<PAGE>   1
                                                                   EXHIBIT 10.29



                              INVESTORS' AGREEMENT

                                   dated as of

                                  May 22, 1998

                                  by and among

                         THERMADYNE HOLDINGS CORPORATION

                     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.,

                          DLJ MILLENNIUM PARTNERS, L.P.

                         DLJ MILLENNIUM PARTNERS-A, L.P.

                             DLJMB FUNDING II, INC.,

                        UK INVESTMENT PLAN 1997 PARTNERS,

                             DLJ EAB PARTNERS, L.P.,

                              DLJ FIRST ESC, L.P.,

                                DLJ ESC II, L.P.

                   and certain other Stockholders named herein





<PAGE>   2



                                TABLE OF CONTENTS

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

<TABLE>
<CAPTION>
                                                                                             PAGE
                                                                                             ----
<S>            <C>                                                                              <C>

                                            ARTICLE 1
                                           DEFINITIONS

SECTION 1.01.  Definitions......................................................................2

                                            ARTICLE 2
                                      CORPORATE GOVERNANCE

SECTION 2.01.  Composition of the Board........................................................10
SECTION 2.02.  Removal.........................................................................10
SECTION 2.03.  Vacancies.......................................................................11
SECTION 2.04.  Meetings........................................................................11
SECTION 2.05.  Action by the Board.............................................................11
SECTION 2.06.  Conflicting Charter or Bylaw Provisions.........................................11

                                            ARTICLE 3
                                    RESTRICTIONS ON TRANSFER

SECTION 3.01.  General.........................................................................12
SECTION 3.02.  Legends.........................................................................12
SECTION 3.03.  Permitted Transferees...........................................................13
SECTION 3.04.  Restrictions on Transfers by Management Stockholders............................13

                                            ARTICLE 4
                               TAG-ALONG RIGHTS; DRAG-ALONG RIGHTS

SECTION 4.01.  Rights to Participate in Transfer...............................................15
SECTION 4.02.  Right to Compel Participation in Certain Transfers..............................16
SECTION 4.03.  Certain Rights..................................................................18

                                            ARTICLE 5
                                       REGISTRATION RIGHTS

SECTION 5.01.  Demand Registration.............................................................18
SECTION 5.02.  Incidental Registration.........................................................21
SECTION 5.03.  Holdback Agreements.............................................................23
SECTION 5.04.  Registration Procedures.........................................................23
SECTION 5.05.  Indemnification by the Company..................................................26
SECTION 5.06.  Indemnification by Participating Stockholders...................................27
</TABLE>






<PAGE>   3


<TABLE>
<CAPTION>
                                                                                             PAGE
                                                                                             ----
<S>            <C>                                                                              <C>
SECTION 5.07.  Conduct of Indemnification Proceedings..........................................28
SECTION 5.08.  Contribution....................................................................28
SECTION 5.09.  Participation in Public Offering................................................30
SECTION 5.10.  Other Indemnification...........................................................30
SECTION 5.11.  Cooperation by the Company......................................................30

                                            ARTICLE 6
                                          MISCELLANEOUS

SECTION 6.01.  Entire Agreement................................................................31
SECTION 6.02.  Binding Effect; Benefit.........................................................31
SECTION 6.03.  Exclusive Financial and Investment Banking Advisor..............................31
SECTION 6.04.  Assignability...................................................................31
SECTION 6.05.  Amendment; Waiver; Termination..................................................31
SECTION 6.06.  Notices.........................................................................32
SECTION 6.07.  Headings........................................................................33
SECTION 6.08.  Counterparts....................................................................33
SECTION 6.09.  Applicable Law..................................................................33
SECTION 6.10.  Specific Enforcement............................................................33
SECTION 6.11.  Consent to Jurisdiction.........................................................33
</TABLE>






                                       ii
<PAGE>   4



                              INVESTORS' AGREEMENT

         AGREEMENT dated as of May 22, 1998 among (i) Thermadyne Holdings
Corporation, a Delaware corporation (the "COMPANY"), (ii) DLJ Merchant Banking
Partners II, L.P., a Delaware limited partnership, DLJ Offshore Partners II,
C.V. a Netherlands Antilles limited partnership, DLJ Merchant Banking Partners
II-A, L.P., a Delaware limited partnership, DLJ Diversified Partners, L.P., a
Delaware limited partnership, DLJ Diversified Partners-A, L.P., a Delaware
limited partnership, DLJ EAB Partners, L.P., a Delaware limited partnership, DLJ
Millennium Partners, L.P., a Delaware limited partnership, DLJ Millennium
Partners-A, L.P., a Delaware limited partnership, DLJMB Funding II, Inc., a
Delaware corporation, UK Investment Plan 1997 Partners, a Delaware partnership,
DLJ First ESC, L.P., a Delaware limited partnership and DLJ ESC II, L.P., a
Delaware limited partnership, (each of the foregoing, a "DLJ ENTITY", and
collectively, the "DLJ ENTITIES") and (iii) certain other Persons listed on the
signature pages hereof (each a "STOCKHOLDER" and collectively, the "MANAGEMENT
STOCKHOLDERS").


                              W I T N E S S E T H:

         WHEREAS, certain parties hereto have acquired or will be acquiring
securities of Mercury Acquisition Corporation, the predecessor by merger to the
Company, and/or the Company;

         WHEREAS, pursuant to the terms of the Merger Agreement (as defined
below) Mercury Acquisition Corporation has been merged with and into the Company
with the Company as the surviving corporation;

         WHEREAS, the parties hereto desire to enter into this Agreement to
govern certain of their rights, duties and obligations after consummation of the
transactions contemplated by the Merger Agreement;

         NOW, THEREFORE, in consideration of the covenants and agreements
contained herein and in the Merger Agreement, the parties hereto agree as
follows:


<PAGE>   5



                                   ARTICLE 1
                                  DEFINITIONS

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

         "ADVERSE PERSON" means any Person whom the Board of Directors of the
Company determines is a competitor or a potential competitor of the Company or
its subsidiaries.

         "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 stockholder of the Company shall be deemed an
Affiliate of any other stockholder of the Company solely by reason of any
investment in the Company. For the purpose of this definition, the term
"CONTROL" (including with correlative meanings, the terms "CONTROLLING",
"CONTROLLED BY" and "UNDER COMMON CONTROL WITH"), when used with respect to any
Person, means 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, by contract or otherwise.

         "AFFILIATED EMPLOYEE BENEFIT TRUST" means any trust that is a successor
to the assets held by a trust established under an employee benefit plan subject
to ERISA or any other trust established directly or indirectly under such plan
or any other such plan having the same sponsor.

         "AGGREGATE OWNERSHIP" means, with respect to any Stockholder or group
of Stockholders, and with respect to any class of Company Securities, the total
amount of such securities "beneficially owned" (as such term is defined in Rule
13d-3 under the Exchange Act) (without duplication) by such Stockholder or group
of Stockholders as of the date of such calculation (but adjusted in accordance
with the proviso below), calculated on a Fully Diluted basis and taking into
account any stock dividend, stock split or reverse stock split; provided that
such amount of securities shall be increased (without duplication) with respect
to any Other Stockholder, by any stock appreciation rights, options, warrants
(including the Warrants) or other rights to purchase or subscribe for Company
Securities of such Other Stockholder as and when such stock appreciation rights,
options, warrants or other rights have vested.

         "BENCHMARK SECURITIES" means the aggregate number of Common Shares,
Preferred Shares or Warrants sold or proposed to be sold by the DLJ Entities
(other than to their Permitted Transferees) subsequent to the date hereof




                                       2
<PAGE>   6

until the first to occur of (i) the aggregate number of Common Shares, Preferred
Shares or Warrants so sold or proposed to be sold by the DLJ Entities (other
than to their Permitted Transferees) equals 25% of the Initial Ownership of
Common Stock, Preferred Stock or Warrants of the DLJ Entities and (ii) the
aggregate amount in cash (net of any commissions, fees or expenses) collectively
received or to be received by the DLJ Entities, without duplication, as a result
of the sale subsequent to the date hereof or proposed sale of any such Common
Shares, Preferred Shares or Warrants (other than to their Permitted Transferees)
shall equal the aggregate amount invested by the DLJ Entities as of such date in
Common Shares, Preferred Shares or Warrants.

         "BOARD" means the board of directors of the Company.

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

         "BYLAWS" means the Amended and Restated Bylaws of the Company, as
amended from time to time.

         "CHANGE OF CONTROL" means:

                  (a) any "person" (as such term is used in Section 3(a)(9) and
         13(d)(3) of the Exchange Act) other than (A) the DLJ Entities and/or
         their respective Permitted Transferees or (B) any "group" (within the
         meaning of such Section 13(d)(3)) of which the DLJ Entities constitute
         a majority (on the basis of ownership interest), acquires, directly or
         indirectly, by virtue of the consummation of any purchase, merger or
         other combination, securities of the Company representing more than 51%
         of the combined voting power of the Company's then outstanding voting
         securities with respect to matters submitted to a vote of the
         stockholders generally; or

                  (b) a sale or transfer by the Company or any of its
         Subsidiaries of substantially all of the consolidated assets of the
         Company and its Subsidiaries to an entity which is not an Affiliate of
         the Company prior to such sale or transfer.

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

         "COINVESTMENT SHARES" means Shares of the Company purchased under the
Thermadyne Investment Program and designated as Coinvestment Shares.




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<PAGE>   7

         "COMMITTEE" means a committee of the Board designated by the Board to
administer the Plan and composed of not less than the minimum number of persons
from time to time required by Rule 16b-3, each of whom, to the extent necessary
to comply with Rule 16b-3 only, is a "Non-Employee Director" within the meaning
of Rule 16b-3. Until otherwise determined by the Board, the full Board shall be
the Committee under the Plan.

         "CHARTER" means the Amended and Restated Certificate of Incorporation
of the Company, as amended from time to time.

         "CLOSING DATE" means May 22, 1998.

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

         "COMMON STOCK" means the common stock, par value $0.01 per share, of
the Company and any stock into which such Common Stock may thereafter be
converted or changed, and "COMMON SHARES" means shares of Common Stock.

         "COMPANY SECURITIES" means the Common Stock and securities convertible
into or exchangeable for Common Stock, Preferred Stock and options, warrants
(including the Warrants) or other rights to acquire Common Stock, Preferred
Stock or any other equity security issued by the Company.

         "DRAG-ALONG PORTION" means, with respect to any Other Stockholder and
any class of Company Securities, the number of such class of Company Securities
beneficially owned by such Other Stockholder on a Fully Diluted basis (but
without duplication) multiplied by a fraction, the numerator of which is the
number of such class of Company Securities proposed to be sold by the DLJ
Entities on behalf of the DLJ Entities and the Other Stockholders and the
denominator of which is the total number of such class of Company Securities on
a Fully Diluted basis beneficially owned by the Stockholders.

         "ERISA" means the Employee Retirement Income Security Act of 1974,
as amended.

         "EXCHANGE ACT" means the Securities Exchange Act of 1934, as amended.

         "FOUNDING STOCKHOLDER" means either of Randall E. Curran or James H.
Tate.

         "FULLY DILUTED" means, with respect to Common Stock and without
duplication, all outstanding Shares and all Shares issuable in respect of
securities convertible into or exchangeable for Shares, stock appreciation
rights, options,



                                       4
<PAGE>   8



warrants (including the Warrants) and other rights to purchase or subscribe for
Shares or securities convertible into or exchangeable for Common Stock; provided
that, to the extent any of the foregoing stock appreciation rights, options,
warrants or other rights to purchase or subscribe for Shares are subject to
vesting, the Shares subject to vesting shall be included in the definition of
"FULLY DILUTED" only upon and to the extent of such vesting.

         "FIRST PUBLIC OFFERING" means the first sale after the date hereof of
Common Stock pursuant to an effective registration statement under the
Securities Act (other than a registration statement on Form S-8 or any successor
form).

         "INITIAL OWNERSHIP" means, with respect to any Stockholder and any
class of Company Securities, the number of shares of such class of Company
Securities beneficially owned (and (without duplication) which such Persons have
the right to acquire) as of the date hereof, or in the case of any Person that
shall become a party to this Agreement on a later date, as of such date, taking
into account any stock split, stock dividend, reverse stock split or similar
event.

         "OTHER STOCKHOLDERS" means all Stockholders other than the DLJ
Entities, and their respective Permitted Transferees.

         "PERMITTED TRANSFEREE" means:

                           (i) in the case of any DLJ Entity (A) any other DLJ
                  Entity, (B) any general or limited partner of any DLJ Entity
                  (a "DLJ PARTNER"), and any corporation, partnership,
                  Affiliated Employee Benefit Trust or other entity that is an
                  Affiliate of any DLJ Partner (collectively, the "DLJ
                  AFFILIATES"), (C) any managing director, general partner,
                  director, limited partner, officer or employee of any DLJ
                  Entity or of any DLJ Affiliate, or the heirs, executors,
                  administrators, testamentary trustees, legatees or
                  beneficiaries of any of the foregoing persons referred to in
                  this clause (C) (collectively, "DLJ ASSOCIATES"), (D) a trust,
                  the beneficiaries of which, or a corporation, limited
                  liability company or partnership, the stockholders, members or
                  general or limited partners of which, include only DLJ
                  Entities, DLJ Affiliates, DLJ Associates, their spouses or
                  their lineal descendants or (E) a voting trustee for one or
                  more DLJ Entities, DLJ Affiliates or DLJ Associates under the
                  terms of a voting trust designed to conform with the
                  requirements of the Insurance Law of the State of New York;
                  and

                       (ii) in the case of any Other Stockholder (A) any Other
                  Stockholder, (B) a Person to whom Shares are transferred from




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<PAGE>   9


                  such Other Stockholder (1) by will or the laws of descent and
                  distribution or (2) by gift without consideration of any kind;
                  provided that, in the case of clause (2), such transferee is
                  the issue or spouse of such Other Stockholder or (C) a trust
                  that is for the exclusive benefit of such Other Stockholder or
                  its Permitted Transferees under (B) above.

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

         "PREFERRED STOCK" means the 13% senior exchangeable preferred stock,
par value $0.01 per share and due 2010 of the Company, and "PREFERRED SHARES"
means shares of Preferred Stock.

         "PRO RATA PORTION" means the number of Shares a Stockholder holds
(either Purchased Shares or non-Purchased Shares, as the case may be) multiplied
by a fraction, the numerator of which is the number of Shares to be sold by the
DLJ Entities and their Permitted Transferees in a Public Offering and the
denominator of which is the total number of Shares, on a Fully Diluted basis,
held in the aggregate by the DLJ Entities and their Permitted Transferees prior
to such Public Offering.

         "PUBLIC OFFERING" means an underwritten public offering of Registrable
Securities of the Company pursuant to an effective registration statement under
the Securities Act.

         "PURCHASED SHARES" means those shares of Common Stock purchased by a
Management Stockholder on the Closing Date for cash and/or a promissory note
contemplated in the Thermadyne Investment Program.

         "REGISTRABLE SECURITIES" means any Shares or Warrants until (i) a
registration statement covering such Shares or Warrants has been declared
effective by the SEC and such shares have been disposed of pursuant to such
effective registration statement, (ii) such Shares or Warrants are sold under
circumstances in which all of the applicable conditions of Rule 144 are met or
under which they may be sold pursuant to Rule 144(k) or (iii) such Shares or
Warrants are otherwise transferred, the Company has delivered a new certificate
or other evidence of ownership for such Shares or Warrants not bearing the
legend required pursuant to this Agreement and such Shares or Warrants may be
resold without subsequent registration under the Securities Act.






                                       6
<PAGE>   10


         "REGISTRATION EXPENSES" means (i) all registration and filing fees,
(ii) fees and expenses of compliance with securities or blue sky laws (including
reasonable fees and disbursements of counsel in connection with blue sky
qualifications of the Shares or Warrants), (iii) printing expenses, (iv)
internal expenses of the Company (including, without limitation, all salaries
and expenses of its officers and employees performing legal or accounting
duties), (v) reasonable fees and disbursements of counsel for the Company and
customary fees and expenses for independent certified public accountants
retained by the Company (including the expenses of any comfort letters or costs
associated with the delivery by independent certified public accountants of a
comfort letter or comfort letters requested pursuant to Section 5.04(h)), (vi)
the reasonable fees and expenses of any special experts retained by the Company
in connection with such registration, (vii) reasonable fees and expenses of one
counsel for the Stockholders participating in the offering selected (A) by the
DLJ Entities, in the case of any offering in which such entities participate, or
(B) in any other case, by the Other Stockholders holding the majority of Shares
or Warrants to be sold for the account of all Other Stockholders in the
offering, (viii) fees and expenses in connection with any review of underwriting
arrangements by the National Association of Securities Dealers, Inc. (the
"NASD") including fees and expenses of any "QUALIFIED INDEPENDENT UNDERWRITER"
and (ix) fees and disbursements of underwriters customarily paid by issuers or
sellers of securities; but shall not include any underwriting fees, discounts or
commissions attributable to the sale of Registrable Securities, or any
out-of-pocket expenses (except as set forth in clause (vii) above) of the
Stockholders (or the agents who manage their accounts) or any fees and expenses
of underwriter's counsel.

         "RESTRICTION TERMINATION DATE" means the earlier to occur of (a) the
second anniversary of the First Public Offering and (b) the fifth anniversary of
the Closing Date.

         "RULE 144" means Rule 144 and Rule 144A (or any successor provisions)
under the Securities Act.

         "SEC" means the Securities and Exchange Commission.

         "SECURITIES ACT" means the Securities Act of 1933, as amended.

         "SHARES" means shares of Common Stock and shares of Preferred Stock.

         "STOCKHOLDER" means each Person (other than the Company) who shall be a
party to or bound by this Agreement, whether in connection with the execution
and delivery hereof as of the date hereof, pursuant to Section 6.04, or
otherwise, so long as such Person shall (i) beneficially own any Company
Securities, or (ii)



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<PAGE>   11



have any stock appreciation rights, options, warrants or other rights to
purchase or subscribe for Company Securities.

         "SUBJECT SECURITIES" means any Company Securities beneficially owned
by the Management Stockholders.

         "TAG-ALONG PORTION" means

         (i) where the Selling Person is selling Preferred Stock, the number of
shares of Preferred Stock held by the Tagging Person or the Selling Person, as
the case may be, multiplied by a fraction, the numerator of which is the number
of shares of Preferred Stock proposed to be sold in the Tag-Along Sale pursuant
to Section 4.01, and the denominator of which is the aggregate number of shares
of Preferred Stock owned by all Stockholders;

         (ii) where the Selling Person is selling Common Stock, the number of
shares of Common Stock held (or, without duplication, acquirable under the
Warrants) by the Tagging Person or the Selling Person, as the case may be,
multiplied by a fraction, the numerator of which is the number of shares of
Common Stock proposed to be sold in the Tag-Along Sale pursuant to Section 4.01,
and the denominator of which is the aggregate number of shares of Common Stock
on a Fully Diluted basis owned by all Stockholders, and

         (iii) where the Selling Person is selling Warrants, the number of
shares of Common Stock held (or, without duplication, acquirable under the
Warrants) by the Tagging Person or the Selling Person, as the case may be,
multiplied by a fraction the numerator of which is the number of shares of
Common Stock for which the Warrants proposed to be sold in the Tag-Along Sale
pursuant to Section 4.01 are exercisable, and the denominator of which is the
aggregate number of shares of Common Stock on a Fully Diluted basis owned by all
Stockholders,

         provided that where a Tag-Along Right includes the right to sell Common
Stock, any holder of Warrants may, in lieu of exercising Warrants, transfer
Warrants for some or all of that number of shares of Common Stock as would
otherwise have constituted its Tag-Along Portion, in which event the price to be
received with respect to each such Warrant shall be the price per share of
Common Stock applicable to the Tag-Along Offer, less the then applicable
exercise price of the Warrants owned by such holder.

         "THERMADYNE INVESTMENT PROGRAM" means the Thermadyne Holdings
Corporation Direct Investment Program.



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<PAGE>   12



         "THERMADYNE NEW OPTION PROGRAM" means the Thermadyne Holdings
Corporation Management Incentive Plan.

         "THIRD PARTY" means a prospective purchaser of Shares in an
arm's-length transaction from a Stockholder where such purchaser is not a
Permitted Transferee of such Stockholder.

         "WARRANTS" means the warrants issued by the Company to Stockholders for
the purchase of an aggregate of 353,428 shares of Common Stock (subject to
adjustment as provided for herein).

         "WARRANT SHARES" means shares of Common Stock issuable by the Company
upon exercise of the Warrants.

          (b) The term "DLJ ENTITIES", to the extent such entities shall have
transferred any of their Shares to "Permitted Transferees", shall mean the DLJ
Entities and the Permitted Transferees of the DLJ Entities, taken together, and
any right or action that may be taken at the election of the DLJ Entities may be
taken at the election of the DLJ Entities and such Permitted Transferees.

          (c) The term "Other Stockholders", to the extent such stockholders
shall have transferred any of their Shares to "Permitted Transferees", shall
mean the Other Stockholders and the Permitted Transferees of the Other
Stockholders, taken together, and any right or action that may be taken at the
election of the Other Stockholders may be taken at the election of the Other
Stockholders and such Permitted Transferees.

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

<TABLE>
<CAPTION>
                           Term                               Section
                           ----                               -------
<S>                                                           <C> 
                  Applicable Holdback Period                  5.03
                  beneficially own                            1.01(a)
                  Demand Registration                         5.01(e)
                  DLJSC                                       6.03
                  Drag-Along Rights                           4.02(a)
                  Holders                                     5.01(e)
                  Incidental Registration                     5.01(e)
                  Indemnified Party                           5.07
                  Indemnifying Party                          5.07
</TABLE>





                                       9
<PAGE>   13


<TABLE>
<S>                                                           <C>    
                  Independent Director                        2.01(a)
                  Inspectors                                  5.04(g)
                  Maximum Offering Size                       5.01(e)
                  Nominee                                     2.03(a)
                  Records                                     5.04(g)
                  Section 4.01 Response Notice                4.01(a)
                  Section 4.02 Notice                         4.02(a)
                  Section 4.02 Notice Period                  4.02(a)
                  Section 4.02 Sale                           4.02(a)
                  Section 4.02 Sale Price                     4.02(a)
                  Selling Person                              4.01(a)
                  Selling Stockholder                         5.01(e)
                  Tag-Along Notice                            4.01(a)
                  Tag-Along Notice Period                     4.01(a)
                  Tag-Along Offer                             4.01(a)
                  Tag-Along Right                             4.01(a)
                  Tag-Along Sale                              4.01(a)
                  Tagging Person                              4.01(a)
                  transfer                                    3.01(a)
</TABLE>

                                    ARTICLE 2
                              CORPORATE GOVERNANCE

         SECTION 2.01. Composition of the Board. (a) The Board shall consist
initially of seven directors, five of whom will be designated by DLJ Merchant
Banking Partners II, L.P., one of whom will be Randall E. Curran and one of whom
will be James H. Tate, in each case for so long as such person is employed by
the Company; provided that at least one of the directors designated by DLJ
Merchant Banking Partners II, L.P. shall not be either an "Affiliate" or an
"Associate" (as such terms are used within the meaning of Rule 12b-2 under the
Exchange Act) of the DLJ Entities or the Other Stockholders (the "INDEPENDENT
DIRECTOR") and such Independent Director shall be designated by DLJ Merchant
Banking Partners II, L.P. after consultation with the Other Stockholders. The
DLJ Entities shall be permitted at any time to increase the number of directors
from seven to eight and DLJ Merchant Banking Partners II, L.P. shall be
permitted to designate the eighth director.


          (b) Each Stockholder entitled to vote for the election of directors to
the Board agrees that it will vote its Shares or execute written consents, as
the case may be, and take all other necessary action (including causing the
Company to call a special meeting of stockholders) in order to ensure that the
composition of



                                       10
<PAGE>   14


the Board is as set forth in this Section 2.01; provided that the Other
Stockholders shall not be required to vote for the board-designees of the DLJ
Entities if the aggregate number of Common Shares held by the DLJ Entities is
less than 10% of their Initial Ownership of Common Shares.

         SECTION 2.02. Removal. Each Stockholder agrees that if, at any time, it
is then entitled to vote for the removal of directors of the Company, it will
not vote any of its Shares in favor of the removal of any director who shall
have been designated or nominated pursuant to Section 2.01 unless such removal
shall be for cause or the Persons entitled to designate or nominate such
director shall have consented to such removal in writing.

         SECTION 2.03. Vacancies. If, as a result of death, disability,
retirement, resignation, removal (with or without cause) or otherwise, there
shall exist or occur any vacancy of the Board:

         (a) the Person or Persons entitled under Section 2.01 to designate or
nominate such director whose death, disability, retirement, resignation or
removal resulted in such vacancy may designate another individual (the
"NOMINEE") to fill such capacity and serve as a director of the Company; and

         (b) each Stockholder then entitled to vote for the election of the
Nominee as a director of the Company agrees that it will vote its Shares, or
execute a written consent, as the case may be, in order to ensure that the
Nominee is elected to the Board.

         SECTION 2.04.  Meetings.  The Board shall hold a regularly scheduled
meeting at least once every calendar quarter.

         SECTION 2.05. Action by the Board. (a) A quorum of the Board shall
consist of four directors, of whom at least three must be designees of DLJ
Merchant Banking Partners II, L.P.; provided that the DLJ Entities shall have
the right at any time to increase the number of directors necessary to
constitute a quorum of the Board. All actions of the Board shall require the
affirmative vote of at least a majority of the directors present at a duly
convened meeting of the Board at which a quorum is present or the unanimous
written consent of the Board; provided that, in the event there is a vacancy on
the Board and an individual has been nominated to fill such vacancy, the first
order of business shall be to fill such vacancy.

          (b) The Board may create executive, compensation and audit committees,
as well as such other committees as it may determine. The DLJ Entities shall be
entitled to majority representation on any committee created by



                                       11
<PAGE>   15



the Board and, to the extent not prohibited by or inadvisable under applicable
law, the Other Stockholders shall be entitled to at least one representative on
any such committee.

         SECTION 2.06. Conflicting Charter or Bylaw Provisions. Each Stockholder
shall vote its Shares or execute written consents, as the case may be, and take
all other actions necessary, to ensure that the Company's Charter and Bylaws
facilitate and do not at any time conflict with any provision of this Agreement.



                                    ARTICLE 3
                            RESTRICTIONS ON TRANSFER

         SECTION 3.01. General. (a) Each Stockholder understands and agrees that
the Company Securities purchased pursuant to the applicable subscription
agreement or the Thermadyne Investment Program and the Thermadyne New Option
Program have not been registered under the Securities Act and are restricted
securities. Each Stockholder agrees that it will not, directly or indirectly,
sell, assign, transfer, grant a participation in, pledge or otherwise dispose of
("TRANSFER") any Company Securities (or solicit any offers to buy or otherwise
acquire, or take a pledge of any Company Securities) except in compliance with
the Securities Act and the terms and conditions of this Agreement.

                Any attempt to transfer any Company Securities not in compliance
with this Agreement shall be null and void and the Company shall not, and shall
cause any transfer agent not to, give any effect in the Company's stock records
to such attempted transfer.

         SECTION 3.02. Legends. In addition to any other legend that may be
required, each certificate for shares of Common Stock or Preferred Stock and
each Warrant that is issued to any Stockholder shall bear a legend in
substantially the following form:

         "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. THIS SECURITY IS ALSO SUBJECT TO ADDITIONAL
RESTRICTIONS ON TRANSFER AS SET FORTH IN THE INVESTORS' AGREEMENT DATED AS OF
MAY 22, 1998, COPIES OF WHICH MAY BE




                                       12
<PAGE>   16


OBTAINED UPON REQUEST FROM THERMADYNE HOLDINGS CORPORATION OR ANY SUCCESSOR
THERETO."

                If any Company Securities shall cease to be Registrable
Securities under clause (i) or clause (ii) of the definition thereof, the
Company shall, upon the written request of the holder thereof, issue to such
holder a new certificate evidencing such securities without the first sentence
of the legend required by this Section endorsed thereon. If any Company
Securities cease to be subject to any and all restrictions on transfer set forth
in this Agreement, the Company shall, upon the written request of the holder
thereof, issue to such holder a new certificate evidencing such Company
Securities without the second sentence of the legend required by this Section
endorsed thereon.

         SECTION 3.03. Permitted Transferees. Notwithstanding anything in this
Agreement to the contrary, any Stockholder may at any time transfer any or all
of its Company Securities to one or more of its Permitted Transferees without
the consent of the Board or any other Stockholder or group of Stockholders and
without compliance with Sections 3.04 and 4.01 so long as (a) such Permitted
Transferee shall have agreed in writing to be bound by the terms of this
Agreement and (b) the transfer to such Permitted Transferee is not in violation
of applicable federal or state securities laws.

         SECTION 3.04.  Restrictions on Transfers by Management Stockholders.

         (a) Each Management Stockholder and each Permitted Transferee of such
Management Stockholder may transfer its Company Securities only as follows:

                  (i) in a transfer made in compliance with Section 4.01 or
         4.02, 4.03 or as permitted or required by the Thermadyne Investment
         Program, the Thermadyne New Option Program or any employment contract
         between the Company or any Subsidiary and an employee;

                  (ii) subject to the Public Offering Limitations, in a Public
         Offering in connection with the exercise of its rights under Article 5
         hereof;

                  (iii) in a transfer made at the conclusion of the Applicable
         Holdback Period (as defined in Section 5.03) following a Public
         Offering, in compliance with Rule 144 promulgated under the Securities
         Act; provided, however, that until the Restriction Termination Date,
         the Aggregate Ownership of such Management Stockholder as a result of
         such transfer shall be equal to or exceed the greater of (x) 50% of
         such




                                       13
<PAGE>   17





         Management Stockholder's Initial Ownership of Common Stock and (y) the
         percentage of such Management Stockholder's Initial Ownership that is
         equal to the Aggregate Ownership of the DLJ Entities as a percentage of
         the DLJ Entities' Initial Ownership; or

                  (iv) following the Restriction Termination Date, to any Third
         Party other than an Adverse Person for consideration consisting solely
         of cash, provided, however, that the number of Shares transferred by
         such Management Stockholder pursuant to this Section 3.04(a)(iv) in any
         twelve-month period shall not exceed 20% of the greater of (x) such
         Management Stockholder's Aggregate Ownership at the beginning of such
         twelve month period and (y) such Management Stockholder's Aggregate
         Ownership as of the date hereof.

         For purposes of this Agreement, "PUBLIC OFFERING LIMITATIONS" means (A)
except as set forth in the proviso at the end of this paragraph, no Management
Stockholder shall be permitted to exercise its rights under Section 5.02 hereof
(x) with respect to the First Public Offering and (y) until such time as the
Aggregate Ownership of the DLJ Entities shall be less than 50% of their
aggregate Initial Ownership of Common Stock and (B) in each Public Offering
following the First Public Offering, such Management Stockholder shall be
entitled to transfer a number of Shares not exceeding such Management
Stockholder's Pro Rata Portion of non-Purchased Shares; provided, however, that
notwithstanding the restrictions set forth in clauses (A) and (B), each
Management Stockholder shall be permitted to exercise its rights pursuant to
Section 5.02 hereof in respect of such Management Stockholder's Pro Rata Portion
of its Purchased Shares in any Public Offering.

         (b) The provisions of Section 3.04(a) shall terminate upon the earliest
to occur of (i) the fifth anniversary of the Closing Date and (ii) a Change of
Control. Notwithstanding the foregoing sentence, the provisions of Section
3.04(a) shall not terminate with respect to any Management Stockholder's Shares
which shall have been pledged to the Company as security in connection with any
indebtedness for borrowed money owed by such Management Stockholder to the
Company unless the proceeds from the sale of such Shares are applied to repay
such indebtedness in full.

         (c) In addition to any other restriction contained in this Agreement
and notwithstanding any other provision of this Section 3.04, neither a
Management Stockholder nor any Permitted Transferee thereof may transfer
Coinvestment Shares (as defined in the Thermadyne Investment Program) prior to
the date such Shares have vested in accordance with the terms of the Thermadyne
Investment Program and the relevant purchase agreement thereunder.




                                       14
<PAGE>   18
                                    ARTICLE 4
                       TAG-ALONG RIGHTS; DRAG-ALONG RIGHTS

         SECTION 4.01. Rights to Participate in Transfer. (a) If DLJ Entities
(the "SELLING PERSON") propose to transfer (other than transfers of shares of
Company Securities (i) in a Public Offering, (ii) to any Permitted Transferee of
any of the DLJ Entities or (iii) any transfer of Preferred Stock or any transfer
of Warrants made in conjunction with such a transfer of Preferred Stock), in a
transaction otherwise permitted by Article 3 hereof, a number of Company
Securities of any class of securities of the Company equal to or exceeding 10%
of the Aggregate Ownership of the DLJ Entities of securities of such class in a
single transaction or in a series of related transactions on the date of the
proposed sale (a "TAG-ALONG SALE"), the Other Stockholders may, at their option,
elect to exercise their rights under this Section 4.01 (each such Stockholder, a
"TAGGING PERSON"). In the event of such a proposed transfer, the Selling Person
shall provide each Other Stockholder written notice of the terms and conditions
of such proposed transfer ("TAG-ALONG NOTICE") and offer each Tagging Person the
opportunity to participate in such sale. The Tag-Along Notice shall identify the
number and type of Company Securities subject to the offer ("TAG-ALONG OFFER"),
the cash price at which the transfer is proposed to be made, and all other
material terms and conditions of the Tag-Along Offer, including the form of the
proposed agreement, if any. From the date of the Tag-Along Notice, each Tagging
Person shall have the right (a "TAG-ALONG RIGHT"), exercisable by written notice
("SECTION 4.01 RESPONSE NOTICE") given to the Selling Person within 10 Business
Days (the "TAG-ALONG NOTICE PERIOD"), to request that the Selling Person include
in the proposed transfer the number of Company Securities held by such Tagging
Person as is specified in such notice; provided that if the aggregate number of
Company Securities proposed to be sold by the Selling Person and all Tagging
Persons in such transaction exceeds the number of Company Securities which can
be sold on the terms and conditions set forth in the Tag-Along Notice, then only
the Tag- Along Portion of Company Securities of each Tagging Person shall be
sold pursuant to the Tag-Along Offer and the Selling Person shall sell its
Tag-Along Portion of Company Securities and such additional Company Securities
as permitted by Section 4.01(d). If the Tagging Persons exercise their Tag-Along
Rights hereunder, each Tagging Person shall deliver, together with its Section
4.01 Response Notice, to the Selling Person the certificate or certificates
representing the Company Securities of such Tagging Person to be included in the
transfer, together with a limited power-of-attorney authorizing the Selling
Person to transfer such Securities on the terms set forth in the Tag-Along
Notice.




                                       15
<PAGE>   19


Delivery of such certificate or certificates representing the Company Securities
to be transferred and the limited power-of-attorney authorizing the Selling
Person to transfer such Company Securities shall constitute an irrevocable
acceptance of the Tag-Along Offer by such Tagging Persons. If, at the end of a
120 day period after such delivery, the Selling Person has not completed the
transfer of all such Company Securities on substantially the same terms and
conditions set forth in the Tag-Along Notice, the Selling Person shall return to
each Tagging Person the limited power-of-attorney (and all copies thereof)
together with all certificates representing the Company Securities which such
Tagging Person delivered for transfer pursuant to this Section 4.01.

         (b) Concurrently with the consummation of the Tag-Along Sale, the
Selling Person shall notify the Tagging Persons thereof, shall remit to the
Tagging Persons the total consideration (by bank or certified check) for the
Company Securities of the Tagging Persons transferred pursuant thereto, and
shall, promptly after the consummation of such Tag-Along Sale, furnish such
other evidence of the completion and time of completion of such transfer and the
terms thereof as may be reasonably requested by the Tagging Persons.

         (c) If at the termination of the Tag-Along Notice Period any Tagging
Person shall not have elected to participate in the Tag-Along Sale, such Tagging
Person will be deemed to have waived its rights under Section 4.01(a) with
respect to the transfer of its securities pursuant to such Tag-Along Sale.

         (d) If any Tagging Person declines to exercise its Tag-Along Rights or
elects to exercise its Tag-Along Rights with respect to less than such Tagging
Person's Tag-Along Portion, the DLJ Entities shall be entitled to transfer,
pursuant to the Tag-Along Offer, a number of Company Securities held by the DLJ
Entities equal to the number of Company Securities constituting the portion of
such Tagging Person's Tag-Along Portion with respect to which Tag-Along Rights
were not exercised.

         (e) The DLJ Entities and any Tagging Person who exercises the Tag-
Along Rights pursuant to this Section 4.01 may sell the Company Securities
subject to the Tag-Along Offer on the terms and conditions set forth in the Tag-
Along Notice (provided, however, that the cash price payable in any such sale
may exceed the cash price specified in the Tag-Along Notice by up to 10%) within
120 days of the date on which Tag-Along Rights shall have been waived, exercised
or expire.

         SECTION 4.02. Right to Compel Participation in Certain Transfers. (a)
If (i) the DLJ Entities propose to transfer not less than 50% of their Initial
Ownership of Common Stock to a Third Party in a bona fide sale or (ii) the DLJ



                                       16
<PAGE>   20



Entities propose a transfer in which the shares of Common Stock to be
transferred by the DLJ Entities and their Permitted Transferees constitute more
than 50% of the outstanding shares of Common Stock (a "SECTION 4.02 SALE"), the
DLJ Entities may at their option require all Other Stockholders to sell the
Drag-Along Portion of the Subject Securities ("DRAG-ALONG RIGHTS") then held by
every Other Stockholder, and (subject to and at the closing of the Section 4.02
Sale) to exercise all, but not less than all, of the options or Warrants held by
every Other Stockholder and to sell all of the shares of Common Stock received
upon such exercise to such Third Party, for the same consideration per share of
Common Stock and otherwise on the same terms and conditions as the DLJ Entities;
provided that any Other Stockholder who holds options or Warrants the exercise
price per share of which is greater than the per share price at which the Shares
are to be sold to the Third Party may, if required by the DLJ Entities to
exercise such options, in place of such exercise, submit to irrevocable
cancellation thereof without any liability for payment of any exercise price
with respect thereto. In the event the Section 4.02 Sale is not consummated with
respect to any shares acquired upon exercise of such options or Warrants, or the
Section 4.02 Sale is not consummated, such options or Warrants shall be deemed
not to have been exercised or canceled, as applicable. DLJMB shall provide
written notice of such Section 4.02 Sale to the Other Stockholders (a "SECTION
4.02 NOTICE") not later than the 15th day prior to the proposed Section 4.02
Sale. The Section 4.02 Notice shall identify the transferee, the number of
Subject Securities, the consideration for which a transfer is proposed to be
made (the "SECTION 4.02 SALE PRICE") and all other material terms and conditions
of the Section 4.02 Sale. The number of shares of Common Stock, Preferred Stock,
and/or Warrants to be sold by each Other Stockholder will be the Drag-Along
Portion of the shares of Common Stock, Preferred Stock, and/or Warrants that
such Other Stockholder owns. Subject to Sections 4.02 and 4.03, each Other
Stockholder shall be required to participate in the Section 4.02 Sale on the
terms and conditions set forth in the Section 4.02 Notice and to tender all its
Subject Securities as set forth below. The price payable in such transfer shall
be the Section 4.02 Sale Price. Not later than the 10th day following the date
of the Section 4.02 Notice (the "SECTION 4.02 NOTICE PERIOD"), each of the Other
Stockholders shall deliver to a representative of DLJMB designated in the
Section 4.02 Notice certificates representing all Subject Securities
representing the Drag Along Portion held by such Other Stockholder, duly
endorsed, together with all other documents required to be executed in
connection with such Section 4.02 Sale. If an Other Stockholder should fail to
deliver such certificates to DLJMB, the Company shall cause the books and
records of the Company to show that such Subject Securities are bound by the
provisions of this Section 4.02 and Section 4.03 and that such Subject
Securities shall be transferred to the purchaser of the Subject Securities
immediately upon surrender for transfer by the holder thereof.



                                       17
<PAGE>   21


         (b) The DLJ Entities shall have a period of 90 days from the date of
receipt of the Section 4.02 Notice to consummate the Section 4.02 Sale on the
terms and conditions set forth in such Section 4.02 Sale Notice. If the Section
4.02 Sale shall not have been consummated during such period, DLJMB shall return
to each of the Other Stockholders all certificates representing Subject
Securities that such Other Stockholder delivered for transfer pursuant hereto,
together with any documents in the possession of DLJMB executed by the Other
Stockholder in connection with such proposed transfer, and all the restrictions
on transfer contained in this Agreement or otherwise applicable at such time
with respect to Common Stock owned by the Other Stockholders shall again be in
effect.

         (c) Concurrently with the consummation of the transfer of Company
Securities pursuant to this Section 4.02 and Section 4.03, DLJMB shall give
notice thereof to all Stockholders, shall remit to each of the Stockholders who
have surrendered their certificates the total consideration (by bank or
certified check) for the Subject Securities transferred pursuant hereto and
shall furnish such other evidence of the completion and time of completion of
such transfer and the terms thereof as may be reasonably requested by such
Stockholders.

         SECTION 4.03. Certain Rights. It is understood and agreed that the
employment agreements or associated restricted stock purchase agreements between
one or more Management Stockholders and the Company or any Subsidiary may
contain provisions permitting or requiring, under certain circumstances, such
Management Stockholders to sell to the Company or a Subsidiary, and permitting
or requiring, under certain circumstances, the Company or such Subsidiary to
purchase from such Management Stockholder, Company Securities. Such provisions
may, by the terms of such agreements, remain effective notwithstanding that the
employment relationship created by such employment agreements has been
terminated, in which event such provisions are deemed to be incorporated herein
and made a part hereof, to the extent appropriate.



                                    ARTICLE 5
                               REGISTRATION RIGHTS

         SECTION 5.01.  Demand Registration. (a) If the Company shall receive a
written request by the DLJ Entities or their Permitted Transferees (any such
requesting Person, a "SELLING STOCKHOLDER") that the Company effect the
registration under the Securities Act of all or a portion of such Selling





                                       18
<PAGE>   22

Stockholder's Registrable Securities, and specifying the intended method of
disposition thereof, then the Company shall promptly give written notice of such
requested registration (a "DEMAND REGISTRATION") at least 5 days prior to the
anticipated filing date of the registration statement relating to such Demand
Registration to the Other Stockholders and thereupon will use its best efforts
to effect, as expeditiously as possible, the registration under the Securities
Act of:

                  (i) the Registrable Securities which the Company has been so
         requested to register by the Selling Stockholders, then held by the
         Selling Stockholders; and

                  (ii) subject to the restrictions set forth in Section 3.04,
         all other Registrable Securities of the same type as that to which the
         request by the Selling Stockholders relates which any Other Stockholder
         entitled to request the Company to effect an Incidental Registration
         (as such term is defined in Section 5.02) pursuant to Section 5.02 (all
         such Stockholders, together with the Selling Stockholders, the
         "HOLDERS") has requested the Company to register by written request
         received by the Company within 2 days after the receipt by such Holders
         of such written notice given by the Company,

all to the extent necessary to permit the disposition (in accordance with the
intended methods thereof as aforesaid) of the Registrable Securities so to be
registered; provided that, subject to Section 5.01(d) hereof, the Company shall
not be obligated to effect more than six Demand Registrations for the DLJ
Entities; and provided further that the Company shall not be obligated to effect
a Demand Registration unless the aggregate proceeds expected to be received from
the sale of the Common Stock to be included in such Demand Registration, in the
reasonable opinion of DLJMB exercised in good faith, equals or exceeds (x)
$50,000,000 if such Demand Registration would constitute the First Public
Offering, or (y) $10,000,000 in all other cases. In no event will the Company be
required to effect more than one Demand Registration within any four-month
period.

          (b) Promptly after the expiration of the 2-day period referred to in
Section 5.01(a)(ii) hereof, the Company will notify all the Holders to be
included in the Demand Registration of the other Holders and the number of
Registrable Securities requested to be included therein. The Selling
Stockholders requesting a registration under this Section may, at any time prior
to the effective date of the registration statement relating to such
registration, revoke such request, without liability to any of the other
Holders, by providing a written notice to the Company revoking such request, in
which case such request, so revoked, shall be considered a Demand Registration
unless the participating Stockholders reimburse the



                                       19
<PAGE>   23


Company for all costs incurred by the Company in connection with such
registration, or unless such revocation arose out of the fault of the Company,
in which case such request shall not be considered a Demand Registration.

         (c) The Company will pay all Registration Expenses in connection with
any Demand Registration.

         (d) A registration requested pursuant to this Section shall not be
deemed to have been effected (i) unless the registration statement relating
thereto (A) has become effective under the Securities Act and (B) has remained
effective for a period of at least 180 days (or such shorter period in which all
Registrable Securities of the Holders included in such registration have
actually been sold thereunder); provided that if after any registration
statement requested pursuant to this Section becomes effective (x) such
registration statement is interfered with by any stop order, injunction or other
order or requirement of the SEC or other governmental agency or court and (y)
less than 75% of the Registrable Securities included in such registration
statement has been sold thereunder, such registration statement shall not be
considered a Demand Registration or (ii) if the Maximum Offering Size (as
defined below) is reduced in accordance with Section 5.01(e) such that less than
66 2/3% of the Registrable Securities of the Selling Stockholders sought to be
included in such registration are included.

         (e) If a Demand Registration involves an Underwritten Public Offering
and the managing underwriter shall advise the Company and the Selling
Stockholders that, in its view, (i) the number of Registrable Securities
requested to be included in such registration (including any securities which
the Company proposes to be included which are not Registrable Securities) or
(ii) the inclusion of some or all of the Registrable Securities owned by the
Holders, in any such case, exceeds the largest number of securities which can be
sold without having an adverse effect on such offering, including the price at
which such securities can be sold (the "MAXIMUM OFFERING SIZE"), the Company
will include in such registration, in the priority listed below, up to the
Maximum Offering Size:

                       (A) first, all Benchmark Securities requested to be
                  registered by the Selling Stockholder and by all other DLJ
                  Entities and their Permitted Transferees (allocated, if
                  necessary for the offering not to exceed the Maximum Offering
                  Size, pro rata among such entities on the basis of the
                  relative number of shares of Registrable Securities requested
                  to be registered);




                                       20
<PAGE>   24



                       (B) second, all Registrable Securities (other than
                  Benchmark Securities) requested to be included in such
                  registration by all DLJ Entities and their Permitted
                  Transferees and any other Holder (allocated, if necessary for
                  the offering not to exceed the Maximum Offering Size, pro rata
                  among such DLJ Entities and their Permitted Transferees and
                  such other Holders on the basis of the relative number of
                  shares of Registrable Securities (excluding any Benchmark
                  Securities) requested to be included in such registration);
                  and

                       (C) third, any securities proposed to be registered by
                  the Company.

         (f) If, in connection with any Demand Registration pursuant to this
Section with respect to the Preferred Stock, any Selling Stockholder shall seek
to transfer any Warrants together with shares of Preferred Stock, the Company
shall at the request of any such Stockholder effect a registration of such
Warrants to which the provisions of this Article 5 shall apply mutatis mutandis
and a registration, pursuant to a shelf registration statement, so as to permit
the resale of the shares of Common Stock for which any Warrants so transferred
may be exercisable. The Company shall maintain the effectiveness of any such
shelf registration statement, and take all actions necessary to permit resale of
such Common Stock as may be required by applicable state securities laws.

         SECTION 5.02. Incidental Registration. (a) If the Company proposes to
register any Company Securities under the Securities Act (other than a
registration (A) on Form S-8 or S-4 or any successor or similar forms, (B)
relating to Common Stock issuable upon exercise of employee stock options or in
connection with any employee benefit or similar plan of the Company or (C) in
connection with a direct or indirect acquisition by the Company of another
company), whether or not for sale for its own account, it will each such time,
subject to the provisions of Section 5.02(b), give prompt written notice at
least 30 days prior to the anticipated filing date of the registration statement
relating to such registration to each DLJ Entity and each Other Stockholder,
which notice shall set forth such Stockholder's rights under this Section 5.02
and shall offer such Stockholders the opportunity to include in such
registration statement such number of Registrable Securities of the same type as
are proposed to be registered as each such Stockholder may request (an
"INCIDENTAL REGISTRATION"). Upon the written request of any such Stockholder
made within 15 days after the receipt of notice from the Company (which request
shall specify the number of Registrable Securities intended to be disposed of by
such Stockholder), the Company will use its best efforts to effect the
registration under the Securities Act of all Registrable Securities which the
Company has been so requested to register by such



                                       21
<PAGE>   25


Stockholders, to the extent requisite to permit the disposition of the
Registrable Securities so to be registered; provided that (I) if such
registration involves a Public Offering, all such Stockholders requesting to be
included in the Company's registration must sell their Registrable Securities to
the underwriters selected as provided in Section 5.04(f) on the same terms and
conditions as apply to the Company and (II) if, at any time after giving written
notice of its intention to register any stock pursuant to this Section 5.02(a)
and prior to the effective date of the registration statement filed in
connection with such registration, the Company shall determine for any reason
not to register such securities, the Company shall give written notice to all
such Stockholders and, thereupon, shall be relieved of its obligation to
register any Registrable Securities in connection with such registration
(without prejudice, however, to rights of any DLJ Entity under Section 5.01). No
registration effected under this Section 5.02 shall relieve the Company of its
obligations to effect a Demand Registration to the extent required by Section
5.01. The Company will pay all Registration Expenses in connection with each
registration of Registrable Securities requested pursuant to this Section 5.02.

         (b) If a registration pursuant to this Section 5.02 involves a Public
Offering (other than in the case of a Public Offering requested by any DLJ
Entity or any of their Permitted Transferees or the Other Stockholders in a
Demand Registration, in which case the provisions with respect to priority of
inclusion in such offering set forth in Section 5.01(e) shall apply) and the
managing underwriter advises the Company that, in its view, the number of Shares
that the Company and such Stockholders intend to include in such registration
exceeds the Maximum Offering Size, the Company will include in such
registration, in the following priority, up to the Maximum Offering Size:

                  (i) first, so much of the securities proposed to be registered
         by the Company as would not cause the offering to exceed the Maximum
         Offering Size;

                  (ii) second, all Benchmark Securities requested to be included
         in such registration statement by the DLJ Entities and their Permitted
         Transferees (allocated, if necessary for the offering not to exceed the
         Maximum Offering Size, pro rata among such entities on the basis of the
         relative number of shares of Registrable Securities requested to be so
         included); and

                  (iii) third, all Registrable Securities other than Benchmark
         Securities requested to be included in such registration by any DLJ
         Entity and its Permitted Transferees or any Other Stockholder pursuant
         to this Section 5.02 (allocated, if necessary for the offering not to
         exceed the



                                       22
<PAGE>   26



         Maximum Offering Size, pro rata among such Stockholders on the basis of
         the relative number of shares of Registrable Securities (excluding any
         Benchmark Securities) so requested to be included in such
         registration).

         SECTION 5.03. Holdback Agreements. If any registration of Registrable
Securities shall be in connection with a Public Offering, each DLJ Entity and
its Permitted Transferees and each Other Stockholder agrees not to effect any
public sale or distribution, including any sale pursuant to Rule 144, or any
successor provision, under the Securities Act, of any Registrable Securities,
and not to effect any such public sale or distribution of any other Common Stock
of the Company or of any stock convertible into or exchangeable or exercisable
for any Common Stock of the Company (in each case, other than as part of such
Public Offering) during the 14 days prior to the effective date of such
registration statement (except as part of such registration) or during the
period after such effective date equal to the lesser of (i) such period of time
as agreed between such managing underwriter and the Company and (ii) 180 days
(such lesser period, the "APPLICABLE HOLDBACK PERIOD").

         SECTION 5.04. Registration Procedures. Whenever Stockholders request
that any Registrable Securities be registered pursuant to Section 5.01 or 5.02,
the Company will, subject to the provisions of such Sections, use its best
efforts to effect the registration and the sale of such Registrable Securities
in accordance with the intended method of disposition thereof as quickly as
practicable, and in connection with any such request:

         (a) The Company will as expeditiously as possible prepare and file with
the SEC a registration statement on any form for which the Company then
qualifies or which counsel for the Company shall deem appropriate and which form
shall be available for the sale of the Registrable Securities to be registered
thereunder in accordance with the intended method of distribution thereof, and
use its best efforts to cause such filed registration statement to become and
remain effective for a period of not less than 180 days.

         (b) The Company will, if requested, prior to filing a registration
statement or prospectus or any amendment or supplement thereto, furnish to
participating Stockholder and each underwriter, if any, of the Registrable
Securities covered by such registration statement copies of such registration
statement as proposed to be filed, and thereafter the Company will furnish to
such Stockholder and underwriter, if any, such number of copies of such
registration statement, each amendment and supplement thereto (in each case
including all exhibits thereto and documents incorporated by reference therein),
the prospectus included in such registration statement (including each
preliminary prospectus) and such other documents as such Stockholder or
underwriter may reasonably



                                       23
<PAGE>   27


request in order to facilitate the disposition of the Registrable Securities
owned by such Stockholder.

         (c) After the filing of the registration statement, the Company will
promptly notify each Stockholder holding Registrable Securities covered by such
registration statement of any stop order issued or threatened by the SEC and
take all reasonable actions required to prevent the entry of such stop order or
to remove it if entered.

         (d) The Company will use its best efforts to (i) register or qualify
the Registrable Securities covered by such registration statement under such
other securities or blue sky laws of such jurisdictions in the United States as
any Stockholder holding such Registrable Securities reasonably (in light of such
Stockholder's intended plan of distribution) requests and (ii) cause such
Registrable Securities to be registered with or approved by such other
governmental agencies or authorities as may be necessary by virtue of the
business and operations of the Company and do any and all other acts and things
that may be reasonably necessary or advisable to enable such Stockholder to
consummate the disposition of the Registrable Securities owned by such
Stockholder; provided that the Company will not be required to (A) qualify
generally to do business in any jurisdiction where it would not otherwise be
required to qualify but for this paragraph (d), (B) subject itself to taxation
in any such jurisdiction or (C) consent to general service of process in any
such jurisdiction.

         (e) The Company will immediately notify each Stockholder holding such
Registrable Securities, at any time when a prospectus relating thereto is
required to be delivered under the Securities Act, of the occurrence of an event
requiring the preparation of a supplement or amendment to such prospectus so
that, as thereafter delivered to the purchasers of such Registrable Securities,
such prospectus will not contain an untrue statement of a material fact or omit
to state any material fact required to be stated therein or necessary to make
the statements therein not misleading and promptly prepare and make available to
each such Stockholder any such supplement or amendment.

         (f) (i) The DLJ Entities will have the right, in their sole discretion,
to select an underwriter or underwriters in connection with any Public Offering
resulting from the exercise by any such DLJ Entity or its Permitted Transferee
of a Demand Registration, which underwriter or underwriters may include any
Affiliate of any DLJ Entity and (ii) the Company will select an underwriter or
underwriters in connection with any other Public Offering. In connection with
any Public Offering, the Company will enter into customary agreements (including
an underwriting agreement in customary form) and take such other




                                       24
<PAGE>   28

actions as are reasonably required in order to expedite or facilitate the
disposition of Registrable Securities in any such Public Offering, including the
engagement of a "qualified independent underwriter" in connection with the
qualification of the underwriting arrangements with the NASD.

         (g) Upon the execution of confidentiality agreements in form and
substance satisfactory to the Company, the Company will make available for
inspection by any Stockholder and any underwriter participating in any
disposition pursuant to a registration statement being filed by the Company
pursuant to this Section 5.04 and any attorney, accountant or other professional
retained by any such Stockholder or underwriter (collectively, the
"INSPECTORS"), all financial and other records, pertinent corporate documents
and properties of the Company (collectively, the "RECORDS") as shall be
reasonably necessary to enable them to exercise their due diligence
responsibility, and cause the Company's officers, directors and employees to
supply all information reasonably requested by any Inspectors in connection with
such registration statement. Records that the Company determines, in good faith,
to be confidential and that it notifies the Inspectors are confidential shall
not be disclosed by the Inspectors unless (i) the disclosure of such Records is
necessary to avoid or correct a misstatement or omission in such registration
statement or (ii) the release of such Records is ordered pursuant to a subpoena
or other order from a court of competent jurisdiction. Each Stockholder agrees
that information obtained by it as a result of such inspections shall be deemed
confidential and shall not be used by it as the basis for any market
transactions in the Company Securities or its Affiliates unless and until such
is made generally available to the public. Each Stockholder further agrees that
it will, upon learning that disclosure of such Records is sought in a court of
competent jurisdiction, give notice to the Company and allow the Company, at its
expense, to undertake appropriate action to prevent disclosure of the Records
deemed confidential.

         (h) The Company will furnish to each such Stockholder and to each such
underwriter, if any, a signed counterpart, addressed to such underwriter, of (i)
an opinion or opinions of counsel to the Company and (ii) a comfort letter or
comfort letters from the Company's independent public accountants, each in
customary form and covering such matters of the type customarily covered by
opinions or comfort letters, as the case may be, as a majority of such
Stockholders or the managing underwriter therefor reasonably requests.

         (i) The Company will otherwise use its best efforts to comply with all
applicable rules and regulations of the SEC, and make available to its
stockholders, as soon as reasonably practicable, an earnings statement covering
a period of 12 months, beginning within three months after the effective date of
the




                                       25
<PAGE>   29


registration statement, which earnings statement shall satisfy the provisions of
Section 11(a) of the Securities Act.

         The Company may require each such Stockholder to promptly furnish in
writing to the Company such information regarding the distribution of the
Registrable Securities as the Company may from time to time reasonably request
and such other information as may be legally required in connection with such
registration.

         Each such Stockholder agrees that, upon receipt of any notice from the
Company of the happening of any event of the kind described in Section 5.04(e),
such Stockholder will forthwith discontinue disposition of Registrable
Securities pursuant to the registration statement covering such Registrable
Securities until such Stockholder's receipt of the copies of the supplemented or
amended prospectus contemplated by Section 5.04(e), and, if so directed by the
Company, such Stockholder will deliver to the Company all copies, other than any
permanent file copies then in such Stockholder's possession, of the most recent
prospectus covering such Registrable Securities at the time of receipt of such
notice. In the event that the Company shall give such notice, the Company shall
extend the period during which such registration statement shall be maintained
effective (including the period referred to in Section 5.04(a)) by the number of
days during the period from and including the date of the giving of notice
pursuant to Section 5.04(e) to the date when the Company shall make available to
such Stockholder a prospectus supplemented or amended to conform with the
requirements of Section 5.04(e).

         SECTION 5.05. Indemnification by the Company. The Company agrees to
indemnify and hold harmless each Stockholder holding Registrable Securities
covered by a registration statement, its officers, directors and agents, and
each person, if any, who controls such Stockholder within the meaning of Section
15 of the Securities Act or Section 20 of the Exchange Act from and against any
and all losses, claims, damages and liabilities caused by any untrue statement
or alleged untrue statement of a material fact contained in any registration
statement or prospectus relating to the Registrable Securities (as amended or
supplemented if the Company shall have furnished any amendments or supplements
thereto) or any preliminary prospectus, or caused by any omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein not misleading, except insofar as such
losses, claims, damages or liabilities are caused by any such untrue statement
or omission or alleged untrue statement or omission based upon information
furnished in writing to the Company by such Stockholder or on such Stockholder's
behalf expressly for use therein; provided that with respect to any untrue
statement or omission or alleged untrue statement or omission made in any
preliminary prospectus, or in any



                                       26
<PAGE>   30



prospectus, as the case may be, the indemnity agreement contained in this
paragraph shall not apply to the extent that any such loss, claim, damage,
liability or expense results from the fact that a current copy of the prospectus
(or, in the case of a prospectus, the prospectus as amended or supplemented) was
not sent or given to the person asserting any such loss, claim, damage,
liability or expense at or prior to the written confirmation of the sale of the
Registrable Securities concerned to such person if it is determined that the
Company has provided such prospectus and it was the responsibility of such
Stockholder to provide such person with a current copy of the prospectus (or
such amended or supplemented prospectus, as the case may be) and such current
copy of the prospectus (or such amended or supplemented prospectus, as the case
may be) would have cured the defect giving rise to such loss, claim, damage,
liability or expense. The Company also agrees to indemnify any underwriters of
the Registrable Securities, their officers and directors and each person who
controls such underwriters on substantially the same basis as that of the
indemnification of the Stockholders provided in this Section 5.05.

         SECTION 5.06. Indemnification by Participating Stockholders. Each
Stockholder holding Registrable Securities included in any registration
statement agrees, severally but not jointly, to indemnify and hold harmless the
Company, its officers, directors and agents and each person, if any, who
controls the Company within the meaning of either Section 15 of the Securities
Act or Section 20 of the Exchange Act to the same extent as the foregoing
indemnity from the Company to such Stockholder, but only (i) with respect to
information furnished in writing by such Stockholder or on such Stockholder's
behalf expressly for use in any registration statement or prospectus relating to
the Registrable Securities, or any amendment or supplement thereto, or any
preliminary prospectus or (ii) to the extent that any loss, claim, damage,
liability or expense described in Section 5.05 results from the fact that a
current copy of the prospectus (or, in the case of a prospectus, the prospectus
as amended or supplemented) was not sent or given to the person asserting any
such loss, claim, damage, liability or expense at or prior to the written
confirmation of the sale of the Registrable Securities concerned to such person
if it is determined that it was the responsibility of such Stockholder to
provide such person with a current copy of the prospectus (or such amended or
supplemented prospectus, as the case may be) and such current copy of the
prospectus (or such amended or supplemented prospectus, as the case may be)
would have cured the defect giving rise to such loss, claim, damage, liability
or expense. Each such Stockholder also agrees to indemnify and hold harmless
underwriters of the Registrable Securities, their officers and directors and
each person who controls such underwriters on substantially the same basis as
that of the indemnification of the Company provided in this Section 5.06. As a
condition to including Registrable Securities in any registration statement
filed in accordance with Article 5 hereof, the Company may require that it shall
have




                                       27
<PAGE>   31


received an undertaking reasonably satisfactory to it from any underwriter to
indemnify and hold it harmless to the extent customarily provided by
underwriters with respect to similar securities.

         SECTION 5.07. Conduct of Indemnification Proceedings. In case any
proceeding (including any governmental investigation) shall be instituted
involving any person in respect of which indemnity may be sought pursuant to
this Article 5, such person (an "INDEMNIFIED PARTY") shall promptly notify the
person against whom such indemnity may be sought (the "INDEMNIFYING PARTY") in
writing and the Indemnifying Party shall assume the defense thereof, including
the employment of counsel reasonably satisfactory to such Indemnified Party, and
shall assume the payment of all fees and expenses; provided that the failure of
any Indemnified Party so to notify the Indemnifying Party shall not relieve the
Indemnifying Party of its obligations hereunder except to the extent that the
Indemnifying Party is materially prejudiced by such failure to notify. In any
such proceeding, any Indemnified Party shall have the right to retain its own
counsel, but the fees and expenses of such counsel shall be at the expense of
such Indemnified Party unless (i) the Indemnifying Party and the Indemnified
Party shall have mutually agreed to the retention of such counsel or (ii) in the
reasonable judgment of such Indemnified Party representation of both parties by
the same counsel would be inappropriate due to actual or potential differing
interests between them. It is understood that the Indemnifying Party shall not,
in connection with any proceeding or related proceedings in the same
jurisdiction, be liable for the reasonable fees and expenses of more than one
separate firm of attorneys (in addition to any local counsel) at any time for
all such Indemnified Parties, and that all such fees and expenses shall be
reimbursed as they are incurred. In the case of any such separate firm for the
Indemnified Parties, such firm shall be designated in writing by the Indemnified
Parties. The Indemnifying Party shall not be liable for any settlement of any
proceeding effected without its written consent, but if settled with such
consent, or if there be a final judgment for the plaintiff, the Indemnifying
Party shall indemnify and hold harmless such Indemnified Parties from and
against any loss or liability (to the extent stated above) by reason of such
settlement or judgment. No Indemnifying Party shall, without the prior written
consent of the Indemnified Party, effect any settlement of any pending or
threatened proceeding in respect of which any Indemnified Party is or could have
been a party and indemnity could have been sought hereunder by such Indemnified
Party, unless such settlement includes an unconditional release of such
Indemnified Party from all liability arising out of such proceeding.

         SECTION 5.08. Contribution. If the indemnification provided for in this
Article 5 is unavailable to the Indemnified Parties in respect of any losses,
claims, damages or liabilities referred to herein, then each such Indemnifying
Party, in



                                       28
<PAGE>   32

lieu of indemnifying such Indemnified Party, shall contribute to the amount paid
or payable by such Indemnified Party as a result of such losses, claims, damages
or liabilities (i) as between the Company and the Stockholders holding
Registrable Securities covered by a registration statement on the one hand and
the underwriters on the other, in such proportion as is appropriate to reflect
the relative benefits received by the Company and such Stockholders on the one
hand and the underwriters on the other, from the offering of the Registrable
Securities, or if such allocation is not permitted by applicable law, in such
proportion as is appropriate to reflect not only the relative benefits but also
the relative fault of the Company and such Stockholders on the one hand and of
such underwriters on the other in connection with the statements or omissions
which resulted in such losses, claims, damages or liabilities, as well as any
other relevant equitable considerations and (ii) as between the Company on the
one hand and each such Stockholder on the other, in such proportion as is
appropriate to reflect the relative fault of the Company and of each such
Stockholder in connection with such statements or omissions, as well as any
other relevant equitable considerations. The relative benefits received by the
Company and such Stockholders on the one hand and such underwriters on the other
shall be deemed to be in the same proportion as the total proceeds from the
offering (net of underwriting discounts and commissions but before deducting
expenses) received by the Company and such Stockholders bear to the total
underwriting discounts and commissions received by such underwriters, in each
case as set forth in the table on the cover page of the prospectus. The relative
fault of the Company and such Stockholders on the one hand and of such
underwriters on the other shall be determined by reference to, among other
things, whether the untrue or alleged untrue statement of a material fact or the
omission or alleged omission to state a material fact relates to information
supplied by the Company and such Stockholders or by such underwriters. The
relative fault of the Company on the one hand and of each such Stockholder on
the other shall be determined by reference to, among other things, whether the
untrue or alleged untrue statement of a material fact or the omission or alleged
omission to state a material fact relates to information supplied by such party,
and the parties' relative intent, knowledge, access to information and
opportunity to correct or prevent such statement or omission.

         The Company and the Stockholders agree that it would not be just and
equitable if contribution pursuant to this Section 5.08 were determined by pro
rata allocation (even if the underwriters were treated as one entity for such
purpose) or by any other method of allocation which does not take account of the
equitable considerations referred to in the immediately preceding paragraph. The
amount paid or payable by an Indemnified Party as a result of the losses,
claims, damages or liabilities referred to in the immediately preceding
paragraph shall be deemed to include, subject to the limitations set forth
above, any legal or other expenses reasonably incurred by such Indemnified Party
in connection with investigating or



                                       29
<PAGE>   33


defending any such action or claim. Notwithstanding the provisions of this
Section 5.08, no underwriter shall be required to contribute any amount in
excess of the amount by which the total price at which the Registrable
Securities underwritten by it and distributed to the public were offered to the
public exceeds the amount of any damages which such underwriter has otherwise
been required to pay by reason of such untrue or alleged untrue statement or
omission or alleged omission, and no Stockholder shall be required to contribute
any amount in excess of the amount by which the total price at which the
Registrable Securities of such Stockholder were offered to the public exceeds
the amount of any damages which such Stockholder has otherwise been required to
pay by reason of such untrue or alleged untrue statement or omission or alleged
omission. No person guilty of fraudulent misrepresentation (within the meaning
of Section 11(f) of the Securities Act) shall be entitled to contribution from
any person who was not guilty of such fraudulent misrepresentation. Each such
Stockholder's obligation to contribute pursuant to this Section 5.08 is several
in the proportion that the proceeds of the offering received by such Stockholder
bears to the total proceeds of the offering received by all such Stockholders
and not joint.

         SECTION 5.09. Participation in Public Offering. No Person may
participate in any Public Offering hereunder unless such Person (a) agrees to
sell such Person's securities on the basis provided in any underwriting
arrangements approved by the Persons entitled hereunder to approve such
arrangements an (b) completes and executes all questionnaires, powers of
attorney, indemnities, underwriting agreements and other documents reasonably
required under the terms of such underwriting arrangements and the provisions of
this Agreement in respect of registration rights.

         SECTION 5.10. Other Indemnification. Indemnification similar to that
specified herein (with appropriate modifications) shall be given by the Company
and each Stockholder participating therein with respect to any required
registration or other qualification of securities under any federal or state law
or regulation or governmental authority other than the Securities Act.

         SECTION 5.11. Cooperation by the Company. In the event any Stockholder
shall transfer any Registrable Securities pursuant to Rule 144A under the
Securities Act, the Company shall cooperate with such Stockholder (which shall
include, without limitation, making registration rights with respect to the
Registrable Securities to be sold (or securities issuable or to be issued in
exchange therefor) available to the ultimate purchasers thereof) and shall
provide to such Stockholder such information as such Stockholder shall
reasonably request.





                                       30
<PAGE>   34


                                    ARTICLE 6
                                  MISCELLANEOUS

         SECTION 6.01. Entire Agreement. This Agreement and the Securities
Purchase Agreement constitute the entire agreement among the parties hereto and
supersede all prior agreements and understandings, oral and written, among the
parties hereto with respect to the subject matter hereof.

         SECTION 6.02. Binding Effect; Benefit. This Agreement shall inure to
the benefit of and be binding upon the parties hereto and their respective
heirs, successors, legal representatives and permitted assigns. Nothing in this
Agreement, expressed or implied, shall confer on any Person other than the
parties hereto, and their respective heirs, successors, legal representatives
and permitted assigns, any rights, remedies, obligations or liabilities under or
by reason of this Agreement.

         SECTION 6.03. Exclusive Financial and Investment Banking Advisor.
During the period from and including the date hereof through and including the
fifth anniversary of the date hereof, Donaldson, Lufkin & Jenrette Securities
Corporation ("DLJSC"), or any Affiliate of DLJSC that the DLJ Entities may
choose in their sole discretion, shall be engaged as the exclusive financial and
investment banking advisor of the Company. DLJSC or such Affiliate shall be
entitled to reimbursement from the Company for all expenses incurred by DLJSC or
such Affiliate (including, without limitation, fees and expenses of counsel) as
financial and investment banking advisor of the Company.

         SECTION 6.04. Assignability. This Agreement shall not be assignable by
any party hereto, except that any Person acquiring Shares who is required by the
terms of this Agreement or any employment agreement or stock purchase, option,
stock option or other compensation plan of the Company or any Subsidiary to
become a party hereto shall (unless already bound hereby) execute and deliver to
the Company an agreement to be bound by this Agreement and shall thenceforth be
a "STOCKHOLDER". Any Stockholder who ceases to own beneficially any Shares shall
cease to be bound by the terms hereof (other than the provisions of Sections
5.05, 5.06, 5.07, 5.08, and 5.10 applicable to such Stockholder with respect to
any offering of Registrable Securities completed before the date such
Stockholder ceased to own any Shares).

         SECTION 6.05. Amendment; Waiver; Termination. No provision of this
Agreement may be waived except by an instrument in writing executed by the party
against whom the waiver is to be effective. No provision of this Agreement may
be amended or otherwise modified except by an instrument in writing





                                       31
<PAGE>   35

executed by the Company with the approval of the Board and Stockholders holding
at least 75% of the outstanding Shares; provided that any amendment or other
modification of this Agreement that would adversely affect any Founding
Stockholder may be effected only with the consent of such Stockholder.

         SECTION 6.06. Notices. All notices, requests and other communications
to any party hereunder shall be in writing (including facsimile transmissions
and shall be given,

         if to the Company or the Management Stockholders, to:

                  Thermadyne Holdings Corporation
                           101 South Hanley Road
                           St. Louis, Missouri 63105
                           (314) 721-5573
                           Attention:  James H. Tate
                                 Stephanie N. Josephson
                           Fax: (314) 746-2374

         with a copy to:

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

         and a copy to the DLJ Entities at their addresses listed below.

         if to the DLJ Entities, to:
                  DLJ Merchant Banking Partners II, L.P.
                           277 Park Avenue
                           New York, New York 10172
                           Attention: Peter T. Grauer
                           Fax:  (212) 892-7552

         with a copy to:





                                       32
<PAGE>   36

                  Davis Polk & Wardwell
                           450 Lexington Avenue
                           New York, New York  10017
                           Attention:  George R. Bason, Jr.
                           Fax:  (212) 450-4800

         All 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.
Any notice, request or other written communication sent by facsimile
transmission shall be confirmed by certified mail, return receipt requested,
posted within one Business Day, or by personal delivery, whether courier or
otherwise, made within two Business Days after the date of such facsimile
transmission.

         Any Person who becomes a Stockholder shall provide its address and fax
number to the Company, which shall promptly provide such information to each
other Stockholder.

         SECTION 6.07.  Headings.  The headings contained in this Agreement are
for convenience only and shall not affect the meaning or interpretation of this
Agreement.

         SECTION 6.08. Counterparts. This Agreement may be executed in any
number of counterparts, each of which shall be deemed to be an original and all
of which together shall be deemed to be one and the same instrument.

         SECTION 6.09. Applicable Law. THIS AGREEMENT SHALL BE GOVERNED BY, AND
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF DELAWARE WITHOUT REGARD
TO THE CONFLICTS OF LAW RULES OF SUCH STATE.

         SECTION 6.10. Specific Enforcement. Each party hereto acknowledges that
the remedies at law of the other parties for a breach or threatened breach of
this Agreement would be inadequate and, in recognition of this fact, any party
to this Agreement, without posting any bond, and in addition to all other
remedies which may be available, shall be entitled to obtain equitable relief in
the form of specific performance, a temporary restraining order, a temporary or
permanent injunction or any other equitable remedy which may then be available.

         SECTION 6.11.  Consent to Jurisdiction.  Any suit, action or proceeding
seeking to enforce any provision of, or based on any matter arising out of or in



                                       33
<PAGE>   37

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 non-exclusive 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 6.06 shall be deemed
effective service of process on such party.



                                       34
<PAGE>   38


         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:                                
                                           Title:                               
                                                                                
                                                                                
                                        DLJ MERCHANT BANKING PARTNERS II, L.P.  
                                                                                
                                                                                
                                        BY DLJ MERCHANT BANKING II, INC.        
                                        Managing General Partner                
                                                                                
                                                                                
                                        By: /s/ IVY DODES                       
                                           ----------------------------------   
                                           Name:  Ivy Dodes                     
                                           Title:  Vice President               
                                                                                
                                                                                
                                        DLJ MERCHANT BANKING                    
                                          PARTNERS II-A, L.P.                   
                                                                                
                                                                                
                                        BY DLJ MERCHANT BANKING II,             
                                           INC., Managing General Partner       
                                                                                
                                                                                
                                        By: /s/ IVY DODES                       
                                           ----------------------------------   
                                           Name:  Ivy Dodes                     
                                           Title:  Vice President               
                                                                                
                                                                                
                                        





                                       35
<PAGE>   39


                                        DLJ OFFSHORE PARTNERS II, C.V.         
                                                                               
                                                                               
                                        BY DLJ MERCHANT BANKING II,            
                                               INC., Advisory General Partner  
                                                                               
                                                                               
                                        By: /s/ IVY DODES                      
                                           ----------------------------------  
                                           Name:  Ivy Dodes
                                           Title:  Vice President              
                                                                               
                                                                               
                                        DLJ DIVERSIFIED PARTNERS, L.P.         
                                                                               
                                                                               
                                        BY DLJ DIVERSIFIED PARTNERS,           
                                               INC., Managing General Partner  
                                                                               
                                                                               
                                        By: /s/ IVY DODES                      
                                           ----------------------------------  
                                           Name:  Ivy Dodes
                                           Title:  Vice President              
                                                                               
                                                                               
                                        DLJ DIVERSIFIED PARTNERS-A, L.P.       
                                                                               
                                                                               
                                        BY DLJ DIVERSIFIED PARTNERS, INC.,     
                                              Managing General Partner         
                                                                               
                                                                               
                                        By: /s/ IVY DODES                      
                                           ----------------------------------  
                                           Name:  Ivy Dodes
                                           Title:  Vice President              
                                                                               
                                                                               
                                        DLJMB FUNDING II, INC.                 
                                                                               
                                                                               
                                        By: /s/ IVY DODES                      
                                           ----------------------------------  
                                           Name:  Ivy Dodes
                                           Title:  Vice President              
                                                                               
                                                                               
                                                                               
                                        





                                       36
<PAGE>   40

                                        DLJ EAB PARTNERS, L.P.               
                                                                             
                                                                             
                                        BY DLJ LBO PLANS MANAGEMENT          
                                              CORPORATION, General Partner   
                                                                             
                                                                             
                                        By:  /s/ IVY DODES
                                           ----------------------------------
                                           Name:  Ivy Dodes
                                           Title:  Vice President
                                                                             
                                                                             
                                        DLJ MILLENNIUM PARTNERS, L.P.        
                                                                             
                                                                             
                                        BY DLJ MERCHANT BANKING II,          
                                               INC., Managing General Partner
                                                                             
                                                                             
                                        By:  /s/ IVY DODES
                                           ----------------------------------
                                           Name:  Ivy Dodes
                                           Title:  Vice President
                                                                             
                                                                             
                                        UK INVESTMENT PLAN 1997              
                                          PARTNERS                           
                                                                             
                                                                             
                                        DONALDSON, LUFKIN & JENRETTE,        
                                          INC., General Partner              
                                                                             
                                                                             
                                        By:  /s/ IVY DODES
                                           ----------------------------------
                                           Name:  Ivy Dodes
                                           Title:  Vice President
                                                                             
                                        



                                       37
<PAGE>   41




                                        DLJ FIRST ESC, L.P.                  
                                                                             
                                                                             
                                        BY DLJ LBO PLANS MANAGEMENT          
                                              CORPORATION, as General Partner
                                                                             
                                                                             
                                        By:  /s/ IVY DODES
                                           ----------------------------------
                                           Name:  Ivy Dodes
                                           Title:  Vice President
                                                                             
                                                                             
                                        DLJ ESC II, L.P.                     
                                                                             
                                        BY DLJ LBO PLANS MANAGEMENT          
                                              CORPORATION, as General Partner
                                                                             
                                                                             
                                        By:  /s/ IVY DODES
                                           ----------------------------------
                                           Name:  Ivy Dodes
                                           Title:  Vice President
                                                                             
                                                                             
                                        DLJ MILLENNIUM PARTNERS-A, L.P.      
                                                                             
                                        BY DLJ MERCHANT BANKING II, INC.,    
                                                 Managing General Partner    
                                                                             

                                        By:  /s/ IVY DODES
                                           ----------------------------------
                                           Name:  Ivy Dodes
                                           Title:  Vice President
                                                                             
                                                                             
                                        /s/ RANDALL E. CURRAN                
                                        -------------------------------------
                                        Randall E. Curran                    
                                                                             
                                        /s/ JAMES H. TATE
                                        -------------------------------------
                                        James H. Tate                        
                                                                             
                                        /s/ MICHAEL E. MAHONEY               
                                        -------------------------------------
                                        Michael E. Mahoney                   
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
                                                                             
<PAGE>   42

                                        /s/ JOHN D. MCCULLOCH
                                        -------------------------------------
                                        John D. McCulloch                    
                                                                             
                                        /s/ MICHAEL C. O'CONNELL
                                        -------------------------------------
                                        Michael C. O'Connell                 
                                                                             
                                        /s/ JAMES R. DELANY
                                        -------------------------------------
                                        James R. Delany                      
                                                                             
                                        /s/ HOYT H. FITZSIMMONS, JR.
                                        -------------------------------------
                                        Hoyt H. Fitzsimmons, Jr.             
                                                                             
                                        /s/ DENNIS KLANJSCEK
                                        -------------------------------------
                                        Dennis Klanjscek                     
                                                                             
                                        /s/ ROBERT D. MADDOX
                                        -------------------------------------
                                        Robert D. Maddox                     
                                                                             
                                        /s/ THOMAS C. DRURY
                                        -------------------------------------
                                        Thomas C. Drury                      
                                                                             
                                        /s/ STEPHANIE N. JOSEPHSON
                                        -------------------------------------
                                        Stephanie N. Josephson