing or assignment of any Tax liability or
benefit, or the transfer or assignment of income, revenues, receipts, or gains
for the principal purpose of determining any person's Tax liability.

         "TRANSACTION DOCUMENTS" means this Agreement, the Notes, the Warrants,
the Indenture and the Registration Rights Agreement.

         "TRANSACTIONS" means the transactions contemplated by the Transaction
Documents.

         "WARRANTS" means warrants to purchase an aggregate of 436,965 shares of
Common Stock, a specimen certificate substantially the form of which is attached
hereto as Exhibit C.

         (b) Each of the following terms is defined in the Section set forth
opposite such term:

<TABLE>
<CAPTION>

TERM                                           SECTION
<S>                                            <C>
Authorizations                                 3.09
Buyers                                         recitals
Closing                                        2.02
Company                                        recitals
Damages                                        7.02
DLJ Buyers                                     recitals
Environmental Laws                             3.08(a)
ERISA                                          3.08(a)
Indemnified Party                              7.03
Indemnifying Party                             7.03
intellectual property                          3.19
Issuer                                         2.01
Parent                                         recitals
Parent Securities                              3.04
Purchase Price                                 2.01
</TABLE>



                                       4
<PAGE>   9


                                    ARTICLE 2
                                PURCHASE AND SALE

         SECTION 2.01. Purchase and Sale. Upon the terms and subject to the
conditions of this Agreement, Parent and the Company (each, an "ISSUER") agree
to issue and sell to each Buyer, and each Buyer agrees, severally and not
jointly, to purchase from the applicable Issuer at the Closing such Notes and
Warrants as are set forth opposite such Buyer's name on Schedule 2.01. The
aggregate purchase price (the "PURCHASE PRICE") for the Notes and the Warrants
applicable to each Buyer is set forth opposite such Buyer's name on Schedule
2.01. The aggregate Purchase Price payable by all Buyers shall be paid at
Closing as provided in Section 2.02.

         SECTION 2.02. Closing. The closing (the "CLOSING") of the purchase and
sale of the Securities hereunder shall take place at the offices of Davis Polk &
Wardwell, 450 Lexington Avenue, New York, New York, as soon as possible after
satisfaction of the conditions set forth in Article 6, or at such other time or
place as the parties hereto may agree. At the Closing:

         (a) Each Buyer shall deliver to the applicable Issuer the amounts set
forth opposite its name on Schedule 2.01 with respect to the Notes and the
Warrants to be purchased by it, in immediately available funds by wire transfer
to an account of the applicable Issuer designated by such Issuer, by notice to
the Buyers, not later than two business days prior to the Closing Date.

         (b) The applicable Issuer shall deliver to each Buyer duly-executed
Notes and Warrants, as the case may be, in the amounts set forth opposite such
Buyer's name on Schedule 2.01.

         SECTION 2.03. Purchase Price Allocation. The Issuers and the Buyers
agree that the Purchase Price shall be allocated to the Notes and the Warrants
for U.S. federal income tax purposes in a manner to be mutually agreed by the
Issuers and the Buyers.

                                    ARTICLE 3
                  REPRESENTATIONS AND WARRANTIES OF THE ISSUERS

         Parent and the Company jointly and severally represent and warrant to
the Buyers as of the Closing Date that:


                                       5
<PAGE>   10


         SECTION 3.01. Corporate Existence and Power. (a) Each Issuer is a
corporation duly incorporated or a limited liability company duly organized,
validly existing and in good standing under the laws of its jurisdiction of
incorporation or organization, as the case may be, and has all requisite power
and authority to carry on its business as now conducted. Each Issuer is duly
qualified to do business as a foreign corporation or foreign limited liability
company, as the case may be, and is in good standing in each jurisdiction where
such qualification is necessary, except for those jurisdictions where failure to
be so qualified would not, individually or in the aggregate, have a Material
Adverse Effect.

         (b) All equity interests of each of the Issuers have been duly
authorized and validly issued and are fully paid, non-assessable and not subject
to any preemptive or similar rights.

         (c) Neither Issuer nor any of its subsidiaries is in violation of its
respective organizational documents or in default in the performance of any
obligation, agreement, covenant or condition contained in any indenture, loan
agreement, mortgage, lease or other agreement or instrument to which such Issuer
or any of its subsidiaries is a party or by which such Issuer or any of its
subsidiaries or their respective property is bound, except for such defaults
which, singly or in the aggregate, would not have a Material Adverse Effect.

         SECTION 3.02. Corporate Authorization. The execution, delivery and
performance by each Issuer of the Transaction Documents to which such Issuer is
a party and the consummation of the transactions contemplated thereby are within
such Issuer's powers and have been duly authorized by all necessary action on
the part of such Issuer. This Agreement constitutes (and, when executed and
delivered, each other Transaction Document to which each Issuer is a party will
constitute) a valid and binding agreement of each Issuer, enforceable against
each of the Issuers in accordance with its terms except as (i) the
enforceability thereof may be limited by bankruptcy, insolvency or similar laws
affecting creditors' rights generally, (ii) rights of acceleration and the
availability of equitable remedies may be limited by equitable principles of
general applicability and (iii) rights to indemnity and contribution thereunder
may be limited by applicable law.

         SECTION 3.03. Noncontravention. The execution, delivery and performance
by each Issuer of the Transaction Documents to which such Issuer is a party and
the consummation of the transactions contemplated thereby do not and will not
(i) require any consent, approval, authorization or other order of, or
qualification with, any court or governmental body or agency (except such as may
be required under federal securities or Blue Sky laws of the various states or
have been or will be obtained prior to the Closing Date), (ii) conflict with or
constitute a breach of any of the terms or provisions of, or a default under,
(A) the charter or


                                       6
<PAGE>   11


bylaws or limited liability company agreement of such Issuer or any of its
subsidiaries or (B) any indenture, loan agreement, mortgage, lease or other
agreement or instrument that is material to such Issuer and its subsidiaries,
taken as a whole, to which such Issuer or any of its subsidiaries is a party or
by which such Issuer or any of its subsidiaries or their respective property is
bound, (iii) violate or conflict with any applicable law or any rule,
regulation, judgment, order or decree of any court or any governmental body or
agency having jurisdiction over such issuer any of its subsidiaries or their
respective property, (iv) result in the imposition or creation of (or the
obligation to create or impose) a Lien under, any agreement or instrument to
which such Issuer or any of its subsidiaries is a party or by which such Issuer
or any of its subsidiaries or their respective property is bound, or (v) result
in the termination, suspension or revocation of any Authorization (as defined
below) of such Issuer or any of its subsidiaries or result in any other
impairment of the rights of the holder of any such Authorization, except, in the
case of clauses (i), (ii)(B), (iv) and (v), as would not, singly or in the
aggregate, have a Material Adverse Effect.

         SECTION 3.04. Capitalization; Indebtedness. (a) The authorized capital
stock of Parent consists of 30,000,000 shares of Common Stock and 15,000,000
shares of Preferred Stock. After giving effect to the Closing, there will be
outstanding (i) 3,590,326 shares of Common Stock and 2,000,000 shares of
Preferred Stock, (ii) options to purchase 342,356 shares of Common Stock, (iii)
the rights associated with Parent's rights plan in place as of the date hereof
and (iv) the Warrants.

         (b) All outstanding shares of capital stock of Parent have been duly
authorized and validly issued and are fully paid and non-assessable. Other than
the Parent Securities, there are no outstanding (i) shares of capital stock or
voting securities of Parent, (ii) securities of Parent convertible into or
exchangeable for shares of capital stock or voting securities of Parent or (iii)
options or other rights to acquire from Parent, or other obligation of Parent to
issue, any capital stock, voting securities or securities convertible into or
exchangeable for capital stock or voting securities of Parent (the items in
clauses 3.04(B)(I), 3.04(B)(II), 3.04(B)(III) and 3.04(b)(iv) being referred to
collectively as the "PARENT SECURITIES"). There are no outstanding obligations
of Parent or any Subsidiary to repurchase, redeem or otherwise acquire any
Parent Securities, except the obligation of Parent to redeem its Preferred Stock
in accordance with the terms thereof.

         (c) When executed and delivered pursuant to this Agreement, the Notes
and the Warrants will constitute valid and binding obligations of the applicable
Issuer. Upon the consummation of the Closing, the shares of Common Stock
issuable upon the exercise of the Warrants will have been duly authorized and
reserved for issuance upon exercise of the Warrants and, when issued upon such


                                       7
<PAGE>   12


exercise and payment of the exercise price thereof, will be validly issued,
fully paid and non-assessable, and the issuance of such shares is not subject to
any preemptive or similar rights.

         SECTION 3.05. Subsidiaries. (a) The entities listed on Schedule 3.05
hereto are the only subsidiaries, direct or indirect, of Parent. Except as
otherwise set forth on such Schedule, all of the outstanding equity interests of
each of Parent's subsidiaries have been duly authorized and validly issued and
are fully paid and non-assessable, as applicable, and are owned by Parent,
directly or indirectly through one or more subsidiaries, free and clear of any
Lien.

         SECTION 3.06. Parent 34 Act Reports. Parent has made all required
filings under the 1934 Act. All of the information contained in the Parent 34
Act Reports is correct in all material respects as of the date thereof and not
misleading.

         SECTION 3.07. Litigation. (a) No action has been taken and no law,
statute, rule or regulation or order has been enacted, adopted or issued by any
governmental agency or body which prevents the execution, delivery and
performance of any of the Transaction Documents, or suspends the sale of the
Notes or the Warrants in any jurisdiction and no injunction, restraining order
or other order or relief of any nature by a federal or state court or other
tribunal of competent jurisdiction has been issued with respect to any Issuer
which would prevent or suspend the issuance or sale of the Notes or the Warrants
in any jurisdiction.

         (b) There are no legal or governmental proceedings pending or
threatened to which either Issuer or any of its subsidiaries is or could be a
party or to which any of their respective property is or could be subject, which
might result, singly or in the aggregate, in a Material Adverse Effect.

         SECTION 3.08. Environmental Matters. (a) Neither Issuer nor any of its
subsidiaries has violated any foreign, federal, state or local law or regulation
relating to the protection of human health and safety, the environment or
hazardous or toxic substances or wastes, pollutants or contaminants
("ENVIRONMENTAL LAWS"), any provisions of the Employee Retirement Income
Security Act of 1974, as amended ("ERISA"), or any provisions of the Foreign
Corrupt Practices Act or the rules and regulations promulgated thereunder,
except for such violations which, singly or in the aggregate, would not have a
Material Adverse Effect.

         (b) Except as otherwise set forth in the Parent 1934 Act Reports, there
are no costs or liabilities associated with Environmental Laws (including,
without


                                       8
<PAGE>   13


limitation, any capital or operating expenditures required for clean-up, closure
of properties or compliance with Environmental Laws or any Authorization, any
related constraints on operating activities and any potential liabilities to
third parties) which would, singly or in the aggregate, have a Material Adverse
Effect.

         SECTION 3.09. Licenses and Permits. Each Issuer and its subsidiaries
has such permits, licenses, consents, exemptions, franchises, authorizations and
other approvals (each, an "AUTHORIZATION") of, and has made all filings with and
notices to, all governmental or regulatory authorities and self-regulatory
organizations and all courts and other tribunals, including without limitation,
under any applicable Environmental Laws, as are necessary to own, lease, license
and operate its respective properties and to conduct its business, except where
the failure to have any such Authorization or to make any such filing or notice
would not, singly or in the aggregate, have a Material Adverse Effect. Each such
Authorization is valid and in full force and effect and each Issuer and its
subsidiaries is in compliance with all the terms and conditions thereof and with
the rules and regulations of the authorities and governing bodies having
jurisdiction with respect thereto; and no event has occurred (including, without
limitation, the receipt of any notice from any authority or governing body)
which allows or, after notice or lapse of time or both, would allow, revocation,
suspension or termination of any such Authorization or results or, after notice
or lapse of time or both, would result in any other impairment of the rights of
the holder of any such Authorization; and such Authorizations contain no
restrictions that are burdensome to such Issuer or any of its subsidiaries;
except, in each case, where such failure to be valid and in full force and
effect or to be in compliance, the occurrence of any such event or the presence
of any such restriction would not, singly or in the aggregate, have a Material
Adverse Effect.

         SECTION 3.10. Financial Statements. The historical financial
statements, together with related notes forming part of the Parent 34 Act
Reports (and any amendment or supplement thereto), present fairly the
consolidated financial position, results of operations and changes in financial
position of Parent and its subsidiaries on the basis stated in the Parent 34 Act
Reports at the respective dates or for the respective periods to which they
apply; such statements and related schedules and notes have been prepared in
accordance with generally accepted accounting principles consistently applied
throughout the periods involved, except as disclosed therein; and the other
financial and statistical information and data set forth in the Parent 34 Act
Reports (and any amendment or supplement thereto) are, in all material respects,
accurately presented and prepared on a basis consistent with such financial
statements and the books and records of Parent.

         SECTION 3.11. Investment Company Act. None of the Issuers is or, after
giving effect to the offering and sale of the Securities and the application of
the

                                       9
<PAGE>   14


net proceeds thereof will be, and "investment company," as such term is defined
in the Investment Company Act of 1940 as amended.

         SECTION 3.12. Registration Obligations. There are no contracts,
agreements or understanding between any Issuer and any person granting such
person the right to require such Issuer to file a registration statement under
the 1933 Act with respect to any securities of such Issuer or to require such
Issuer to include such securities with the securities registered pursuant to any
Issuer registration statement, except as contemplated in the Registration Rights
Agreement and the Investors' Agreement dated as of May 22, 1998 among Parent and
the investors and stockholders party thereto.

         SECTION 3.13. No Violation of Regulation G, T, U or X. Neither Issuer
nor any agent thereof acting on the behalf of them has taken, and none of them
will take, any action that may cause the Transaction Agreements or the issuance
or sale of the Securities to violate Regulation G (12 C.F.R. Part 207),
Regulation T (12 C.F.R. Part 220), Regulation U (12 C.F.R. Part 221) or
Regulation X (12 C.F.R. Part 224) of the Board of Governors of the Federal
Reserve System.

         SECTION 3.14. No Ratings Decline. No "nationally recognized statistical
rating organization" (as such term is defined for purposes of Rule 436(g)(2)
under the 1933 Act (i) has imposed (or has informed any Issuer that it is
considering imposing) any condition (financial or otherwise) on such Issuer's
retaining any rating assigned to such Issuer or any securities of such Issuer or
(ii) has indicated to such Issuer that it is considering (A) the downgrading
suspension, or withdrawal of, or any review for a possible change that does not
indicate the direction of the possible change in, any rating so assigned or (B)
any change in the outlook for any rating of such Issuer or any securities of
such Issuer.

         SECTION 3.15. No Material Change. Since the respective dates as of
which information is given in the Parent 34 Act Reports other than as set forth
in the Parent 34 Act Reports (exclusive of any amendments or supplements thereto
subsequent to the date of this Agreement), (i) there has not occurred any
material adverse change or any development involving a prospective material
adverse change in the condition, financial or otherwise, or the earnings,
business, management or operations of Parent and its subsidiaries, taken as a
whole, (ii) there has not been any material adverse change or any development
involving a prospective material adverse change in the capital stock or in the
long-term debt of Parent or any of its subsidiaries and (iii) neither Parent nor
any of its subsidiaries has incurred any material liability or obligation,
direct or contingent.

         SECTION 3.16. No Solicitation. No form of general solicitation or
general advertising (as defined in Regulation D under the 1933 Act) was used by
any


                                       10
<PAGE>   15


Issuer or any of its representatives (other than the DLJ Buyers, as to whom the
Issuers make no representation) in connection with the offer and sale of the
Securities contemplated here, including, but not limited to, articles, notices
or other communications published in any newspaper, magazine or similar medium
or broadcast over television or radio, or any seminar or meeting whose attendees
have been invited by any general solicitation or general advertising. No
securities of the same class as the Notes or the Warrants have been issued and
sold by any Issuer within the six-month period immediately prior to the date
hereof.

         SECTION 3.17. Labor Matters. There is no (i) material unfair labor
practice complaint, grievance or arbitration proceeding pending or threatened
against either Issuer before the National Labor Relations Board or any state or
local labor relations board or (ii) strike, labor dispute, slowdown or stoppage
pending or threatened against either Issuer, except for such actions specified
in clause (i) or (ii) above, which, singly or in the aggregate, would not have a
Material Adverse Effect. To the best of the Issuers' knowledge, no collective
bargaining organizing activities are taking place with respect to either Issuer,
which, singly or in the aggregate, would have a Material Adverse Effect.

         SECTION 3.18. Accounting Controls. Each Issuer maintains a system of
internal accounting controls sufficient to provide reasonable assurance that (i)
transactions are executed in accordance with management's general or specific
authorizations, (ii) transactions are recorded as necessary to permit
preparation of financial statements in conformity with generally accepted
accounting principles and to maintain asset accountability, (iii) access to
assets is permitted only in accordance with management's general or specific
authorization, and (iv) the recorded accountability for assets is compared with
the existing assets at reasonable intervals and appropriate action is taken with
respect to any differences.

         SECTION 3.19. Intellectual Property. Except as otherwise set forth in
the Parent 34 Act Reports, Parent and its subsidiaries own or possess, or can
acquire on reasonable terms, all patents, patent rights, licenses, inventions,
copyrights, know-how (including trade secrets and other unpatented and/or
unpatentable proprietary or confidential information, systems or procedures),
trademarks, service marks and trade names ("INTELLECTUAL PROPERTY") currently
employed by them in connection with the business now operated by them, except
where the failure to own or possess or otherwise be able to acquire such
intellectual property would not, singly or in the aggregate, have a Material
Adverse Effect; and, to the best of the Issuers' knowledge, neither Parent nor
any of its subsidiaries has received any notice of infringement of or conflict
with asserted rights of others with respect to any of such intellectual property
which, singly or in the aggregate, if the subject of an unfavorable decision,
ruling or finding, would have a Material Adverse Effect.


                                       11
<PAGE>   16



         SECTION 3.20. Indenture. Prior to the effectiveness of any registration
statement relating to the Notes, the Indenture is not required to be qualified
under the TIA.

         SECTION 3.21. No Registration. No registration under the 1933 Act of
the Securities is required for the sale of the Securities to the Buyers as
contemplated hereby or for exempt resales assuming the accuracy of the Buyers'
representations and warranties and agreements set forth in Article 4.

         SECTION 3.22. Certificates. Each certificate signed by an officer of
any Issuer and delivered to the Buyers or counsel for the Buyers shall be deemed
to be a representation and warranty by such Issuer to the Buyers as to the
matters covered thereby.


                                    ARTICLE 4
                  REPRESENTATIONS AND WARRANTIES OF THE BUYERS

         Each Buyer, severally as to itself and not jointly, represents and
warrants to Parent and the Company as of the Closing Date that:

         SECTION 4.01. Corporate/Partnership Existence and Power. Such Buyer is
a partnership duly organized or a corporation duly incorporated, validly
existing and in good standing under the laws of its jurisdiction of
organization.

         SECTION 4.02. Corporate/Partnership Authorization. The execution,
delivery and performance by such Buyer of the Transaction Documents to which it
is a party and the consummation of the transactions contemplated thereby are
within the powers (corporate, partnership or otherwise) of such Buyer and have
been duly authorized by all necessary action on the part of such Buyer. This
Agreement constitutes (and, when executed and delivered, each other Transaction
Document to which such Buyer is a party will constitute) a valid and binding
agreement of such Buyer.

         SECTION 4.03. Governmental Authorization. The execution, delivery and
performance by such Buyer of the Transaction Documents to which it is a party
and the consummation of the transactions contemplated thereby require no action
by or in respect of, or filing with, any governmental body, agency or official
(other than any filing pursuant to the HSR Act that may be required by a holder
of the Warrants in connection with the exercise of the Warrants).


                                       12
<PAGE>   17


         SECTION 4.04. Noncontravention. The execution, delivery and performance
by such Buyer of the Transaction Documents to which it is a party and the
consummation of the transactions contemplated thereby do not and will not (i)
violate the partnership agreement or certificate of incorporation or bylaws, as
the case may be, of such Buyer, (ii) violate any material indenture, agreement
or mortgage to which such Buyer is a party or by which such Buyer is bound, or
(iii) assuming compliance with the matters referred to in Section 4.03, violate
any applicable material law, rule, regulation, judgment, injunction, order or
decree or require any material consent of any other Person.

         SECTION 4.05. Purchase for Investment. Such Buyer acknowledges that the
Securities have not been registered under the 1933 Act or any state securities
laws and that the purchase and sale of the Securities contemplated hereby is to
be effected pursuant to an exemption from the registration requirements imposed
by such laws. In this regard, such Buyer is purchasing the Securities to be
purchased by it hereunder for its own account and not with a view to, or for
sale in connection with, any distribution thereof in violation of the 1933 Act.
Such Buyer (either alone or together with its advisors) is an "accredited
investor" (as defined in Regulation D under the 1933 Act), has sufficient
knowledge and experience in financial and business matters so as to be capable
of evaluating the merits and risks of its investment in such Securities and is
capable of bearing the economic risks of such investment. Such Buyer has been
given the opportunity to ask questions of, and receive answers from, management
of Parent concerning its investment in the Issuers.

         SECTION 4.06. Litigation. There is no action, suit, investigation or
proceeding pending against, or to the knowledge of such Buyer threatened against
or affecting, such Buyer before any court or arbitrator or any governmental
body, agency or official which in any manner challenges or seeks to prevent,
enjoin, alter or materially delay the Transactions.

         SECTION 4.07. Finders' Fees. There is no investment banker, broker,
finder or other intermediary which has been retained by or is authorized to act
on behalf of such Buyer who might be entitled to any fee or commission from such
Buyer or from Parent or any of its Affiliates upon consummation of the
Transactions.


                                       13
<PAGE>   18



                                    ARTICLE 5
                            COVENANTS OF THE PARTIES

         Each party hereto agrees that:

         SECTION 5.01. Best Efforts; Further Assurances. Subject to the terms
and conditions of this Agreement, such party will use its best efforts to take,
or cause to be taken, all actions and to do, or cause to be done, all things
necessary or desirable under applicable laws and regulations to consummate the
Transactions. Such party agrees to execute and deliver such other documents,
certificates, agreements and other writings and to take such other actions as
may be necessary or desirable in order to consummate or implement expeditiously
the Transactions.

         SECTION 5.02. Certain Filings. The parties hereto shall cooperate with
one another (i) in determining whether any action by or in respect of, or filing
with, any governmental body, agency, official or authority is required, or any
actions, consents, approvals or waivers are required to be obtained from parties
to any material contracts, in connection with the consummation of the
Transactions and (ii) in taking such actions or making any such filings,
furnishing information required in connection therewith and seeking timely to
obtain any such actions, consents, approvals or waivers.

         SECTION 5.03. Public Announcements. The parties agree to consult with
each other before issuing any press release or making any public statement with
respect to any Transaction Document or the Transactions and, except as may be
required by applicable law or any listing agreement with any national securities
exchange, will not issue any such press release or make any such public
statement prior to such consultation.

                                    ARTICLE 6
                              CONDITIONS TO CLOSING

         SECTION 6.01. Conditions to Obligations of each Party. The obligations
of each party to consummate the Closing are subject to the satisfaction of the
following conditions:

                  (a) No provision of any applicable law or regulation and no
         judgment, injunction, order or decree shall prohibit the consummation
         of the Closing.


                                       14
<PAGE>   19


                  (b) No proceeding challenging this Agreement or any of the
         Transactions or seeking to prohibit, alter, prevent or materially delay
         the Closing shall have been instituted by any Person before any court,
         arbitrator or governmental body, agency or official and be pending,
         where, in the reasonable judgment of the Buyers, on the one hand, or
         the Issuers, on the other hand, there is a significant possibility of a
         determination in accordance with the plaintiff's demand.

         SECTION 6.02. Conditions to Obligation of the Buyers. The obligation of
the Buyers to consummate the Closing is subject to the satisfaction of the
following further conditions:

                  (a) (i) The Issuers shall have performed in all material
         respects all of their obligations hereunder required to be performed by
         them on or prior to the Closing Date and (ii) the representations and
         warranties of the Issuers contained in this Agreement and in any
         certificate or other writing delivered by either of them pursuant
         hereto shall be true in all material respects at and as of the Closing
         Date (it being understood that where any such representation and
         warranty already includes a material adverse effect or materiality
         exception, no further materiality exception is to be permitted by this
         Section 6.02(a)(ii)).

                  (b) There shall not be threatened, instituted or pending any
         action or proceeding by any Person before any court or governmental
         authority or agency, domestic or foreign, (i) seeking to restrain,
         prohibit or otherwise interfere with the ownership or operation by
         Parent or any of its Affiliates of all or any material portion of the
         business or assets of Parent or any Subsidiary, or to compel Parent or
         any of its Affiliates to dispose of all or any material portion of such
         businesses or assets, (ii) seeking to impose or confirm limitations on
         the ability of any Buyer or any of its Affiliates effectively to
         exercise full rights of ownership of its Securities or (iii) seeking to
         require divestiture by any Buyer or any of its Affiliates of any of its
         Securities.

                  (c) There shall not be any action taken, or any statute, rule,
         regulation, injunction, order or decree proposed (where, in the
         reasonable judgment of the Buyers, there is a significant possibility
         that such proposal will be enacted), enacted, enforced, promulgated,
         issued or deemed applicable to the purchase of their Securities, by any
         court, government or governmental authority or agency, domestic or
         foreign, that, in the reasonable judgment of any Buyer has a
         significant possibility of, directly


                                       15
<PAGE>   20


         or indirectly, resulting in any of the consequences referred to in
         clauses 6.02(b)(i) through 6.02(b)(iii) above.

                  (d) Each of the Transaction Documents (other than the
         Indenture) shall have been executed and delivered by the parties
         thereto other than the Buyers, the conditions to closing of each of the
         parties to the Transaction Documents (other than the Buyers) as set
         forth in such Transaction Documents shall have been satisfied or waived
         and, assuming due execution and delivery by the Buyers, each such
         Transaction Document shall be in full force and effect.

                  (e) The costs and expenses of the Buyers referred to in
         Section 8.03, shall have been paid by the Issuers.

                  (f) The Buyers shall have received an opinion or opinions of
         Weil, Gotshal & Manges (or other counsel reasonably satisfactory to the
         Buyers), counsel to the Issuers, dated the Closing Date, in form and
         substance reasonably satisfactory to the Buyers. In rendering such
         opinion, such counsel may rely upon certificates of public officers
         and, as to matters of fact, upon certificates of officers of the
         Issuers, copies of which certificates shall be contemporaneously
         delivered to the Buyers.

                  (g) The Buyers shall have received all documents they may
         reasonably request relating to the existence of each Issuer and the
         authority of each Issuer for each of the Transaction Documents, all in
         form and substance reasonably satisfactory to the Buyers.

         SECTION 6.03. Conditions to Obligation of the Issuers. The obligation
of the Issuers to consummate the Closing is subject to the satisfaction of the
following further conditions:

                  (a) (i) The Buyers shall have performed in all material
         respects all of their obligations hereunder required to be performed by
         them at or prior to the Closing Date and (ii) the representations and
         warranties of the Buyers contained in this Agreement and in any
         certificate or other writing delivered by the Buyers pursuant hereto
         shall be true in all material respects at and as of the Closing Date
         (it being understood that where any such representation and warranty
         already includes a material adverse effect or materiality exception, no
         further materiality exception is to be permitted by this Section
         6.03(a)(ii)).

                  (b) There shall not be threatened, instituted or pending any
         action or proceeding by any Person before any court or governmental
         authority or



                                       16
<PAGE>   21



         agency, domestic or foreign, seeking to restrain or prohibit the
         ownership or operation by Parent or its Affiliates of all or any
         material portion of the business or assets of Parent or any Subsidiary,
         or to compel Parent or its Affiliates to dispose of all or any material
         portion of such businesses or assets.

                  (c) There shall not be any action taken, or any statute, rule,
         regulation, injunction, order or decree proposed (where, in the
         reasonable judgment of the Issuers, there is a significant possibility
         that such proposal will be enacted), enacted, enforced, promulgated,
         issued or deemed applicable to the sale of Securities, by any court,
         government or governmental authority or agency, domestic or foreign
         that, in the reasonable judgment of the Issuers has a significant
         possibility of, directly or indirectly, resulting in any of the
         consequences referred to in Section 6.03(b) above.

                  (d) Each of the Transaction Documents (other than the
         Indenture) shall have been executed and delivered by the parties
         thereto other than the Issuers and, assuming due execution and delivery
         by the Issuers, each such Transaction Document shall be in full force
         and effect.

                  (e) The Issuers shall have received all documents they may
         reasonably request relating to the existence of the Buyers and the
         authority of such Persons for each of the Transaction Documents, all in
         form and substance reasonably satisfactory to the Issuers.

                                    ARTICLE 7
                            SURVIVAL; INDEMNIFICATION

         SECTION 7.01. Survival. The covenants, agreements, representations and
warranties of the parties hereto contained in this Agreement or in any
certificate or other writing delivered pursuant hereto or in connection herewith
shall survive the Closing until eighteen months after the Closing Date; provided
that the representations and warranties contained in Sections 3.04, 3.05, 3.08,
and the covenants and agreements set forth in Articles 7 and 8 shall survive
indefinitely. Notwithstanding the preceding sentence, any covenant, agreement,
representation or warranty in respect of which indemnity may be sought under
this Agreement shall survive the time at which it would otherwise terminate
pursuant to the preceding sentence, if notice of the inaccuracy or breach
thereof giving rise to such right of indemnity shall have been given to the
party against whom such indemnity may be sought prior to such time.


                                       17
<PAGE>   22


         SECTION 7.02. Indemnification. (a) Parent and the Company, without
duplication, hereby jointly and severally indemnify each Buyer against and agree
to hold such Buyer harmless from any and all damage, loss, liability and expense
(including, without limitation, reasonable expenses of investigation and
reasonable attorneys' fees and expenses in connection with any action, suit or
proceeding) ("DAMAGES") incurred or suffered by such Buyer arising out of any
misrepresentation or breach of warranty, covenant or agreement made or to be
performed by Parent or the Company pursuant to this Agreement.

         (b) Each Buyer, severally but not jointly, hereby indemnifies Parent
and the Company, without duplication, against and agrees to hold each of them
harmless from any and all Damages incurred or suffered by them arising out of
any misrepresentation or breach of warranty, covenant or agreement made or to be
performed by such Buyer pursuant to this Agreement.

         (c) Any amount paid by Parent, any Subsidiary or the Buyers under
Article 7 will be treated as an adjustment to the Purchase Price unless a Final
Determination causes any such amount not to constitute an adjustment to the
Purchase Price for Federal Tax purposes. In the event of such a Final
Determination, the Buyers, Parent or any Subsidiary, as the case may be, shall
pay an amount that reflects the hypothetical Tax consequences of the receipt or
accrual of such payment, using the maximum statutory rate (or rates, in the case
of an item that affects more than one Tax) applicable to the recipient of such
payment for the relevant year, reflecting for example, the effect of deductions
available for interest paid or accrued and for Taxes such as state and local
income Taxes.

         SECTION 7.03. Procedures. The party seeking indemnification under
Section 7.02 (the "INDEMNIFIED PARTY") agrees to give prompt notice to the party
against whom indemnity is sought (the "INDEMNIFYING PARTY") of the assertion of
any claim, or the commencement of any suit, action or proceeding in respect of
which indemnity may be sought under such Section. The Indemnifying Party may at
the request of the Indemnified Party participate in and control the defense of
any such suit, action or proceeding at its own expense. The Indemnifying Party
shall not be liable under Section 7.02 for any settlement effected without its
consent of any claim, litigation or proceeding in respect of which indemnity may
be sought hereunder.


                                       18
<PAGE>   23

                                    ARTICLE 8
                                  MISCELLANEOUS

         SECTION 8.01. Notices. All notices, requests and other communications
to any party hereunder shall be in writing (including facsimile transmission)
and shall be given,

if to the DLJ Buyers, to:

                  c/o DLJ Merchant Banking Partners II, L.P.
                  277 Park Avenue
                  New York, NY 10172
                  Attention: William F. Dawson, Jr.
                  Fax: (212) 892-7272

                  with a copy to:

                  Davis Polk & Wardwell
                  450 Lexington Avenue
                  New York, NY  10017
                  Attention: Richard D. Truesdell, Jr.
                  Fax: (212) 450-4800

if to the Issuers, to:

                  Thermadyne Holdings Corporation
                  101 South Hanley Road
                  St. Louis, Missouri 63105
                  Attention: Jim Tate or Stephanie Josephson
                  Fax: (314) 746-2374
                       (314) 746-2327

with a copy to:

                  R. Scott Cohen, Esq.
                  Weil, Gotshal & Manges LLP
                  100 Crescent Court
                  Suite 1300
                  Dallas, TX 75201-6950
                  Fax: (214) 746-7777



                                       19
<PAGE>   24


All such notices, requests and other communications shall be deemed received on
the date of receipt by the recipient thereof if received prior to 5 p.m. in the
place of receipt and such day is a business day in the place of receipt.
Otherwise, any such notice, request or communication shall be deemed not to have
been received until the next succeeding business day in the place of receipt.

         SECTION 8.02. Amendments and Waivers. (a) Any provision of this
Agreement may be amended or waived if, but only if, such amendment or waiver is
in writing and is signed, in the case of an amendment, by each party to this
Agreement, or in the case of a waiver, by the party against whom the waiver is
to be effective, provided that the DLJ Buyers agree that DLJ Merchant Banking
Partners II, L.P. may agree to an amendment or waiver on behalf of, and as agent
for, all DLJ Buyers.

         (b) No failure or delay by any party in exercising any right, power or
privilege hereunder shall operate as a waiver thereof nor shall any single or
partial exercise thereof preclude any other or further exercise thereof or the
exercise of any other right, power or privilege. The rights and remedies herein
provided shall be cumulative and not exclusive of any rights or remedies
provided by law.

         SECTION 8.03. Expenses. All costs and expenses incurred in connection
with the Transaction Documents shall be paid by the party incurring such cost or
expense; provided that (i) any costs and expenses (including fees and expenses
of counsel) of each Buyer shall be reimbursed by the Issuers at the Closing and
(ii) all transfer, documentary, sales, use, stamp, registration, value added and
other such Taxes and fees (including any penalties and interest) incurred in
connection with transactions contemplated by this Agreement shall be paid by
Parent when due, and Parent will, at its own expense, file all necessary Tax
returns and other documentation with respect to all such Taxes and fees, and, if
required by applicable law, the Buyers will join in the execution of any such
Tax returns and other documentation.

         SECTION 8.04. Successors and Assigns. The provisions of this Agreement
shall be binding upon and inure to the benefit of the parties hereto and their
respective successors and assigns; provided that no party may assign, delegate
or otherwise transfer any of its rights or obligations under this Agreement
without the consent of each other party hereto.

         SECTION 8.05. Governing Law. This Agreement shall be governed by and
construed in accordance with the law of the State of New York, without regard to
the conflicts of law rules of such state.


                                       20
<PAGE>   25



         SECTION 8.06. Jurisdiction. Except as otherwise expressly provided in
this Agreement, the parties hereto agree that any suit, action or proceeding
seeking to enforce any provision of, or based on any matter arising out of or in
connection with, this Agreement or the transactions contemplated hereby may be
brought in the United States District Court for the Southern District of New
York or any other New York State court sitting in New York City, and each of the
parties hereby consents to the jurisdiction of such courts (and of the
appropriate appellate courts therefrom) in any such suit, action or proceeding
and irrevocably waives, to the fullest extent permitted by law, any objection
which it may now or hereafter have to the laying of the venue of any such suit,
action or proceeding in any such court or that any such suit, action or
proceeding which is brought in any such court has been brought in an
inconvenient forum. Process in any such suit, action or proceeding may be served
on any party anywhere in the world, whether within or without the jurisdiction
of any such court. Without limiting the foregoing, each party agrees that
service of process on such party as provided in Section 8.01 shall be deemed
effective service of process on such party.

         SECTION 8.07. WAIVER OF JURY TRIAL. EACH OF THE PARTIES HERETO HEREBY
IRREVOCABLY WAIVES ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING
ARISING OUT OF OR RELATED TO THIS AGREEMENT OR THE TRANSACTIONS CONTEMPLATED
HEREBY.

         SECTION 8.08. Counterparts; Third Party Beneficiaries. This Agreement
may be signed in any number of counterparts, each of which shall be an original,
with the same effect as if the signatures thereto and hereto were upon the same
instrument. No provision of this Agreement is intended to confer upon any Person
other than the parties hereto any rights or remedies hereunder.

         SECTION 8.09. Appointment of Agent. Each of the DLJ Buyers hereby
irrevocably constitutes and appoints DLJ Merchant Banking Partners II, L.P. as
its agent and true and lawful attorney in fact with full power and discretion,
in the name of and for and on behalf of each of the DLJ Buyers, in connection
with all matters arising from, contemplated by or relating to the Transaction
Documents. The powers of DLJ Merchant Banking Partners II, L.P. include, without
limitation, the power to represent each of the DLJ Buyers with respect to all
aspects of the Transaction Documents, which power shall include, without
limitation, the power to (i) waive any conditions of the Transaction Documents,
(ii) amend the Transaction Documents in any respect, (iii) receive notices or
other communications, (iv) deliver any notices, certificates or other documents
required and (v) take all such other action and to do all such other things as
DLJ Merchant Banking Partners II, L.P. deems necessary or advisable with respect
to the Transaction Documents. The Issuers shall have the right to rely upon the
acts


                                       21
<PAGE>   26


taken or omitted to be taken by DLJ Merchant Banking Partners II, L.P. on behalf
of the DLJ Buyers, and shall have no duty to inquire as to the acts and
omissions of DLJ Merchant Banking Partners II, L.P.

         SECTION 8.10. Entire Agreement. The Transaction Documents constitute
the entire agreement between the parties with respect to the subject matter of
the Transaction Documents and supersede all prior agreements and understandings,
both oral and written, between the parties with respect to the subject matter of
the Transaction Documents.

         SECTION 8.11. Captions. The captions herein are included for
convenience of reference only and shall be ignored in the construction or
interpretation hereof.

         SECTION 8.12. Enforcement of Voting Rights. In the event that after
December 15, 2004 the Company does not pay interest in cash on four consecutive
Interest Payment Dates (as defined in the Indenture) or on six Interest Payment
Dates, each of the DLJ Buyers agrees to cause, to the extent such DLJ Buyers and
their affiliates shall have the power to cause, two people selected by the
Holders (as defined in the Indenture) of a majority of the Accreted Value (as
defined in the Indenture) of the Notes, voting as a single class, to be elected
to the Board of Directors of Parent. Further, each of the DLJ Buyers agrees to
cause, to the extent such DLJ Buyers shall have the power to cause, such
directors to serve on the Board of Directors of Parent until such time as the
Company pays interest in cash on four consecutive Interest Payment Dates
following their election.


                                       22
<PAGE>   27


         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed by their respective authorized officers as of the day and year
first above written.


                                THERMADYNE HOLDINGS CORPORATION.


                                By: /s/ JAMES H. TATE
                                   -------------------------------------------
                                   Name:     JAMES H. TATE
                                   Title:    SR. VP & CFO

                                THERMADYNE MFG. LLC


                                By: /s/ JAMES H. TATE
                                   -------------------------------------------
                                   Name:     JAMES H. TATE
                                   Title:    SR. VP & CFO


                                DLJ MERCHANT BANKING PARTNERS II, L.P.


                                By: /s/ WILLIAM F. DAWSON, JR.
                                   -------------------------------------------
                                   Name:     William F. Dawson, Jr.
                                   Title:    Principal


                                DLJ MERCHANT BANKING PARTNERS II-A,
                                  L.P.


                                By: /s/ WILLIAM F. DAWSON, JR.
                                   -------------------------------------------
                                   Name:     William F. Dawson, Jr.
                                   Title:    Principal


                                DLJ OFFSHORE PARTNERS II, C.V.


                                By: /s/ WILLIAM F. DAWSON, JR.
                                   -------------------------------------------
                                   Name:     William F. Dawson, Jr.
                                   Title:    Principal




                                       23
<PAGE>   28



                                DLJ DIVERSIFIED PARTNERS, L.P.


                                By: /s/ IVY DODES
                                   --------------------------------------------
                                   Name:     IVY DODES
                                   Title:    Vice President


                                DLJ DIVERSIFIED PARTNERS-A, L.P.


                                By: /s/ IVY DODES
                                   --------------------------------------------
                                   Name:     IVY DODES
                                   Title:    Vice President


                                DLJM FUNDING II, INC.


                                By: /s/ IVY DODES
                                   --------------------------------------------
                                   Name:     IVY DODES
                                   Title:    Vice President


                                DLJ MILLENNIUM PARTNERS, L.P.


                                By: /s/ WILLIAM F. DAWSON, JR.
                                   -------------------------------------------
                                   Name:     William F. Dawson, Jr.
                                   Title:    Principal


                                DLJ MILLENNIUM PARTNERS-A, L.P.


                                By: /s/ WILLIAM F. DAWSON, JR.
                                   -------------------------------------------
                                   Name:     William F. Dawson, Jr.
                                   Title:    Principal


                                DLJ EAB PARTNERS, L.P.


                                By: /s/ IVY DODES
                                   -------------------------------------------
                                   Name:     IVY DODES
                                   Title:    Vice President




                                       24
<PAGE>   29




                                DLJ ESC II L.P.


                                By: /s/ IVY DODES
                                   -------------------------------------------
                                   Name:     IVY DODES
                                   Title:    Vice President


                                DLJ FIRST ESC, L.P.


                                By: /s/ IVY DODES
                                   -------------------------------------------
                                   Name:     IVY DODES
                                   Title:    Vice President





                                       25
<PAGE>   30

                                                                   Schedule 2.01


                     Notes to be Purchased from the Company
                                       and
                      Warrants to be Purchased from Parent


<TABLE>
<CAPTION>

    BUYERS                              SECURITIES                       PURCHASE PRICE
----------------------------------------------------------------------------------------
<S>                             <C>                                      <C>
DLJ Merchant Banking            (1) $15,748,000 Initial Accreted          $15,748,000
Partners II, L.P.               Value of Notes
                                (2) Warrants to purchase 275,255
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJ Merchant Banking            (1) $627,000 Initial Accreted             $   627,000
Partners II-A, L.P.             Value of Notes
                                (2) Warrants to purchase 10,962
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJ Offshore Partners           (1) $774,000 Initial Accreted             $   774,000
II, C.V.                        Value of Notes
                                (2) Warrants to purchase 13,536
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJ Diversified                 (1) $921,000 Initial Accreted             $   921,000
Partners, L.P.                  Value of Notes
                                (2) Warrants to purchase 16,093
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJ Diversified                 (1) $342,000 Initial Accreted             $   342,000
Partners-A, L.P.                Value of Notes
                                (2) Warrants to purchase 5,976
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJMB Funding II, Inc.          (1) $3,212,000 Initial Accreted           $ 3,212,000
                                Value of Notes
                                (2) Warrants to purchase 56,152
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJ Millennium                  (1) $255,000 Initial Accreted             $   255,000
Partners, L.P.                  Value of Notes
                                (2) Warrants to purchase 4,451
                                shares of Common Stock
----------------------------------------------------------------------------------------
</TABLE>


<PAGE>   31



<TABLE>
<CAPTION>

    BUYERS                              SECURITIES                       PURCHASE PRICE
----------------------------------------------------------------------------------------
<S>                             <C>                                       <C>
DLJ Millennium                  (1) $50,000 Initial Accreted Value        $   50,000
Partners-A, L.P.                amount at maturity of Notes
                                (2) Warrants to purchase 868
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJ EAB Partners, L.P.          (1) $71,000 Initial Accreted Value        $   71,000
                                amount at maturity of Notes
                                (2) Warrants to purchase 1,236
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJ ESC II L.P.                 (1) $2,970,000 Initial Accreted           $2,970,000
                                Value of Notes
                                (2) Warrants to purchase 51,906
                                shares of Common Stock
----------------------------------------------------------------------------------------
DLJ First ESC, L.P.             (1) $30,000 Initial Accreted Value        $   30,000
                                of Notes
                                (2) Warrants to purchase 530
                                shares of Common Stock
----------------------------------------------------------------------------------------
----------------------------------------------------------------------------------------
TOTALS                          1) $25,000,000 Initial Accreted           $25,000,000
                                Value of Notes
                                (2) Warrants to purchase 436,965
                                shares of Common Stock
----------------------------------------------------------------------------------------
</TABLE>



<PAGE>   32



                                  Schedule 3.05
<TABLE>
<CAPTION>

NAME                                       JURISDICTION OF ORGANIZATION
----                                       -----------------------------
<S>                                        <C>
Arcair Stoody Europe S.A                   Belgium

BBM Srl*                                   Italy

C&G Systems Holding, Inc.                  Delaware

C&G Systems, Inc.                          Illinois

Canadian Cylinder Company                  Canada

Comet Property Holdings, Inc.              Philippines

Comweld Group Pty. Ltd                     Australia

Comweld Malaysia SDN BHD                   Malaysia

Comweld Philippines Inc.                   Philippines

Coyne Natural Gas Systems, Inc.            Missouri

Duxtech Pty. Ltd.                          Australia

Genset SpA                                 Italy

Marison Cylinder Company                   Delaware

MECO Holding Company                       Delaware

Metalservice SA                            Chile

Modern Engineering Company, Inc.           Missouri

Ocim Srl*                                  Italy

Palco Trading Company*                     Dubai

Philippine Welding Equipment Inc.*         Philippines

PT Thermadyne Utama Indonesia              Indonesia

PT Comweld Indonesia                       Indonesia

Quetack Pty. Ltd                           Australia

Quetala Pty. Ltd.                          Australia

Quetala Unit Trust                         Australia

Soltec SA                                  Chile

Stoody Company                             Delaware

TAG Realty, Inc.                           Texas

Tecmo Srl                                  Italy

Tec. Mo. Cut Srl*                          Italy

Tec. Mo. Control Srl*                      Italy

THC Italia Srl                             Italy

Thermadyne Asia/Pacific PTE Ltd.           Singapore

Thermadyne Asia SDN BHD                    Malaysia
</TABLE>



<PAGE>   33


<TABLE>
<CAPTION>

NAME                                       JURISDICTION OF ORGANIZATION
----                                       ----------------------------
<S>                                        <C>
Thermadyne Australia Pty. Ltd.             Australia

Thermadyne Brazil Holdings, Ltd.           Cayman Islands

Thermadyne Capital Corp.                   Delaware

Thermadyne Chile Holdings, Ltd.            Cayman Islands

Thermadyne Cylinder Company                California

Thermadyne de Brasil S.C. Ltda             Brazil

Thermadyne de Mexico S.A. de C.V           Mexico

Thermadyne Foreign Sales Corporation       Barbados

Thermadyne Hong Kong Limited               Hong Kong

Thermadyne Industries, Inc.                Delaware

Thermadyne Industries Limited              United Kingdom

Thermadyne International Corp.             Delaware

Thermadyne Italia Srl                      Italy

Thermadyne Japan, K.K                      Japan

Thermadyne Korea, Limited                  Korea

Thermadyne Receivables, Inc.               Delaware

Thermadyne South America Holdings, Ltd.    Cayman Islands

Thermadyne Thailand Co. Ltd.*              Thailand

Thermadyne Victor Ltda                     Brazil

Thermadyne Welding Products Canada, Ltd.   Canada

Thermal Arc, Inc.                          Delaware

Thermal Arc Philippines, Inc.              Philippines

Thermal Dynamics Corp.                     Delaware

Tweco Products, Inc.                       Delaware

Victor Coyne International, Inc.           Delaware

Victor Equipment Company                   Delaware

Victor Gas Systems, Inc.                   Delaware

Wichita Warehouse Corp.                    Kansas
</TABLE>


100% of the stock of all domestic subsidiaries are pledged pursuant to the
Credit Agreement.

65% of the stock of all foreign subsidiaries are pledged pursuant to the Credit
Agreement.


*These subsidiaries are not 100% owned.


<PAGE>   34


                                                                       EXHIBIT A



         THIS NOTE IS SUBJECT TO, AND IS TRANSFERABLE ONLY UPON COMPLIANCE WITH,
THE PROVISIONS OF A SUBSCRIPTION AGREEMENT DATED AS OF DECEMBER 22, 1999. COPIES
OF THE ABOVE REFERENCED AGREEMENT ARE ON FILE AT THE OFFICE OF THE COMPANY AT
101 SOUTH HANLEY ROAD, ST. LOUIS, MISSOURI 63105.

         THIS NOTE HAS NOT BEEN REGISTERED UNDER THE U.S. SECURITIES ACT OF
1933, AS AMENDED (THE "SECURITIES ACT"), AND ACCORDINGLY, MAY NOT BE OFFERED OR
SOLD WITHIN THE U.S. OR TO, OR FOR THE ACCOUNT OR BENEFIT OF, U.S. PERSONS
EXCEPT AS SET FORTH IN THE FOLLOWING SENTENCE. BY ITS ACQUISITION HEREOF, THE
HOLDER (1) REPRESENTS THAT (A) IT IS A "QUALIFIED INSTITUTIONAL BUYER" (AS
DEFINED IN RULE 144A UNDER THE SECURITIES ACT), (B) IT IS AN INSTITUTIONAL
"ACCREDITED INVESTOR" (AS DEFINED IN RULE 501 (a)(1), (2), (3) OR (7) OF
REGULATION D UNDER THE SECURITIES ACT) (AN "INSTITUTIONAL ACCREDITED INVESTOR"),
OR (C) IT IS NOT A U.S. PERSON AND IS ACQUIRING THIS NOTE IN AN OFFSHORE
TRANSACTION IN COMPLIANCE WITH REGULATION S UNDER THE SECURITIES ACT, (2) AGREES
THAT IT WILL NOT, WITHIN THE TIME PERIOD REFERRED TO IN RULE 144(k) UNDER THE
SECURITIES ACT AS IN EFFECT ON THE DATE OF THE TRANSFER OF THIS NOTE, RESELL OR
OTHERWISE TRANSFER THIS NOTE EXCEPT (A) TO THE COMPANY OR ANY SUBSIDIARY
THEREOF, (B) TO A QUALIFIED INSTITUTIONAL BUYER IN COMPLIANCE WITH RULE 144A
UNDER THE SECURITIES ACT, (C) INSIDE THE U.S. TO AN INSTITUTIONAL ACCREDITED
INVESTOR THAT, PRIOR TO SUCH TRANSFER, FURNISHES TO THE COMPANY A SIGNED LETTER
CONTAINING CERTAIN REPRESENTATIONS AND AGREEMENTS RELATING TO THE RESTRICTIONS
ON TRANSFER OF THIS NOTE (THE FORM OF WHICH LETTER CAN BE OBTAINED FROM THE
COMPANY), AND IF SUCH TRANSFER IS IN RESPECT OF AN AGGREGATE ACCRETED VALUE OF
NOTES OF LESS THAN $100,000, AN OPINION OF COUNSEL ACCEPTABLE TO THE COMPANY
THAT SUCH TRANSFER IS IN COMPLIANCE WITH THE SECURITIES ACT, (D) OUTSIDE THE
U.S. IN AN OFFSHORE TRANSACTION IN COMPLIANCE WITH RULE 903 OR RULE 904, AS
APPLICABLE, UNDER THE SECURITIES ACT, (E) PURSUANT TO THE EXEMPTION FROM
REGISTRATION PROVIDED BY


<PAGE>   35


RULE 144 UNDER THE SECURITIES ACT (IF AVAILABLE), (F) PURSUANT TO AN EFFECTIVE
REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR (G) PURSUANT TO ANOTHER
EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND IN
ACCORDANCE WITH SECTION 3.14(J) OF THE INDENTURE AND (3) AGREES THAT IT WILL
DELIVER TO EACH PERSON TO WHOM THIS NOTE IS TRANSFERRED A NOTICE SUBSTANTIALLY
TO THE EFFECT OF THIS LEGEND. IN CONNECTION WITH ANY TRANSFER OF THIS NOTE
WITHIN THE TIME PERIOD REFERRED TO ABOVE, THE HOLDER MUST CHECK THE APPROPRIATE
BOX SET FORTH ON THE REVERSE HEREOF RELATING TO THE MANNER OF SUCH TRANSFER AND
SUBMIT THIS CERTIFICATE TO THE COMPANY. IF THE PROPOSED TRANSFEREE IS AN
INSTITUTIONAL ACCREDITED INVESTOR OR A NON-U.S. PERSON THAT, IN EITHER CASE, IS
NOT A QUALIFIED INSTITUTIONAL BUYER, THE HOLDER MUST, PRIOR TO SUCH TRANSFER,
FURNISH TO THE COMPANY SUCH CERTIFICATIONS, LEGAL OPINIONS OR OTHER INFORMATION
AS THE COMPANY MAY REASONABLY REQUIRE TO CONFIRM THAT SUCH TRANSFER IS BEING
MADE PURSUANT TO AN EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE
REGISTRATION REQUIREMENTS OF THE SECURITIES ACT.

         AS USED HEREIN, THE TERMS "OFFSHORE TRANSACTION," "U.S." AND "U.S.
PERSON" HAVE THE MEANINGS GIVEN TO THEM BY REGULATION S UNDER THE SECURITIES
ACT. THE INDENTURE CONTAINS A PROVISION REQUIRING THE COMPANY TO REFUSE TO
REGISTER ANY TRANSFER OF THIS NOTE IN VIOLATION OF THE FOREGOING RESTRICTIONS.

                                      THERMADYNE MFG. LLC.

                                Junior Subordinated Note due 2009


                                                      Initial Accreted Value
No. ___                                               $__________

         THERMADYNE MFG. LLC, a Delaware limited liability company (the
"COMPANY"), which term includes any successor Persons under the Indenture
hereinafter referred to), for value received, promises to pay to __________, or
its registered assigns, the Accreted Value (as defined below) of this Note, on
December 15, 2009.

                                        2

<PAGE>   36



         "ACCRETED VALUE" means with respect to this Note, as of any date of
determination, the sum of: (a) the Accreted Value of such Note on the
immediately preceding Interest Payment Date (in the event such date of
determination falls before the first Interest Payment Date, the "Initial
Accreted Value" specified on the face hereof) plus (b) an amount determined by
multiplying (i) the amount referred to in clause (a) by (ii) 15% (provided that
the accretion rate applicable to any period or portion of a period during which
no interest accrues that occurs after December 15, 2004 shall be 16%) by (iii)
the number of days in the period from and including the preceding Interest
Payment Date to such date of determination divided by 360, less (c) any interest
that accrues with respect to such period in accordance with the terms of the
Note.

Interest Rate:

         Prior to December 15, 2004, unless a Cash Payment Notice (as defined
         below) is properly delivered by the Company, no interest shall accrue
         or be payable with respect to the Notes. If the Company elects to pay
         interest on any Interest Payment Date prior to December 15, 2004, the
         Company shall give written notice (each such notice a "CASH PAYMENT
         NOTICE") of such election to Holders five business days prior to the
         immediately preceding Interest Payment Date. Commencing on such
         immediately preceding Interest Payment Date until such Interest Payment
         Date for which a Cash Payment Notice has been properly delivered,
         interest will accrue and be payable at a rate of 15% per annum to
         Holders of record of the Notes at the close of business on the Regular
         Record Date immediately preceding the Interest Payment Date for which
         such Cash Payment Notice has been properly delivered, whether or not a
         Business Day. Failure to pay interest after proper delivery of a Cash
         Payment Notice for any reason shall not constitute a breach of this
         Note or the Indenture and the Accreted Value shall be determined as if
         such Cash Payment Notice had not been delivered. On or after December
         15, 2004 interest will accrue and be payable at a rate of 15% per annum
         on each Interest Payment Date to Holders of record of the Notes at the
         close of business on the immediately preceding Regular Record Date;
         provided, that if and for so long as payment of interest on the Notes
         is prohibited under the terms of the Credit Agreement (as defined in
         the Indenture) interest shall not accrue or be payable with respect to
         the Notes.

         Interest Payment Dates:    March 15, June 15, September 15 and
                                    December 15 of each year.

         Regular Record Dates:      March 1, June 1, September 1 and
                                    December 1 of each year.

                                        3

<PAGE>   37


         Reference is hereby made to the further provisions of this Note set
forth on the reverse hereof, which further provisions shall for all purposes
have the same effect as if set forth at this place.

         IN WITNESS WHEREOF, the Company has caused this Note to be signed
manually or by facsimile by its duly authorized officers.

         Date: December 22, 1999

                                            THERMADYNE MFG. LLC, as Issuer


                                            By:
                                               --------------------------------
                                               Name:
                                               Title:

                                        4
<PAGE>   38


                               THERMADYNE MFG. LLC

                        Junior Subordinated Note due 2009


         This Note is one of a duly authorized issue of Notes of the Company
consisting of other Junior Subordinated Notes due 2009 of the Company issued on
December 22, 1999 and any replacement Notes issued in exchange for, or in lieu
of, the foregoing in accordance with the Indenture. The Notes are limited in
aggregate principal at maturity to the Accreted Value attributable to
$25,000,000. All of such Notes shall be treated as a single issue and vote
together as one class for all purposes of this Note and the Indenture.

         1. Incorporation by Reference of Provisions of the Indenture.
Capitalized terms used herein and not otherwise defined shall have the meanings
set forth in the Indenture (as amended in accordance herewith, the "INDENTURE")
attached hereto as Exhibit A. At all times during which an indenture is not
required to be qualified under the TIA with respect to the Notes or the
Indenture has not otherwise been executed and delivered, to the extent not
inconsistent with any other terms of the Notes set forth herein, all of the
terms and conditions of the Indenture shall be and are hereby incorporated by
this reference in the Notes as if fully set forth herein, and shall be binding
upon the Company and, by accepting a Note, each Holder, and inure to the benefit
of the Holders of the Notes, except that, to the extent that the Indenture
requires (i) any notices, certificates or other items to be delivered by the
Company to the Trustee or any Paying Agent, such notices, certificates or other
items shall be delivered instead to each Holder, (ii) any notices, certificates
or other items to be delivered to the Trustee shall be delivered instead to the
Company (and shall be delivered by the Company to each Holder), (iii) any
notices, certificates or other items to be delivered by the Trustee to the
Holders, such notices, certificates or other items shall be delivered instead by
the Company to the Holders, (iv) any payments to be made by the Company to the
Trustee or Paying Agent for payment to Holders, such payments shall instead be
paid directly by the Company to the applicable Holder in the same manner as set
forth in Section 3 below, (v) approval of the form of Notes or notations,
legends or endorsements thereon by the Trustee, the Holders of a majority in
outstanding principal amount of the Notes shall instead approve such form and
notations, legends or endorsements (the form of Notes delivered to the initial
Holders on the date of original issuance of the Notes and notations, legends and
endorsements thereon being deemed to have been so approved) , (vi) any Note to
be authenticated by the Trustee or an Authenticating Agent, the Notes shall
instead be authenticated by the Company (the execution and delivery of any Note
by manual signature of the Company to be deemed to constitute such
authentication for all purposes), (vii) that a Person other than the Company and


                                       5
<PAGE>   39


any Affiliate thereof act as Paying Agent for presentation or surrender of Notes
for payment, the Company or any Affiliate thereof may nonetheless so act, (viii)
the Company to initially appoint the Trustee as Registrar or Paying Agent (to
the extent of acting as agent for receiving surrender or presentations of, but
not deposits of payments on, Notes) and agents for service of demands and
notices in connection with the Notes, the Company instead hereby appoints its
office at 101 South Hanley Road, Suite 300, St. Louis, MO 63105 for such purpose
(with Section 4.02 of the Indenture not to apply thereto), (ix) Notes to be
canceled by the Trustee, such Notes shall instead be canceled by the Company,
(x) the Opinions of Counsel to be delivered to the Trustee pursuant to the
Indenture shall instead be delivered to the Holders, (xi) any Notes to be
surrendered or forwarded to the Trustee or any Paying Agent or Registrar, such
Notes shall be surrendered or forwarded instead to the Company, (xii) any
notices, certificates or other items to be delivered by the Holders to the
Registrar or Paying Agent, such notices, certificates or other items shall be
delivered instead to the Company and (xiii) Notes to be redeemed upon a partial
redemption to be selected by the Trustee, such Notes shall be selected instead
by the Company.

         2. Accreted Value and Interest; Subordination. The Company agrees to
pay the Accreted Value of this Note on December 15, 2009.

         The Company agrees to pay interest on the Accreted Value of this Note
at the rate and in the manner specified below.

         "ACCRETED VALUE" means with respect to this Note, as of any date of
determination, the sum of: (a) the Accreted Value of such Note on the
immediately preceding Interest Payment Date (in the event such date of
determination falls before the first Interest Payment Date, the "Initial
Accreted Value" specified on the face hereof) plus (b) an amount determined by
multiplying (i) the amount referred to in clause (a) by (ii) 15% (provided that
the accretion rate applicable to any period or portion of a period during which
no interest accrues on the Notes that occurs after December 15, 2004 shall be
16%) by (iii) the number of days in the period from and including the preceding
Interest Payment Date to such date of determination divided by 360, less (c) any
interest that accrues with respect to such period in accordance with the terms
of the Note.

Interest Rate:

         Prior to December 15, 2004, unless a Cash Payment Notice (as defined
         below) is properly delivered by the Company, no interest shall accrue
         or be payable with respect to the Notes. If the Company elects to pay
         interest on any Interest Payment Date prior to December 15, 2004, the
         Company shall give written notice (each such notice a "CASH PAYMENT
         NOTICE") of such



                                       6
<PAGE>   40


         election to Holders five business days prior to the immediately
         preceding Interest Payment Date. Commencing on such immediately
         preceding Interest Payment Date until such Interest Payment Date for
         which a Cash Payment Notice has been properly delivered, interest will
         accrue and be payable at a rate of 15% per annum to Holders of record
         of the Notes at the close of business on the Regular Record Date
         immediately preceding the Interest Payment Date for which such Cash
         Payment Notice has been properly delivered, whether or not a Business
         Day. Failure to pay interest after proper delivery of a Cash Payment
         Notice for any reason shall not constitute a branch of this Note or the
         Indenture and the Accreted Value shall be determined as if such Cash
         Payment Notice had not been delivered. On or after December 15, 2004
         interest will accrue and be payable at a rate of 15% per annum on each
         Interest Payment Date to Holders of record of the Notes at the close of
         business on the immediately preceding Regular Record Date; provided,
         that if and for so long as payment of interest on the Notes is
         prohibited under the terms of the Credit Agreement (as defined in the
         Indenture) interest shall not accrue or be payable with respect to the
         Notes.

         Interest on this Note will accrue as and to the extent set forth above;
provided that, after December 15, 2004 if there is no failure or delay in the
payment of interest and if this Note is authenticated between a Regular Record
Date and the next succeeding Interest Payment Date, interest shall accrue from
such Interest Payment Date. Interest will be computed on the basis of a 360-day
year of twelve 30-day months.

         The Company shall pay interest on overdue payments of interest and
Accreted Value, to the extent lawful, at a rate per annum equal to 1% per annum
in excess of the rate of interest applicable to the Notes.

         The indebtedness evidenced by the Notes is, to the extent and in the
manner provided in the Indenture, subordinate and junior in right of payment to
the prior payment in full of all Senior Indebtedness and all Senior Subordinated
Indebtedness, and this Note is issued subject to such provisions. Each Holder of
this Note, by accepting the same, agrees to and shall be bound by such
provisions and agrees to take such action as may be necessary or appropriate to
effectuate the subordination as provided in the Indenture.

         3. Method of Payment. The Company will pay interest on the Notes on
each Interest Payment Date for which interest is to be paid to the Persons who
are Holders (as reflected in the Register at the close of business on the
Regular Record Date immediately preceding the Interest Payment Date), in each
case, even if the Note is canceled on registration of transfer or registration
of exchange after



                                       7
<PAGE>   41


such Regular Record Date; provided that, with respect to the payment of Accreted
Value at maturity, the Company will make payment to the Holder that surrenders
this Note to any Paying Agent (which is initially the Company) on or after
December 15, 2009.

         The Company will make all payments hereunder in money of the United
States that at the time of payment is legal tender for payment of public and
private debts. The Company will make all payments hereunder by wire transfer of
immediately available funds to the accounts specified by the Holder hereof or,
if no such account is specified, by mailing a check to the Holder's registered
address. If a payment date is a date other than a Business Day, payment may be
made at that place on the next succeeding day that is a Business Day and no
interest shall accrue for the intervening period.

         4. Paying Agent and Registrar. Initially, the Company will act as
Paying Agent and Registrar. The Company may change any Paying Agent or Registrar
upon written notice to the Holders. The Company, any Subsidiary or any Affiliate
of any of them may act as Paying Agent, Registrar or co-registrar.

         5. Indenture; Limitations. In the event an indenture is required to be
qualified under the Trust Indenture Act of 1939 (U.S. Code Section
77aaa-77bbbb), as amended from time to time (the "TIA"), with respect to the
Notes, or at any time upon the request of Holders of in excess of 25% in
aggregate principal amount of the outstanding Notes, the Company shall, and at
any other time the Company, in its sole discretion, may, appoint a trustee (the
"TRUSTEE") who satisfies the eligibility requirements set forth in Section 7.10
of the Indenture and, in any such event, the Company shall take whatever actions
are necessary to cause an Indenture substantially in the form of Exhibit A
attached hereto to be executed and delivered by the Company and the Trustee and
to be qualified under the TIA. In such event, (i) this Note shall be deemed to
be one of an issue of Notes of the Company issued under the Indenture; (ii) the
terms of the Notes shall be deemed to include those stated in the Indenture and
those made part of the Indenture by reference to the TIA, as amended from time
to time; and (iii) the Notes shall be subject to all such terms. Holders of
Notes are referred to the Indenture and the TIA for a statement of all such
terms. In such event, the Company may require holders of the Notes, and each
Holder by his or her acceptance hereof agrees upon the Company's request, to
surrender to the Trustee all Notes in the form hereof in exchange for
replacement Notes substantially in the form of Exhibit A to the Indenture.

         The Notes are unsecured junior subordinated obligations of the Company.



                                       8
<PAGE>   42


         6. Optional Redemption. The Notes may be redeemed at the option of the
Company, in whole, at any time and from time to time, on and prior to maturity
at the following Redemption Prices (expressed in percentages of the Accreted
Value thereof on the relevant Redemption Date), plus accrued and unpaid
interest, if any, to the Redemption Date (subject to the right of Holders of
record on the relevant Regular Record Date to receive interest due on the
relevant Interest Payment Date); provided that the Company shall not optionally
redeem any Notes except and to the extent permitted by the Credit Agreement,

                  (a) if redeemed prior to December 15, 2004 at a redemption
         price equal to 115% of the Accreted Value of the Notes; and

                  (b) if redeemed during the 12-month period commencing December
         15 of each of the years set forth below:

<TABLE>
<CAPTION>

          YEAR                REDEMPTION PRICE
          ----                ----------------
<S>                                <C>
2004 ....................          107.5%

2005 ....................          105.0%

2006 ....................          102.5%

2007 and thereafter .....            100%
</TABLE>

         Notice of a redemption will be mailed, first-class postage prepaid, at
least 30 days but not more than 60 days before the Redemption Date to each
Holder's registered address. On and after the Redemption Date, interest ceases
to accrue on, and the Accreted Value shall cease to increase with respect to,
Notes or portions of Notes called for redemption, unless the Company defaults in
the payment of the Redemption Price.

         7. Repurchase upon a Change in Control. Upon the occurrence of a Change
in Control, each Holder shall have the right to require that the Company
repurchase such Holder's Notes at a purchase price in cash equal to 101% of the
Accreted Value thereof on the date of purchase, plus, if applicable, accrued and
unpaid interest, if any, to the date of purchase (subject to the right of
Holders of record on the relevant Regular Record Date to receive interest due on
the relevant Interest Payment Date); provided, that the Company shall not be
required to repurchase Notes upon a Change of Control if the Company is unable
to obtain all necessary consents under the Credit Agreement for such repurchase.


                                       9
<PAGE>   43


         8. Denominations; Transfer; Exchange. The Notes are in fully registered
form without coupons, in denominations of $1,000 and any integral multiples of
$1,000. A Holder may register the transfer or exchange of Notes in accordance
with the Indenture. The Company may require a Holder, among other things, to
furnish appropriate endorsements and transfer documents and to pay any taxes and
fees required by law or permitted by the Indenture.

         9. Persons Deemed Owners. A Holder may be treated as the owner of a
Note for all purposes.

         10. Discharge Prior to Redemption or Maturity. If the Company
irrevocably deposits, or causes to be deposited, with a trustee who could
qualify to serve as Trustee under the Indenture money or U.S. Government
Obligations sufficient to pay the then outstanding Accreted Value of and accrued
interest, if any, on the Notes (a) to redemption or maturity, the Company will
be discharged from the Indenture and the Notes, except in certain circumstances
for certain sections thereof, and (b) to redemption or maturity, the Company
will be discharged from certain covenants set forth in the Indenture.

         11. Amendment; Supplement; Waiver. Subject to certain exceptions, the
Indenture or the Notes may be amended or supplemented with the consent of the
Holders of at least a majority in aggregate Accreted Value of the Notes then
Outstanding. Without notice to or the consent of any Holder, the Company may
amend the Indenture or the Notes to the extent set forth in the Indenture.

         12. Restrictive Covenants. The Indenture contains certain covenants,
including, without limitation, covenants with respect to the following matters:
(i) redemption of or payments on Junior Securities and Parity Securities; (ii)
dividends on Junior Securities; (iii) transactions with Affiliates; and (iv)
repurchase of Notes upon a Change in Control. Within 120 days after the end of
each fiscal year, the Company must report to the Holders on compliance with such
limitations.

         13. Voting. The Subscription Agreement dated as of December 22, 1999
relating to the initial purchase of this Note provides that in the event that
after December 15, 2004 the Company does not pay interest in cash on four
consecutive Interest Payment Dates or on six Interest Payment Dates, the
Principal and its affiliates who are signatories to the Subscription Agreement
shall cause, to the extent that they shall have the power to so cause, two
members selected by the Holders of a majority of the Accreted Value of the
Notes, voting as a single class, to be elected to the Board of Directors of
Parent. Further, the Principal and such affiliates shall cause, to the extent
that they shall have the power to so cause, such directors to serve on the Board
of Directors until such time as the Company pays


                                       10
<PAGE>   44


interest in cash on four consecutive Interest Payment Dates following their
election.

         14. Successor Persons. When a successor person or other entity (other
than a Subsidiary of the Company) assumes all the obligations of its predecessor
under the Notes and the Indenture, the predecessor person will be released from
those obligations.

         15. Abbreviations. Customary abbreviations may be used in the name of a
Holder or an assignee, such as: TEN COM (= tenants in common), TEN ENT (=
tenants by the entireties), JT TEN (= joint tenants with right of survivorship
and not as tenants in common), CUST (= Custodian) and U/G/M/A (= Uniform Gifts
to Minors Act).

         16. Provisions of Indenture. Each Holder, by accepting a Note, agrees,
subject to Section 1 above, to be bound by all of the terms and provisions of
the Indenture, as the same may be amended from time to time.

         17. Notices. Any notices or other communications required or permitted
hereunder shall be in writing, and shall be sufficiently given if made by hand
delivery, by commercial courier service, by telex, by telecopier or registered
or certified mail, postage prepaid, return receipt requested, addressed as
follows:

         if to the Company:

         Thermadyne Holdings Corporation
         101 South Hanley Road
         St. Louis, Missouri 63105
         Facsimile No: (314) 746-2374
                       (314) 746-2327
         Attn: Jim Tate or Stephanie Josephson

with a copy to:

                  R. Scott Cohen, Esq.
                  Weil, Gotshal & Manges LLP
                  100 Crescent Court
                  Suite 1300
                  Dallas, TX 75201-6950
                  Fax: (214) 746-7777



                                       11
<PAGE>   45


         Any notice required to be given to a Holder shall be deemed to have
been given upon the mailing by first class mail, postage prepaid, of such
notices to Holders at their registered address as recorded in the Register and
shall be sufficiently given to a Holder if so mailed within the time prescribed.

         In any case where notice to Holders is given by mail, neither the
failure to mail such notice nor any defect in any notice so mailed to any
particular Holder shall affect the sufficiency of such notice with respect to
other Holders. If a notice or communication is mailed in the manner provided
above, it is duly given, whether or not the addressee receives it.


                                       12
<PAGE>   46


                            [FORM OF TRANSFER NOTICE]



         FOR VALUE RECEIVED the undersigned registered holder hereby sell(s),
assign(s) and transfer(s) unto

Insert Taxpayer Identification No.



--------------------------------------------------------------------------------
(Please print or typewrite name and address including zip code of assignee)



--------------------------------------------------------------------------------
the within Note and all rights thereunder, hereby irrevocably constituting
and appointing



--------------------------------------------------------------------------------
attorney to transfer such Note on the books of the Company with full power of
substitution in the premises.


                                       13
<PAGE>   47


         In connection with any transfer of this Note occurring prior to the
Resale Restriction Termination Date for this Note, the undersigned confirms that
without utilizing any general solicitation or general advertising that:

                                    Check One

         (a) [ ] this Note is being transferred in compliance with the exemption
from registration under the Securities Act of 1933, as amended, provided by Rule
144A thereunder.

                                       or

         (b) [ ] this Note is being transferred other than in accordance with
(a) above and documents are being furnished which comply with the conditions of
transfer set forth in this Note and the Indenture.

         If none of the foregoing boxes is checked, the Company shall not be
obligated to register this Note in the name of any Person other than the Holder
hereof unless and until the conditions to any such transfer of registration set
forth herein and in Section 3.10 of the Indenture shall have been satisfied.

Date:
     ------------------------


----------------------------

                    NOTICE: The signature to this assignment must correspond
                    with the name as written upon the face of the
                    within-mentioned instrument in every particular, without
                    alteration or any change whatsoever.

Signature Guarantee:
                    ----------------------------------------------


         Signatures must be guaranteed by an "ELIGIBLE GUARANTOR INSTITUTION"
meeting the requirements of the Company, which requirements include membership
or participation in the Security Transfer Agent Medallion Program ("STAMP") or
such other "SIGNATURE GUARANTEE PROGRAM" as may be determined by the Company in
addition to, or in substitution for, STAMP, all in accordance with the
Securities Exchange Act of 1934, as amended.




                                       14
<PAGE>   48


              TO BE COMPLETED BY PURCHASER IF (a) ABOVE IS CHECKED.

         The undersigned represents and warrants that it is purchasing this Note
for its own account or an account with respect to which it exercises sole
investment discretion and that it and any such account is a "QUALIFIED
INSTITUTIONAL BUYER" within the meaning of Rule 144A under the Securities Act of
1933, as amended, and is aware that the sale to it is being made in reliance on
Rule 144A and acknowledges that it has received such information regarding the
Company as the undersigned has requested pursuant to Rule 144A or has determined
not to request such information and that it is aware that the transferor is
relying upon the undersigned's foregoing representations in order to claim the
exemption from registration provided by Rule 144A.

Dated:
      -------------------------


-----------------------------------------


                     To be executed by an executive officer



                                       15
<PAGE>   49



                       OPTION OF HOLDER TO ELECT PURCHASE


         If you wish to have this Note purchased by the Company pursuant to
Section 4.10 of the Indenture, check the box: [ ]

         If you wish to have a portion of this Note purchased by the Company
pursuant to 4.10 of the Indenture, state the amount (in Accreted Value) below:

                  $---------------------.


Date:
     ------------------------


Your Signature:
               ---------------------------


(Sign exactly as your name appears on the other side of this Note)


Signature Guarantee:
                    ----------------------------


         Signatures must be guaranteed by an "ELIGIBLE GUARANTOR INSTITUTION"
meeting the requirements of the Registrar, which requirements include membership
or participation in the Security Transfer Agent Medallion Program ("STAMP") or
such other "SIGNATURE GUARANTEE PROGRAM" as may be determined by the Registrar
in addition to, or in substitution for, STAMP, all in accordance with the
Securities Exchange Act of 1934, as amended.
<PAGE>   50


                                   EXHIBIT A

                               Form of Indenture

                               [see Exhibit 4.13]
<PAGE>   51


                                                                       EXHIBIT B

                         Registration Rights Agreement

                               [see Exhibit 4.12]
<PAGE>   52
                                                                       EXHIBIT C


                         THERMADYNE HOLDINGS CORPORATION



                      WARRANT FOR THE PURCHASE OF SHARES OF
                         THERMADYNE HOLDINGS CORPORATION


NO. ___                                                      WARRANT TO PURCHASE
                                                                 _____ SHARES OF
                                                                    COMMON STOCK




               THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
               1933, AS AMENDED, OR ANY STATE SECURITIES LAWS AND MAY NOT BE
               OFFERED OR SOLD EXCEPT IN COMPLIANCE THEREWITH.




         FOR VALUE RECEIVED, THERMADYNE HOLDINGS CORPORATION, a Delaware
corporation (the "COMPANY"), hereby certifies that __________, its successor or
permitted assigns (the "HOLDER"), is entitled, subject to the provisions of this
Warrant, to purchase from the Company, at the times specified herein, __________
fully paid and non-assessable shares of Common Stock of the Company, par value
$0.01 per share (the "WARRANT SHARES"), at a purchase price per share equal to
the Exercise Price (as hereinafter defined). The number of Warrant Shares to be
received upon the exercise of this Warrant and the price to be paid for a
Warrant Share are subject to adjustment from time to time as hereinafter set
forth.

         (a) DEFINITIONS.

         The following terms, as used herein, have the following meanings:

         "AFFILIATE" shall have the meaning given to such term in Rule 12b-2
promulgated under the Securities and Exchange Act of 1934, as amended.

<PAGE>   53

         "BUSINESS DAY" means any day except a Saturday, Sunday or other day on
which commercial banks in the City of New York are authorized by law to close.

         "COMMON STOCK" means the Common Stock, par value $0.01 per share, of
the Company or any other security for which this Warrant may be exercised
pursuant to paragraph (i) hereof after the occurrence of any of the transactions
described in such paragraph.

         "EXERCISE PRICE" means $0.01 per Warrant Share, such Exercise Price to
be adjusted from time to time as provided herein.

         "EXPIRATION DATE" means December 15, 2009 at 5:00 p.m. New York City
time.

         "FAIR MARKET VALUE" means, with respect to one share of Common Stock on
any date, the Current Market Price Per Common Share as defined in paragraph
(h)(3) hereof.

         "PERSON" means an individual, partnership, corporation, limited
liability company, association, trust, or other entity or organization,
including a government or political subdivision or an agency or instrumentality
thereof.

         "PRINCIPAL HOLDERS" means, on any date, the Holders of at least 50% of
the Warrants.

         "SUBSCRIPTION AGREEMENT" means the Subscription Agreement dated as of
the date hereof between the Company, Thermadyne Mfg. LLC and the investors party
thereto.

         "WARRANTS" means the Warrants issued pursuant to the Subscription
Agreement.

         (b) EXERCISE OF WARRANT.

                           (1) The Holder is entitled to exercise this Warrant
                  in whole or in part at any time, or from time to time, until
                  the Expiration Date or, if such day is not a Business Day,
                  then on the next succeeding day that shall be a Business Day.
                  To exercise this Warrant, the Holder shall execute and deliver
                  to the Company a Warrant Exercise Notice substantially in the
                  form annexed hereto. No earlier than ten days after delivery
                  of the Warrant Exercise Notice, the Holder shall deliver to
                  the Company this Warrant Certificate duly executed by the
                  Holder, together with payment of

                                        2

<PAGE>   54



                  the applicable Exercise Price. Upon such delivery and payment,
                  the Holder shall be deemed to be the holder of record of the
                  Warrant Shares subject to such exercise, notwithstanding that
                  the stock transfer books of the Company shall then be closed
                  or that certificates representing such Warrant Shares shall
                  not then be actually delivered to the Holder. Notwithstanding
                  anything herein to the contrary, in lieu of payment in cash of
                  the applicable Exercise Price, the Holder may elect (i) to
                  receive upon exercise of this Warrant, the number of Warrant
                  Shares reduced by a number of shares of Common Stock having
                  the aggregate Fair Market Value equal to the aggregate
                  Exercise Price for the Warrant Shares, (ii) to deliver as
                  payment, in whole or in part of the aggregate Exercise Price,
                  shares of Common Stock having the aggregate Fair Market Value
                  equal to the applicable portion of the aggregate Exercise
                  Price for the Warrant Shares or (iii) to deliver as payment,
                  in whole or in part of the aggregate Exercise Price, such
                  number of Warrants which, if exercised, would result in a
                  number of shares of Common Stock having an aggregate Fair
                  Market Value equal to the applicable portion of the aggregate
                  Exercise Price for the Warrant Shares. Notwithstanding
                  anything to the contrary in this paragraph (b)(1), if the
                  aggregate Fair Market Value of the Common Stock applied or
                  delivered pursuant to (i), (ii) or (iii) above exceeds the
                  aggregate Exercise Price, in no event shall the Holder be
                  entitled to receive any amounts from the Company.

                           (2) The Exercise Price may be paid in cash or by
                  certified or official bank check or bank cashier's check
                  payable to the order of the Company or by any combination of
                  such cash or check. The Company shall pay any and all
                  documentary, stamp or similar issue or transfer taxes payable
                  in respect of the issue or delivery of the Warrant Shares.

                           (3) If the Holder exercises this Warrant in part,
                  this Warrant Certificate shall be surrendered by the Holder to
                  the Company and a new Warrant Certificate of the same tenor
                  and for the unexercised number of Warrant Shares shall be
                  executed by the Company. The Company shall register the new
                  Warrant Certificate in the name of the Holder or in such name
                  or names of its transferee pursuant to paragraph (f) hereof as
                  may be directed in writing by the Holder and deliver the new
                  Warrant Certificate to the Person or Persons entitled to
                  receive the same.


                                        3

<PAGE>   55



                           (4) Upon surrender of this Warrant Certificate in
                  conformity with the foregoing provisions, the Company shall
                  transfer to the Holder of this Warrant Certificate appropriate
                  evidence of ownership of the shares of Common Stock or other
                  securities or property (including any money) to which the
                  Holder is entitled, registered or otherwise placed in, or
                  payable to the order of, the name or names of the Holder or
                  such transferee as may be directed in writing by the Holder,
                  and shall deliver such evidence of ownership and any other
                  securities or property (including any money) to the Person or
                  Persons entitled to receive the same, together with an amount
                  in cash in lieu of any fraction of a share as provided in
                  paragraph (e) below.

         (c) RESTRICTIVE LEGEND. Certificates representing shares of Common
Stock issued pursuant to this Warrant shall bear a legend substantially in the
form of the legend set forth on the first page of this Warrant Certificate to
the extent that and for so long as such legend is applicable.

         (d) RESERVATION OF SHARES. The Company hereby agrees that at all times
it shall reserve for issuance and delivery upon exercise of this Warrant such
number of its authorized but unissued shares of Common Stock or other securities
of the Company from time to time issuable upon exercise of this Warrant as will
be sufficient to permit the exercise in full of this Warrant. All such shares
shall be duly authorized and, when issued upon such exercise, shall be validly
issued, fully paid and non-assessable, free and clear of all liens, security
interests, charges and other encumbrances or restrictions on sale and free and
clear of all preemptive rights.

         (e) FRACTIONAL SHARES. No fractional shares or scrip representing
fractional shares shall be issued upon the exercise of this Warrant and in lieu
of delivery of any such fractional share upon any exercise hereof, the Company
shall pay to the Holder an amount in cash equal to such fraction multiplied by
the Current Market Price Per Common Share (as defined in paragraph (h)(3)) at
the date of such exercise.

         The Company further agrees that it will not change the par value of the
Common Stock from par value $0.01 per share to any higher par value which
exceeds the Exercise Price then in effect, and will reduce the par value of the
Common Stock upon any event described in paragraph (h) that would, but for this
provision, reduce the Exercise Price below the par value of the Common Stock.



                                        4

<PAGE>   56



         (f) EXCHANGE, TRANSFER OR ASSIGNMENT OF WARRANT.

                           (1) This Warrant and the Warrant Shares are subject
                  to the provisions of a Registration Rights Agreement dated as
                  of December 22, 1999. Each holder of this Warrant Certificate
                  by holding the same, consents and agrees that the registered
                  holder hereof may be treated by the Company and all other
                  persons dealing with this Warrant Certificate as the absolute
                  owner hereof for any purpose and as the person entitled to
                  exercise the rights represented hereby. The Holder, by its
                  acceptance of this Warrant, will be subject to the provisions
                  of, and will have the benefits of, the Registration Rights
                  Agreement.

                           (2) Upon surrender of this Warrant to the Company,
                  together with the attached Warrant Assignment Form duly
                  executed, the Company shall, without charge, execute and
                  deliver a new Warrant in the name of the assignee or assignees
                  named in such instrument of assignment (and, if the Holder's
                  entire interest is not being assigned, in the name of the
                  Holder) and this Warrant shall promptly be cancelled.

         (g) LOSS OR DESTRUCTION OF WARRANT. Upon receipt by the Company of
evidence satisfactory to it (in the exercise of its reasonable discretion) of
the loss, theft, destruction or mutilation of this Warrant Certificate, and (in
the case of loss, theft or destruction) of reasonably satisfactory
indemnification, and upon surrender and cancellation of this Warrant
Certificate, if mutilated, the Company shall execute and deliver a new Warrant
Certificate of like tenor and date.

         (h) ANTI-DILUTION PROVISIONS. The Exercise Price of this Warrant and
the number of shares of Common Stock for which this Warrant may be exercised
shall be subject to adjustment from time to time upon the occurrence of certain
events as provided in this paragraph (h); provided that notwithstanding anything
to the contrary contained herein, the Exercise Price shall not be less than the
par value of the Common Stock, as such par value may be reduced from time to
time in accordance with paragraph (e).

                           (1) In case the Company shall at any time after the
                  date hereof (i) declare a dividend or make a distribution on
                  Common Stock payable in Common Stock, (ii) subdivide or split
                  the outstanding Common Stock, (iii) combine or reclassify the
                  outstanding Common Stock into a smaller number of shares, or
                  (iv) issue any shares of its capital stock in a
                  reclassification of



                                        5

<PAGE>   57



                  Common Stock (including any such reclassification in
                  connection with a consolidation or merger in which the Company
                  is the surviving corporation), the Exercise Price in effect at
                  the time of the record date for such dividend or distribution
                  or of the effective date of such subdivision, split,
                  combination or reclassification shall be proportionately
                  adjusted so that, after giving effect to paragraph (h)(5), the
                  exercise of this Warrant after such time shall entitle the
                  holder to receive the aggregate number of shares of Common
                  Stock or other securities of the Company (or shares of any
                  security into which such shares of Common Stock have been
                  reclassified pursuant to clause (iii) or (iv) above) which, if
                  this Warrant had been exercised immediately prior to such
                  time, such holder would have owned upon such exercise and been
                  entitled to receive by virtue of such dividend, distribution,
                  subdivision, split, combination or reclassification. Such
                  adjustment shall be made successively whenever any event
                  listed above shall occur.

                           (2) In case the Company shall fix a record date for
                  the making of a distribution to holders of Common Stock
                  (including any such distribution made in connection with a
                  consolidation or merger in which the Company is the surviving
                  corporation) of evidences of indebtedness, cash, assets or
                  other property (other than dividends payable in Common Stock),
                  the Exercise Price to be in effect after such record date
                  shall be determined by multiplying the Exercise Price in
                  effect immediately prior to such record date by a fraction,
                  the numerator of which shall be the Current Market Price Per
                  Common Share on such record date, less the fair market value
                  (determined as set forth below) of the portion of the
                  evidences of indebtedness, cash, assets or other property so
                  to be distributed which is applicable to one share of Common
                  Stock, and the denominator of which shall be such Current
                  Market Price Per Common Share. Such adjustments shall be made
                  successively whenever such a record date is fixed; and in the
                  event that such distribution is not so made, the Exercise
                  Price shall again be adjusted to be the Exercise Price which
                  would then be in effect if such record date had not been
                  fixed. The fair market value of any such evidences of
                  indebtedness, assets or other property shall be determined by
                  the Board of Directors of the Company; provided that if the
                  Principal Holders shall object to any such determination, the
                  Board of Directors shall retain an independent appraiser
                  reasonably satisfactory to the Principal Holders to determine
                  such fair market value. The Holder shall be notified promptly
                  of any



                                        6

<PAGE>   58



                  such distribution and furnished with a description and the
                  fair market value thereof, as determined by the Board of
                  Directors.

                           (3) For the purpose of any computation under
                  paragraph (e) or paragraph (h)(2) hereof, on any determination
                  date, the Current Market Price Per Common Share shall be
                  deemed to be the average (weighted by daily trading volume) of
                  the Daily Prices (as defined below) per share of the Common
                  Stock for the 20 consecutive trading days ending three days
                  prior to such date. "DAILY PRICE" means (1) if the shares of
                  Common Stock then are listed and traded on the New York Stock
                  Exchange, Inc. ("NYSE"), the closing price on such day as
                  reported on the NYSE Composite Transactions Tape; (2) if the
                  shares of Common Stock then are not listed and traded on the
                  NYSE, the closing price on such day as reported by the
                  principal national securities exchange on which the shares are
                  listed and traded; (3) if the shares of Common Stock then are
                  not listed and traded on any such securities exchange, the
                  last reported sale price on such day on the National Market of
                  the National Association of Securities Dealers, Inc. Automated
                  Quotation System ("NASDAQ"); (4) if the shares of Common Stock
                  then are not listed and traded on any such securities exchange
                  and not traded on the NASDAQ National Market, the average of
                  the highest reported bid and lowest reported asked price on
                  such day as reported by NASDAQ; or (5) if such shares are not
                  listed and traded on any such securities exchange, not traded
                  on the NASDAQ National Market and bid and asked prices are not
                  reported by NASDAQ, then the average of the closing bid and
                  asked prices, as reported by The Wall Street Journal for the
                  over-the-counter market. If on any determination date the
                  shares of Common Stock are not quoted by any such
                  organization, the Current Market Price Per Common Share shall
                  be the fair market value of such shares on such determination
                  date as determined by the Board of Directors, without regard
                  to considerations of the lack of liquidity or applicable
                  regulatory restrictions. If the Principal Holders shall object
                  to any determination by the Board of Directors of the Current
                  Market Price Per Common Share, the Current Market Price Per
                  Common Share shall be the fair market value per share of
                  Common Stock as determined by an independent appraiser
                  retained by the Company and reasonably acceptable to the
                  Principal Holders. The expenses of such independent appraiser
                  shall be paid by (x) the Principal Holders, if the fair market
                  value determined by such appraiser is less than that
                  determined by the Board of Directors, and otherwise



                                                7

<PAGE>   59


                  (y) by the Company. For purposes of any computation under this
                  paragraph (h), the number of shares of Common Stock
                  outstanding at any given time shall not include shares owned
                  or held by or for the account of the Company or its
                  subsidiaries.

                           (4) In the event that, at any time as a result of the
                  provisions of this paragraph (h), the holder of this Warrant
                  upon subsequent exercise shall become entitled to receive any
                  shares of capital stock or other securities of the Company
                  other than Common Stock, the number of such other shares so
                  receivable upon exercise of this Warrant shall thereafter be
                  subject to adjustment from time to time in a manner and on
                  terms as nearly equivalent as practicable to the provisions
                  contained herein.

                           (5) Upon each adjustment of the Exercise Price as a
                  result of the calculations made in paragraphs (h)(1) or (h)(2)
                  hereof, the number of shares for which this Warrant is
                  exercisable immediately prior to the making of such adjustment
                  shall thereafter evidence the right to purchase, at the
                  adjusted Exercise Price, that number of shares of Common Stock
                  obtained by (i) multiplying the number of shares covered by
                  this Warrant immediately prior to this adjustment of the
                  number of shares by the Exercise Price in effect immediately
                  prior to such adjustment of the Exercise Price and (ii)
                  dividing the product so obtained by the Exercise Price in
                  effect immediately after such adjustment of the Exercise
                  Price.

                           (6) The Company shall notify all Holders of the
                  fixing of a record date for the purpose of payment of a cash
                  dividend to holders of Common Stock as soon as reasonably
                  practicable, but in no event less than 20 days prior to any
                  such record date.

                           (7) Not less than 10 nor more than 30 days prior to
                  the record date or effective date, as the case may be, of any
                  action which requires or might require an adjustment or
                  readjustment pursuant to this paragraph (h), the Company shall
                  forthwith file in the custody of the secretary or any
                  assistant secretary at its principal executive office and with
                  its stock transfer agent or its warrant agent, if any, an
                  officers' certificate showing the adjusted Exercise Price
                  determined as herein provided, setting forth in reasonable
                  detail the facts requiring such adjustment and the manner of
                  computing such adjustment. Each such officers' certificate
                  shall be signed by the chairman, president or chief financial
                  officer of the Company and by the secretary or any



                                        8

<PAGE>   60



                  assistant secretary of the Company. Each such officers'
                  certificate shall be made available at all reasonable times
                  for inspection by the Holder or any holder of a Warrant
                  executed and delivered pursuant to paragraph (f) and the
                  Company shall, forthwith after each such adjustment, mail a
                  copy, by first-class mail, of such certificate to the Holder.

                           (8) The Holder shall, at its option, be entitled to
                  receive, in lieu of the adjustment pursuant to paragraph
                  (h)(2) otherwise required thereof, on the date of exercise of
                  the Warrants, the evidences of indebtedness, other securities,
                  cash, property or other assets which such Holder would have
                  been entitled to receive if it had exercised its Warrants for
                  shares of Common Stock immediately prior to the record date
                  with respect to such distribution. The Holder may exercise its
                  option under this paragraph (h)(8) by delivering to the
                  Company a written notice of such exercise within seven days of
                  its receipt of the certificate of adjustment required pursuant
                  to paragraph (h)(7) to be delivered by the Company in
                  connection with such distribution.

         (i) CONSOLIDATION, MERGER, OR SALE OF ASSETS. In case of any
consolidation of the Company with, or merger of the Company into, any other
Person, any merger of another Person into the Company (other than a merger which
does not result in any reclassification, conversion, exchange or cancellation of
outstanding shares of Common Stock) or any sale or transfer of all or
substantially all of the assets of the Company or of the Person formed by such
consolidation or resulting from such merger or which acquires such assets, as
the case may be, the Holder shall have the right thereafter to exercise this
Warrant for the kind and amount of securities, cash and other property
receivable upon such consolidation, merger, sale or transfer by a holder of the
number of shares of Common Stock for which this Warrant may have been exercised
immediately prior to such consolidation, merger, sale or transfer, assuming (i)
such holder of Common Stock is not a Person with which the Company consolidated
or into which the Company merged or which merged into the Company or to which
such sale or transfer was made, as the case may be ("CONSTITUENT PERSON"), or an
Affiliate of a constituent Person and (ii) in the case of a consolidation,
merger, sale or transfer which includes an election as to the consideration to
be received by the holders, such holder of Common Stock failed to exercise its
rights of election, as to the kind or amount of securities, cash and other
property receivable upon such consolidation, merger, sale or transfer (provided
that if the kind or amount of securities, cash and other property receivable
upon such consolidation, merger, sale or transfer is not the same for each share
of Common Stock held immediately prior to such consolidation, merger, sale or
transfer by other than a



                                        9

<PAGE>   61


constituent Person or an Affiliate thereof and in respect of which such rights
of election shall not have been exercised ("NON-ELECTING SHARE"), then for the
purpose of this paragraph (i) the kind and amount of securities, cash and other
property receivable upon such consolidation, merger, sale or transfer by each
non-electing share shall be deemed to be the kind and amount so receivable per
share by a plurality of the non-electing shares). Adjustments for events
subsequent to the effective date of such a consolidation, merger and sale of
assets shall be as nearly equivalent as may be practicable to the adjustments
provided for in this Warrant. In any such event, effective provisions shall be
made in the certificate or articles of incorporation of the resulting or
surviving corporation, in any contract of sale, conveyance, lease or transfer,
or otherwise so that the provisions set forth herein for the protection of the
rights of the Holder shall thereafter continue to be applicable; and any such
resulting or surviving corporation shall expressly assume the obligation to
deliver, upon exercise, such shares of stock, other securities, cash and
property. The provisions of this paragraph (i) shall similarly apply to
successive consolidations, mergers, sales, leases or transfers.

         (j) NOTICES. Any notice, demand or delivery authorized by this Warrant
Certificate shall be in writing and shall be given to the Holder or the Company
as the case may be, at its address (or telecopier number) set forth below, or
such other address (or telecopier number) as shall have been furnished to the
party giving or making such notice, demand or delivery:

         If to the Company:         Thermadyne Holdings Corporation
                                    101 South Hanley Road
                                    St. Louis, Missouri 63105
                                    Fax: (314) 746-2374
                                         (314) 746-2327
                                    Attention: Jim Tate or Stephanie Josephson

         If to the Holder:          c/o DLJ Merchant Banking Partners II, L.P.
                                    277 Park Avenue
                                    New York, NY 10172
                                    Telecopy: (212) 892-7272
                                    Attention: William F. Dawson, Jr.


         Each such notice, demand or delivery shall be effective (i) if given by
telecopy, when such telecopy is transmitted to the telecopy number specified
herein and the intended recipient confirms the receipt of such telecopy or (ii)
if given by any other means, when received at the address specified herein.



                                       10

<PAGE>   62



         (k) RIGHTS OF THE HOLDER. Prior to the exercise of any Warrant, the
Holder shall not, by virtue hereof, be entitled to any rights of a shareholder
of the Company, including, without limitation, the right to vote, to receive
dividends or other distributions or to receive any notice of meetings of
shareholders or any notice of any proceedings of the Company except as may be
specifically provided for herein.

         (l) GOVERNING LAW. THIS WARRANT CERTIFICATE AND ALL RIGHTS ARISING
HEREUNDER SHALL BE CONSTRUED AND DETERMINED IN ACCORDANCE WITH THE INTERNAL LAWS
OF THE STATE OF NEW YORK, AND THE PERFORMANCE THEREOF SHALL BE GOVERNED AND
ENFORCED IN ACCORDANCE WITH SUCH LAWS.

         (m) AMENDMENTS; WAIVERS. Any provision of this Warrant Certificate may
be amended or waived if, and only if, such amendment or waiver is in writing and
signed, in the case of an amendment, by the Principal Holders and the Company,
or in the case of a waiver, by the party against whom the waiver is to be
effective. No failure or delay by either party in exercising any right, power or
privilege hereunder shall operate as a waiver thereof nor shall any single or
partial exercise thereof preclude any other or further exercise thereof or the
exercise of any other right, power or privilege. The rights and remedies herein
provided shall be cumulative and not exclusive of any rights or remedies
provided by law.



                                       11

<PAGE>   63



         IN WITNESS WHEREOF, the Company has duly caused this Warrant
Certificate to be signed by its duly authorized officer and to be dated as of
December 22, 1999.


                                THERMADYNE HOLDINGS CORPORATION


                                By:
                                   ------------------------------------
                                   Name:
                                   Title:



Acknowledged and Agreed:

[HOLDER]


By:
   -----------------------------
   Name:
   Title:



<PAGE>   64



                             WARRANT EXERCISE NOTICE




To:      Thermadyne Holding Corporation

         The undersigned hereby notifies you of its intention to exercise the
Warrant to purchase shares of Common Stock, par value $.01 per share, of
Thermadyne Holdings Corporation. The undersigned intends to exercise the Warrant
to purchase ___________ shares (the "SHARES") at $______ per Share (the Exercise
Price currently in effect pursuant to the Warrant). The undersigned intends to
pay the aggregate Exercise Price for the Shares by __________ [specify any
method permitted by paragraph (b) of the Warrant].

Date:
     -----------------


                                     ---------------------------------
                                     (Signature of Owner)


                                     ---------------------------------
                                     (Street Address)


                                     ---------------------------------
                                     (City)   (State)      (Zip Code)







<PAGE>   65
                             WARRANT ASSIGNMENT FORM



                                                    Dated ___________ ___, _____


      FOR VALUE RECEIVED, _______________________ hereby sells, assigns and
transfers unto ______________________________________(the "ASSIGNEE"),
              (please type or print in block letters)

--------------------------------------------------------------------------------
                                (insert address)

its right to purchase up to ______ shares of Common Stock represented by this
Warrant and does hereby irrevocably constitute and appoint __________________
Attorney, to transfer the same on the books of the Company, with full power of
substitution in the premises.



                               Signature:
                                         ----------------------------------