<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 May 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   2-29697
                        ---------



                             THE TRANZONIC COMPANIES
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)


            Ohio                                 34-0664235
-------------------------------     ------------------------------------
(State or other jurisdiction of     (I.R.S. Employer Identification No.)
incorporation or  organization)       

                  
     30195 Chagrin Blvd., Pepper Pike, Ohio                       44124
--------------------------------------------------            ------------
    (Address of principal executive offices)                   (Zip Code)

Registrant's telephone number, including area code            216/831-5757
                                                              ------------

Indicate by check mark whether the registrant (1) has filed all annual,
quarterly, and other reports required to be filed by Section 13 or 15(d) of the
Securities Exchange Act of 1934 during the preceding 12 months and (2) has been
subject to the filing requirements for at least the past 90 days.

Yes    x        No
   ---------      ---------


Number of Common Shares Outstanding at July 2, 1997            3,494,388
                                                               ---------
<PAGE>   2


<TABLE>
                                                    PART I: FINANCIAL INFORMATION
                                                    -----------------------------
                                                    Item 1. Financial Statements
                                                    ----------------------------

                                                       THE TRANZONIC COMPANIES

                                                Condensed Consolidated Balance Sheets

                                                 May 31, 1997 and February 28, 1997


<CAPTION>
                                                                   May 31,        February 28,
                                Assets                              1997              1997
                                ------                           ------------     ------------
                                                                 (unaudited)
<S>                                                             <C>               <C>       
Current assets
   Cash (including cash equivalents of $10,568,100 at
     May 31, 1997 and $7,484,200 at February 28, 1997)          $  13,777,581        9,310,479
   Receivables, net                                                15,581,563       14,554,312
   Inventories                                                   
     Raw materials                                                  7,323,335        9,199,517
     Finished goods                                                12,525,713       10,290,648
   Deferred income taxes                                              633,043          606,434
   Prepaid expenses and other current assets                          928,739          873,143
                                                                 ------------     ------------
                Total current assets                               50,769,974       44,834,533
                                                                 
Property, plant and equipment, net                                 19,145,089       18,475,743
Other noncurrent assets                                             3,216,906        3,170,213
Intangible assets                                                   8,156,666        5,907,018
                                                                 ------------     ------------
                                                                $  81,288,635       72,387,507
                                                                 ============     ============

                                                                                   (Continued)

                                      (1)
<PAGE>   3
                                                       THE TRANZONIC COMPANIES

                                                Condensed Consolidated Balance Sheets

                                                 May 31, 1997 and February 28, 1997

<CAPTION>
                                                                     May 31,      February 28,
               Liabilities and Shareholders' Equity                   1997            1997
               ------------------------------------                ----------       ----------
                                                                   (unaudited)
<S>                                                          <C>                    <C>       
Current liabilities
   Trade accounts payable                                       $     6,811,555       6,920,955
   Accrued compensation                                               1,842,452       2,827,939
   Other payables and accrued expenses                                5,572,050       3,917,822
                                                                     ----------      ----------
                Total current liabilities                            14,226,057      13,666,716
                                                                                  
Long-term debt                                                        6,500,000               -
Deferred gain                                                         1,712,730       1,752,630
Deferred income taxes                                                   463,314         550,042
Other noncurrent liabilities                                          1,933,312       1,698,573
                                                                                  
Shareholders' equity                                                              
   Serial preferred shares without par value; authorized                          
     200,000, no shares issued                                                -               -
   Common Shares, no par value; shares at stated value,                           
     authorized 12,000,000, issued 3,995,539 at May 31,                           
     1997 and February 28, 1997                                         998,885         998,885
   Additional paid-in capital                                         5,834,824       5,845,141
   Retained earnings                                                 54,192,127      52,573,602
                                                                     ----------      ----------
                                                                     61,025,836      59,417,628
   Less cost of shares held in treasury --                                        
     Common Shares - 512,151 at May 31, 1997 and                                  
       526,201 at February 28, 1997                                   4,572,614       4,698,082
                                                                     ----------      ----------
                Total shareholders' equity                           56,453,222      54,719,546
                                                                     ----------      ----------
                                                                $    81,288,635      72,387,507
                                                                     ==========      ==========

See accompanying notes to condensed consolidated financial statements.
</TABLE>

                                     (2)
<PAGE>   4


<TABLE>
                             THE TRANZONIC COMPANIES

                  Condensed Consolidated Statements of Earnings

                 Three-month periods ended May 31, 1997 and 1996

                                   (Unaudited)


<CAPTION>
                                                                   1997             1996
                                                                   ----             ----
<S>                                                        <C>                    <C>      
Sales                                                      $    37,312,328       34,715,109

Cost and expenses
   Cost of goods sold                                           24,617,425       23,400,738
   Selling, general, and administrative expenses                 9,781,642        8,987,220
                                                               -----------      -----------
                                                                34,399,067       32,387,958
                                                               -----------      -----------

              Operating earnings                                 2,913,261        2,327,151

Interest income                                                    100,352           77,406
Interest expense                                                  (106,636)         (27,979)
                                                               -----------      -----------
              Earnings before income taxes                       2,906,977        2,376,578

Income taxes                                                     1,047,000          842,000
                                                               -----------      -----------
              Net earnings                                 $     1,859,977        1,534,578
                                                               ===========      ===========
Net earnings per Common Share                              $           .53              .44
                                                                       ===              ===
Dividends per Common Share                                 $           .07             .065
                                                                       ===             ====
Average common and common equivalent shares outstanding          3,519,520        3,507,760
                                                               ===========      ===========
Common Shares outstanding at end of period                       3,483,388        3,490,188
                                                               ===========      ===========
See accompanying notes to condensed consolidated financial statements.
</TABLE>

                                      (3)
<PAGE>   5

<TABLE>
                             THE TRANZONIC COMPANIES

                 Condensed Consolidated Statements of Cash Flows

                 Three-month periods ended May 31, 1997 and 1996

                                   (Unaudited)
<CAPTION>

                                                                                           1997              1996
                                                                                           ----              ----
<S>                                                                                <C>                    <C>      
Cash flows from operating activities
   Net earnings                                                                    $     1,859,977        1,534,578
   Adjustments to reconcile net earnings to net cash provided by
     operating activities
       Depreciation and amortization                                                       809,676          827,451
       Deferred income taxes                                                              (113,337)         166,406
   Changes in assets and liabilities, net of effects of acquisitions
     Receivables, net                                                                       75,456          401,288
     Inventories                                                                            27,222        1,321,969
     Prepaid expenses and other current assets                                             (55,596)        (423,226)
     Trade accounts payable                                                               (109,399)        (334,505)
     Accrued compensation                                                                 (985,487)        (890,549)
     Other payables and accrued expenses                                                 1,654,228          534,829
     Other, net                                                                             39,945          (75,774)
                                                                                     -------------      -----------
                Net cash provided by operating activities                                3,202,685        3,062,467
Cash flows from financing activities
   Proceeds from revolving credit                                                        7,300,000                -
   Repayments of long-term debt                                                           (800,000)      (7,000,000)
   Cash dividends                                                                         (241,452)        (225,637)
                                                                                     -------------      -----------
                Net cash provided by (used in) financing activities                      6,258,548       (7,225,637)
Cash flows from investing activities
   Net proceeds from sale of Housewares Division                                                 -        9,725,678
   Purchases of short-term investments                                                           -       (1,989,067)
   Payments for acquisitions, net of cash acquired                                      (4,766,288)               -
   Purchase of treasury shares                                                                   -         (150,851)
   Proceeds on exercise of share options                                                   115,151                -
   Purchases of property, plant and equipment                                             (342,994)        (268,808)
                                                                                     -------------      -----------
                Net cash provided by (used in) investing activities                     (4,994,131)       7,316,952
                                                                                     -------------      -----------
Cash and cash equivalents
   Increase during the period                                                            4,467,102        3,153,782
   Beginning balance                                                                     9,310,479        6,610,933
                                                                                     -------------      -----------
   Ending balance                                                                  $    13,777,581        9,764,715
                                                                                     =============      ===========
Supplemental schedule of noncash investing and financing activities 
   On March 3, 1997, the Company purchased substantially all the
     assets and assumed certain liabilities of Unity Paper Tubes; in 
     conjunction with the acquisition, liabilities were assumed as 
     follows
       Fair value of assets acquired                                               $     4,800,328                -
       Liabilities assumed                                                                 (34,040)               -
                                                                                     -------------      -----------
       Cash paid                                                                   $     4,766,288                -
                                                                                     =============      ===========
Supplemental disclosure of cash flow information
   Income taxes paid                                                               $     1,083,777        1,166,543
   Interest paid                                                                            83,559           36,317
                                                                                     =============      ===========
See accompanying notes to condensed consolidated financial statements.
</TABLE>



                                      (4)
<PAGE>   6

                             THE TRANZONIC COMPANIES

              Notes to Condensed Consolidated Financial Statements

                 Three-month periods ended May 31, 1997 and 1996




Note A    In the opinion of management, the accompanying unaudited condensed
          consolidated financial statements contain such adjustments (all of
          which are normal and recurring in nature) necessary to present fairly
          the financial position of The Tranzonic Companies and subsidiaries
          (Company) at May 31, 1997 and the results of operations for the
          three-month periods ended May 31, 1997 and 1996. The statements should
          be read in conjunction with the consolidated financial statements and
          notes thereto included in the Company's Annual Report to Shareholders
          for the fiscal year ended February 28, 1997.

Note B    Net earnings per Common Share have been calculated based on the
          weighted average Common Shares outstanding during the periods plus the
          incremental shares (calculated using the treasury share method) for
          those outstanding share options which are considered equivalent shares
          and have a dilutive impact on net earnings per Common Share.

          The average Common Shares used in the calculation of net earnings per
          Common Share for the three-month periods ended May 31, 1997 and 1996,
          were 3,519,520 and 3,507,760, respectively. The number of Common
          Shares outstanding at May 31, 1997 and 1996, was 3,483,388 and
          3,490,188, respectively.

Note C    On March 3, 1997, the Company, through its Industrial Packaging
          Division, acquired substantially all the assets and assumed certain
          liabilities of Unity Paper Tubes, a division of Wyndeham Press Group
          PLC, for $4.8 million in cash. Located in Leyland, Lancashire,
          England, Unity Paper Tubes manufactures and distributes spiral-wound
          paper tubes and cores, primarily within the United Kingdom. The
          acquisition was accounted for under the purchase method of accounting.





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<PAGE>   7

                          PART I: FINANCIAL INFORMATION
                          -----------------------------
                 Item 2. Management's Discussion and Analysis of
                 -----------------------------------------------
                  Financial Condition and Results of Operation
                  --------------------------------------------


Safe Harbor Statement
---------------------

With the exception of historical information, the matters discussed in this
Report are forward-looking statements that involve risks and uncertainties, and
actual results could differ materially from those discussed.

Note on Forward-Looking Information
-----------------------------------

Certain statements herein and in future filings by the Company with the
Securities and Exchange Commission and in written and oral statements made by or
with the approval of any authorized executive officer of the Company constitute
"forward-looking statements" within the meaning of Section 27A of the Securities
Act of 1933 and Section 21E of the Securities Exchange Act of 1934. The Company
intends that such forward-looking statements be subject to the safe harbors
created by such Acts. The words and phrases "looking ahead," "we are confident,"
"should be," "will be," "predicted," "believe," "expect," "anticipate," and
similar expressions identify forward-looking statements. These forward-looking
statements reflect the Company's current views in respect of future events and
financial performance, but are subject to many uncertainties and factors
relating to the Company's operations and business environment which may cause
the actual results of the Company to differ materially from any future results
expressed or implied by such forward-looking statements. Examples of such
uncertainties include, but are not limited to, changes in customer demand and
requirements; fluctuations in prices for raw materials; changes in supplier
relationships or agreements; interest rate fluctuations; changes in federal
income tax laws and regulations; competition; changes in labor contracts; any
changes in the Company's financial condition or operating results due to
acquisitions or dispositions of businesses; unanticipated expenses and delays in
the integration of newly-acquired businesses; industry-specific factors; and
worldwide and regional economic and business conditions including, without
limitation, conditions which may affect public securities markets generally, the
paper and allied products industry, or the markets in which the Company
operates. The Company undertakes no obligations to update publicly or revise any
forward-looking statements whether as a result of new information, future
events, or otherwise.

Financial Condition
-------------------

The Company's financial position remains strong. At May 31, 1997, the current
ratio was 3.6:1 as compared to 3.3:1 at February 28, 1997, and working capital
increased to $36.5 million as compared to $31.2 million at fiscal year-end.

On March 3, 1997, the Company acquired for $4.8 million substantially all the
assets and assumed certain liabilities of Unity Paper Tubes, a manufacturer and
distributor of spiral-wound paper tubes and cores, located in the United
Kingdom. The acquisition was financed through the use of the Company's $30.0
million revolving line of credit.



                                      (6)
<PAGE>   8

Results of Operation
--------------------

Revenues in the first fiscal quarter ended May 31, 1997 increased 7.5 percent to
$37.3 million from $34.7 million as recorded in the prior year like period.
Volume revenue gains from existing product lines at Hospital Specialty Company
added to revenue gains recorded by CCP Industries and Baxter Tube Company,
primarily the result of recent acquisitions by both companies.

Gross margins in the current year first quarter increased to 34.0 percent as
compared to 32.6 percent of a year ago. Raw material costs, particularly fluff
pulp, which was in a downward trend during the prior year first fiscal quarter,
helped to improve margin performance. To a lesser degree, improved manufacturing
efficiencies experienced at Baxter Tube Company were mitigated somewhat by an
increase in lower margin sales to a growing wholesale trade business at CCP
Industries.

Additional administrative costs in support of Company-wide growth have (to some
degree) been offset by continued cost control programs, particularly at CCP
Industries. Selling, general, and administrative expenses were up modestly to
26.2 percent of sales in the current year first quarter as compared to 25.9
percent of the prior year like period. As a result, operating margins in the
current year first quarter improved to 7.8 percent, up from 6.7 percent of a
year ago.

Borrowings used to finance the acquisition of Unity Paper Tubes at the beginning
of the current fiscal year, as noted earlier, caused an unfavorable change in
net interest. During the prior year first quarter the Company received
approximately $10.0 million in cash from the sale of its Housewares Division.

Net earnings in the first quarter ended May 31, 1997 increased 21.2 percent to
$1.9 million or 53 cents per share, up from the $1.5 million or 44 cents per
share recorded a year ago.

                                      (7)
<PAGE>   9

                     FORM 10-Q - PART II: OTHER INFORMATION
                     --------------------------------------


Items 1 through 3 and 5 are not applicable or the answer to such items is
negative; therefore, the items have been omitted and no reference is required in
this report.

ITEM 4.  Submission of Matters to a Vote of Security-Holders
------------------------------------------------------------

(a)  The Registrant's annual meeting of shareholders was held on June 16, 1997.

(b)  The following Directors were elected at such annual meeting, each for a
     three-year term expiring in 2000:

                    David J. Golden
                    Morton L. Reitman
                    James C. Spira

(c)  The following matters were voted on at the annual meeting of shareholders:

     (1)  Election of Class III Directors:

                    Director Name                 Votes For    Abstentions
                    -------------                 ---------    -----------
                    David J. Golden               3,071,900      15,231
                    Morton L. Reitman             3,071,900      15,231
                    James C. Spira                3,071,900      15,231

     (2)  Selection of independent auditors for the fiscal year ending February
          28, 1998:

                                                                  Broker
                    Votes For     Votes Against    Abstentions   Non-Votes
                    ---------     -------------    -----------   ---------
                    3,077,977         1,464           7,689          1

ITEM 6.     Exhibits and Reports on Form 8-K
--------------------------------------------
(a)  Exhibits
     --------

     Exhibit Number      Exhibit
     --------------      -------
          27 (1)         Financial Data Schedule
          99             Independent Auditors' Review Report

(b)  Reports on Form 8-K
     -------------------
     No reports on Form 8-K have been filed during the quarter for which this
     report is filed.


---------------------------
(1) Filed only in electronic format pursuant to Item 601(b)(27) of Regulation
S-K.


                                      (8)
<PAGE>   10

                                    SIGNATURE
                                    ---------

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 thereto duly authorized.


                             THE TRANZONIC COMPANIES
                             (Registrant)





Date:  July 3, 1997          By: /s/ Richard J. Pennza
                                ___________________________________
                                Richard J. Pennza
                                (Duly authorized officer and
                                Principal Accounting Officer)




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