<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549

                                   FORM 10-Q

(Mark One)
[x]      QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

For the quarterly period ended         March 31, 1997
                              -------------------------------------------------

                                       OR

[ ]      TRANSITION REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

For the transition period from                       to
                              -----------------------   -----------------------


                   Commission file number       0-23378     
                                         ----------------

                       Thermadyne Holdings Corporation
-------------------------------------------------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)


Delaware                                                             74-2482571
-------------------------------------------------------------------------------
(State or Other Jurisdiction of                                (I.R.S. Employer
Incorporation or Organization)                               Identification No.)

101 S. Hanley, St. Louis, MO                                             63105
-------------------------------------------------------------------------------
(Address of Principal Executive Offices)                          (Zip Code)

Registrant's Telephone Number, Including Area Code       314/721-5573
                                                  -----------------------------

         Indicate by X whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15 (d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.          Yes    X        No
                                                       ------         ------

         Indicate by check mark whether the registrant has filed all documents
and reports required to be filed by Section 12, 13 or 15 (d) of the Securities
Exchange Act of 1934 subsequent to the distribution of securities under a plan
confirmed by a court.                               Yes   X        No
                                                        ------        ------

         The number of shares outstanding of the issuer's common stock, par
value $0.01 per share,  as of May 1, 1997, was 11,054,778.
<PAGE>   2

                         THERMADYNE HOLDINGS CORPORATION

                                      INDEX


<TABLE>
<S>                                                                     <C>
PART I - FINANCIAL INFORMATION

         Item 1.  Financial Statements

         Consolidated Balance Sheets  ....................................  3
         Consolidated Statements of Operations  ..........................  4
         Consolidated Statements of Cash Flows  ..........................  5
         Notes to Consolidated Financial Statements ..................... 6-7

         Item 2.   Management's Discussion and Analysis
                   of Financial Condition and Results of Operations  .... 8-9
                                                                          



PART II - OTHER INFORMATION

         Item 6.  Exhibits and Reports on Form 8-K  ...................... 10


SIGNATURES  .............................................................. 11

</TABLE>
<PAGE>   3
                         THERMADYNE HOLDINGS CORPORATION
                           CONSOLIDATED BALANCE SHEETS
                        (IN THOUSANDS, EXCEPT SHARE DATA)



<TABLE>
<CAPTION>
                                                              March 31,     December 31,
                                                                1997            1996
                                                            ------------    ------------
                                                             (Unaudited)
<S>                                                         <C>             <C>         
ASSETS

Current assets:
    Cash and cash equivalents                               $      7,537    $      1,420
    Accounts receivable, less allowance for
      doubtful accounts of $1,771 and
      $1,649, respectively                                        65,250          54,286
    Inventories                                                   92,059          79,542
    Prepaid expenses and other                                    10,772           9,763
    Net assets of discontinued operations                         29,784          29,455
                                                            ------------    ------------
      Total current assets                                       205,402         174,466
Property, plant and equipment, at cost, net                       82,995          75,624
Deferred financing costs, net                                      7,033           7,508
Intangibles, at cost, net                                         66,015          62,645
Deferred income taxes                                             23,792          23,206
Other assets                                                       1,410           9,956
                                                            ------------    ------------
      Total assets                                          $    386,647    $    353,405
                                                            ============    ============

LIABILITIES AND SHAREHOLDERS' DEFICIT

Current liabilities:
    Accounts payable                                        $     36,070    $     28,266
    Accrued and other liabilities                                 22,594          29,257
    Accrued interest                                              13,438           6,461
    Income taxes payable                                           6,745           7,948
    Deferred income taxes                                          1,324           1,324
    Current maturities of long-term obligations                    3,869           4,205
                                                            ------------    ------------
      Total current liabilities                                   84,040          77,461
Long-term obligations, less current maturities                   440,244         417,135
Other long-term liabilities                                       46,899          44,078
Shareholders' equity (deficit):
    Common stock, $.01 par value, 25,000,000
      shares authorized, 11,045,278 and 11,020,311 shares
      issued and outstanding at March 31, 1997 and
      December 31, 1996, respectively                                110             110
    Additional paid-in capital                                   143,695         143,237
    Accumulated deficit                                         (329,946)       (333,465)
    Foreign currency translation                                   1,605           4,849
                                                            ------------    ------------
      Total shareholders' deficit                               (184,536)       (185,269)
                                                            ------------    ------------
      Total liabilities and shareholders' deficit           $    386,647    $    353,405
                                                            ============    ============
</TABLE>





          See accompanying notes to consolidated financial statements





                                       3
<PAGE>   4
                         THERMADYNE HOLDINGS CORPORATION
                      CONSOLIDATED STATEMENTS OF OPERATIONS
                        (IN THOUSANDS, EXCEPT SHARE DATA)
                                   (UNAUDITED)





<TABLE>
<CAPTION>
                                                  Three Months       Three Months
                                                     Ended              Ended
                                                 March 31, 1997     March 31, 1996
                                                 --------------     --------------
<S>                                               <C>                <C>         
Net sales                                         $    117,751       $    102,233
Operating expenses:
  Cost of goods sold                                    70,342             59,629
  Selling, general and administrative expenses          26,270             23,168
  Amortization of goodwill                                 357             22,328
  Amortization of other intangibles                      1,692              1,809
  Net periodic postretirement benefits                     585                577
                                                  ------------       ------------
Operating income (loss)                                 18,505             (5,278)
Other expense:
  Interest expense                                     (11,538)           (10,826)
  Amortization of deferred financing costs                (460)              (881)
  Other, net                                               406               (831)
                                                  ------------       ------------
Income (loss) from continuing operations before
  income tax provision                                   6,913            (17,816)
Income tax provision                                     2,981              2,851
                                                  ------------       ------------
Income (loss) from continuing operations                 3,932            (20,667)
Discontinued operations:
  Gain (loss) from discontinued operations, net
    of income taxes                                      1,036             (1,200)
                                                  ------------       ------------
Net income (loss)                                 $      4,968       $    (21,867)
                                                  ============       ============

Per share amounts:
  Income (loss) from continuing operations        $       0.35       $      (1.93)
  Net income (loss)                               $       0.44       $      (2.04)

Weighted average shares outstanding                 11,309,909         10,719,547
                                                  ============       ============
</TABLE>





          See accompanying notes to consolidated financial statements





                                       4
<PAGE>   5
                        THERMADYNE HOLDINGS CORPORATION
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                            Three Months      Three Months
                                                               Ended            Ended
                                                           March 31, 1997   March 31, 1996 
                                                           --------------   -------------- 
<S>                                                           <C>              <C>      
Cash flows provided by (used in) operating activities:
  Net income (loss)                                           $  4,968         $(21,867)
  Adjustments to reconcile net income (loss) to
  net cash provided by operating activities:
    Net periodic postretirement benefits                           585              577
    Depreciation                                                 2,876            2,468
    Amortization of goodwill                                       357           22,328
    Amortization of other intangibles                            1,692            1,809
    Amortization of deferred financing costs                       460              881
    Recognition of net operating loss carryforwards                586               --
    Deferred income taxes                                         (586)              --
    Noncash charges for discontinued operations                    565            3,068
Changes in operating assets and liabilities:
    Accounts receivable                                         (2,577)         (10,755)
    Inventories                                                 (4,625)          (5,525)
    Prepaid expenses and other                                    (334)             637
    Accounts payable                                               358            4,402
    Accrued and other liabilities                               (7,762)          (2,404)
    Accrued interest                                             7,249            8,384
    Income taxes payable                                        (1,513)           2,211
    Other long-term liabilities                                   (321)            (503)
    Discontinued operations                                        903             (723)
                                                              --------         --------
    Total adjustments                                           (2,087)          26,855
                                                              --------         --------
         Net cash provided by operating activities               2,881            4,988
                                                              --------         --------
Cash flows provided by (used in) investing activities:
    Capital expenditures, net                                   (2,395)          (1,397)
    Change in other assets                                       8,512             (187)
    Acquisitions, net of cash                                  (27,755)         (74,011)
    Investing activities of discontinued operations               (570)          (1,440)
                                                              --------         --------
      Net cash used in investing activities                    (22,208)         (77,035)
                                                              --------         --------
Cash flows provided by (used in) financing activities:
    Change in long-term receivables                                 17               34
    Repayment of long-term obligations                          (9,928)         (13,064)
    Borrowing of long-term obligations                          33,683           87,856
    Issuance of common stock                                       436              355
    Change in accounts receivable securitization                 4,631            4,610
    Financing activities of discontinued operations             (1,227)             179
    Financing fees                                                  --             (600)
    Other                                                       (2,168)           1,338
                                                              --------         --------
      Net cash provided by financing activities                 25,444           80,708
                                                              --------         --------
Net increase in cash and cash equivalents                        6,117            8,661
Cash and cash equivalents at beginning of period                 1,420            1,838
                                                              --------         --------
Cash and cash equivalents at end of period                    $  7,537         $ 10,499
                                                              ========         ========
</TABLE>





          See accompanying notes to consolidated financial statements





                                       5
<PAGE>   6
                        THERMADYNE HOLDINGS CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                 (IN THOUSANDS)
                                  (UNAUDITED)


1.   BASIS OF PRESENTATION

     UNAUDITED INTERIM CONSOLIDATED FINANCIAL STATEMENTS

     The unaudited interim consolidated financial statements reflect all
material adjustments (only of a normal recurring nature) which are, in the
opinion of management, necessary for a fair presentation of financial position
and results of operations. The results for the three months ended March 31,
1997 are not necessarily indicative of the results that may be expected for a
full fiscal year.

     STATEMENTS OF CASH FLOWS

     For purposes of the Statements of Cash Flows, the Company considers all
highly liquid investments purchased with a maturity of three months or less to
be cash equivalents. Interest and taxes paid were as follows:

<TABLE>
<CAPTION>
                                             Three Months        Three Months
                                               Ended                Ended
                                            March 31, 1997      March 31, 1996
                                            --------------      --------------
     <S>                                       <C>                  <C>
     Interest                                  $ 4,561              $ 5,751
     Taxes                                       3,801                1,401
</TABLE>

     EARNINGS (LOSS) PER SHARE

     Per share amounts for the three months ended March 31, 1997 are based on
the weighted average number of common and common equivalent shares outstanding.
Per share amounts for the three months ended March 31, 1996 are based on the
weighted average number of shares outstanding. All exchange arrangements
contemplated by the Company's 1994 financial restructuring are assumed to have
been completed.

     In February 1997, the Financial Accounting Standards Board issued
Statement No. 128, Earnings per Share, which is required to be adopted on
December 31, 1997. At that time, the Company will be required to change the
method currently used to compute earnings per share and to restate all prior
periods. Under the new requirements for calculating primary earnings per share,
the dilutive effect of stock options will be excluded. The impact is expected
to result in an increase in primary earnings per share for the first quarter
ended March 31, 1997 and March 31, 1996 of $0.01 and $0.0 per share,
respectively. The impact of Statement 128 on the calculation of fully diluted
earnings per share for these quarters is not expected to be material.





                                        6
<PAGE>   7
2.   INVENTORIES

     The composition of inventories at March 31, 1997 was as follows:

<TABLE>
             <S>                                           <C>
             Raw materials                                 $ 13,261
             Work-in-process                                 22,870
             Finished goods                                  58,309
             LIFO Reserve                                    (2,381)
                                                           -------- 

                           Total                           $ 92,059
                                                           ========
</TABLE>





                                       7
<PAGE>   8
                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS

     Included in the following discussions are comparisons of earnings before
interest, taxes, depreciation, amortization, reorganization and restructuring
costs, and extraordinary items ("EBITDA"). The Company believes that EBITDA is
a useful supplement to net earnings (loss) and other consolidated income
statement data in understanding cash flows generated from operations that is
available for taxes, debt service and capital expenditures, but should not be
construed as an alternative to operating income or cash flows from operating
activities (as determined in accordance with generally accepted accounting
principles). EBITDA is also one of the financial measures by which the
Company's covenants are calculated under its debt agreements.

RESULTS OF OPERATIONS

Three Months ended March 31, 1997 compared to Three Months ended March 31, 1996
Net sales from continuing operations for the three months ended March 31, 1997
were $117.8 million, an increase of $15.5 million or 15.2% over net sales from
continuing operations of $102.2 million for the three months ended March 31,
1996. Included in the quarter ended March 31, 1997 are net sales of $6.4
million related to GenSet, which was acquired effective February 1, 1997.
Excluding the effects of GenSet, net sales from continuing operations increased
$9.1 million, or 8.9%, over the same period of the prior year. Domestic sales
through three months were up a modest 1.1% over the comparable period in 1996
and were hampered by strong sales toward the end of 1996. International sales,
excluding the effects of GenSet, were up 23.2% over 1996 due in large part to
strong sales in Asia and Latin America, which were up over the first quarter of
1996 by approximately 40.0% and 60.0%, respectively. Much of the success in
these regions is the result of initiatives begun early in 1996 after the
acquisition of CIGWELD which continue to gain momentum.

Cost of goods sold as a percentage of sales from continuing operations for the
quarter ended March 31, 1997 was 59.7%, compared to 58.3% for the quarter ended
March 31, 1996. This increase is primarily the result of the acquisition of
GenSet as its average gross margin is somewhat lower than the average gross
margin realized by the Company's existing businesses. Also contributing to the
higher percentage was sales mix. The first quarter showed solid sales growth in
certain equipment products which typically carry lower gross margins than many
of the Company's other product lines.

Selling, general and administrative expenses increased to $26.3 million for the
three months ended March 31, 1997, up $3.1 million from $23.2 million for the
three months ended March 31, 1996 primarily due to the addition of GenSet
effective February 1, 1997. As a percentage of sales, selling, general and
administrative expenses were 22.3% and 22.7% for the quarters ended March 31,
1997 and 1996, respectively. The improvement as a percentage of sales results
from certain costs that do not fluctuate directly with sales, such as
depreciation.





                                       8
<PAGE>   9
Amortization of goodwill has decreased $22.0 million in the first quarter of
1997 compared to the same period of the prior year as goodwill recorded in
connection with the Company's 1994 reorganization became fully amortized in
1996.

Interest expense increased $0.7 million from $10.8 million in the first quarter
of 1996 to $11.5 million in the first quarter of 1997 and is largely the result
of debt incurred in the acquisition of GenSet.

Income taxes for the first quarter were $3.0 million on pre-tax income from
continuing operations of $6.9 million compared to an income tax provision of
$2.9 million on a pre-tax loss from continuing operations of $17.8 million for
the three months ended March 31, 1996. The pre-tax loss in 1996 included $22.3
million of non-deductible goodwill amortization.

LIQUIDITY AND CAPITAL RESOURCES

     Working Capital and Cash Flows. Cash provided by operating activities was
$2.9 million for the three months ended March 31, 1997, down $2.1 million from
the $5.0 million for the three months ended March 31, 1996. This decrease in
cash provided by operating activities is the result of a net increase in
operating assets and liabilities of $4.3 million in the first quarter of 1997
compared to the first quarter of 1996 partially offset by an increase in
earnings (adjusted for noncash expenses) of $2.2 million in the quarter ended
March 31, 1997 over the same period of the prior year. Net cash used in
investing activities decreased $54.8 million primarily due to a decrease in
cash used for acquisitions of $46.3 million and an increase in cash provided by
other assets of $8.7 million, partially offset by an increase in capital
expenditures of $1.0 million. Cash provided by financing activities decreased
$55.3 million as the net borrowing of long-term obligations decreased $51.0
million.

     Liquidity. The major uses of cash in the remainder of 1997 are expected to
be for debt service requirements, capital expenditures and tax payments.
Management believes that cash from operating activities, together with
available borrowings under its revolving credit facility, if necessary, will be
sufficient to permit the Company to meet these financial obligations.

     The Company will continue from time to time to explore additional
auxiliary financing methods and other means to lower its cost of capital, which
could include stock issuances or debt financing and the application of the
proceeds therefrom to the payment of bank debt, or the purchase of senior or
senior subordinated notes.





                                       9
<PAGE>   10
PART II.  OTHER INFORMATION

Item 6.  Exhibits and Reports on Form 8-K

      a) Exhibits:
         27 - Financial Data Schedule

      b) Reports on Form 8-K - None.





                                       10
<PAGE>   11
                                   SIGNATURES


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                           THERMADYNE HOLDINGS CORPORATION




                                           By:   /s/ Randall E. Curran         
                                              --------------------------------
                                                     Randall E. Curran
                                              Chairman of the Board, President
                                                and Chief Executive Officer
                                               (Principal Executive Officer)





                                           By:  /s/ James H. Tate               
                                              ---------------------------------
                                                       James H. Tate
                                                  Senior Vice President &
                                                  Chief Financial Officer
                                                  (Principal Financial and
                                                    Accounting Officer)




Date: May 14, 1997
     ---------------





                                       11
<PAGE>   12
                              INDEX TO EXHIBITS



<TABLE>
<CAPTION>
EXHIBIT
NUMBER                   DESCRIPTION
-------                  -----------
<S>           <C>
  27          -  Financial Data Schedule

</TABLE>