<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 DECEMBER 31, 1995

                                       OR

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

                         COMMISSION FILE NUMBER 1-9965



                           KEITHLEY INSTRUMENTS, INC.
             (Exact name of registrant as specified in its charter)


               OHIO                                     34-0794417
   (State or other jurisdiction of                    (I.R.S. Employer
   incorporation or organization)                    Identification No.)

                     28775 AURORA ROAD, SOLON, OHIO  44139
              (Address of principal executive offices)  (Zip Code)

       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (216) 248-0400


        Indicate by check mark 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
                                     --        --

        As of January 31, 1996 there were outstanding 4,408,524 Common Shares,
without par value, and 2,891,886 Class B Common Shares, without par value.
================================================================================


<PAGE>   2
                         PART I.  FINANCIAL INFORMATION
                         -------  ---------------------

ITEM 1.  Financial Statements.
-------  ---------------------

                           KEITHLEY INSTRUMENTS, INC.
                           CONSOLIDATED BALANCE SHEET
                           (In Thousands of Dollars)
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                                         DECEMBER 31,                SEPTEMBER 30,
                                                                         ------------                -------------
                                                                    1995             1994                 1995
                                                                    ----             ----                 ----
<S>                                                                <C>              <C>                 <C>
Assets
------

Current assets:
    Cash and cash equivalents                                      $ 4,727           $ 3,565              $ 3,890
    Accounts receivable and other, net                              19,362            14,679               20,856
    Inventories:
          Raw materials                                              5,698             4,673                4,917
          Work in process                                            3,835             3,328                3,981
          Finished products                                          3,845             3,192                3,762
                                                                   -------          --------              -------
            Total inventories                                       13,378            11,193               12,660
    Other current assets                                             3,116             2,610                2,290
                                                                   -------          --------              -------
            Total current assets                                    40,583            32,047               39,696
                                                                   -------           -------               ------

Property, plant and equipment, at cost                              33,684            31,385               32,527
Less-Accumulated depreciation                                       22,840            20,625               21,984
                                                                   -------           -------               ------
Total property, plant and equipment, net                            10,844            10,760               10,543
                                                                   -------           -------               ------

Intangible assets, net                                               7,605             6,549                6,201
Other assets                                                         8,564             7,190                9,669
                                                                   -------           -------              -------
Total assets                                                       $67,596           $56,546              $66,109
                                                                   =======           =======              =======

Liabilities and Shareholders' Equity
------------------------------------

Current liabilities:
    Short-term debt and current
      installments on long-term debt                               $    71           $   203              $    71
    Accounts payable                                                 8,363             5,934                6,759
    Accrued payroll and related expenses                             4,489             3,190                6,142
    Other accrued expenses                                           5,092             4,061                4,575
    Income taxes payable                                             2,968             1,662                2,580
                                                                   -------           -------              -------
          Total current liabilities                                 20,983            15,050               20,127
                                                                   -------           -------              -------

Long-term debt                                                       5,464             6,731                6,042
Other long-term liabilities                                          3,113             2,668                3,038

Shareholders' equity:
    Paid-in-capital                                                  4,425             3,647                4,162
    Earnings reinvested in the business                             33,093            28,126               32,157
    Cumulative translation adjustment and other                        575               324                  583
    Common shares held in treasury, at cost                            (57)               --                   --
                                                                   -------           -------              -------
          Total shareholders' equity                                38,036            32,097               36,902
                                                                   -------           -------              -------
Total liabilities and shareholders' equity                         $67,596           $56,546              $66,109
                                                                   =======           =======              =======
</TABLE>





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<PAGE>   3
                          KEITHLEY INSTRUMENTS, INC.
                       CONSOLIDATED STATEMENT OF INCOME
              (In Thousands of Dollars Except for Per Share Data)
                                  (Unaudited)



<TABLE>
<CAPTION>
                                                                               FOR THE THREE MONTHS
                                                                                ENDED DECEMBER 31,
                                                                          1995                     1994
                                                                          ----                     ----
<S>                                                                     <C>                        <C>
Net sales                                                               $29,823                    $23,525

Cost of goods sold                                                       11,835                      9,097

Selling, general and administrative expenses                             11,942                     10,412

Product development expenses                                              4,096                      3,205

Amortization of intangible assets                                           132                        116

Financing expenses (net of investment income)                               159                        214
                                                                        -------                    -------

Income before income taxes                                                1,659                        481

Income taxes                                                                514                        135
                                                                        -------                    -------

Net income                                                              $ 1,145                    $   346
                                                                        =======                    =======


Net income per share - primary and fully diluted                        $   .15                    $   .05
                                                                        =======                    =======

Cash dividends per Common Share                                         $  .031                    $  .025
                                                                        =======                    =======
Cash dividends per Class B
Common Share                                                            $  .025                    $  .020
                                                                        =======                    =======
</TABLE>





                                       3
<PAGE>   4
                           KEITHLEY INSTRUMENTS, INC.
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                           (In Thousands of Dollars)
                                  (Unaudited)


<TABLE>
<CAPTION>
                                                                                    FOR THE THREE MONTHS
                                                                                     ENDED DECEMBER 31,
                                                                                            
                                                                                   1995              1994 
                                                                                   ----              -----
<S>                                                                              <C>               <C>
Cash flows from operating activities:
    Net income                                                                   $1,145            $   346
    Expenses not requiring outlay of cash                                         1,118              1,007
    Changes in working capital                                                     (552)            (2,465)
    Other operating activities                                                    1,092                568
                                                                                  -----              -----
    Net cash provided by (used in) operating activities                           2,803               (544)

Cash flows from investing activities:
    Payments for property, plant, and equipment                                  (1,188)              (578)
    Acquisition                                                                    (200)                --
    Other investing activities-net                                                   --                 18
                                                                                  -----              -----
    Net cash used in investing activities                                        (1,388)              (560)

Cash flows from financing activities:
    Net increase (decrease) in short term debt                                       --                 18
    Borrowing (repayment) of long term debt                                        (569)             2,120
    Cash dividends                                                                 (209)              (163)
    Other transactions-net                                                          207                  2
                                                                                  -----              -----
    Net cash provided by (used in) financing activities                            (571)             1,977

Effect of changes in foreign currency exchange rates                                 (7)               (20)

Increase in cash and cash equivalents                                               837                853
Cash and cash equivalents at beginning of period                                  3,890              2,712
                                                                                  -----              -----
Cash and cash equivalents at end of period                                       $4,727             $3,565
                                                                                 ======             =======

Supplemental disclosures of cash flow information
-------------------------------------------------
    Cash paid during the period for:
          Income taxes                                                           $  158             $  318
          Interest                                                                  219                248

Supplemental schedule of noncash investing activities
-----------------------------------------------------
    The company's acquisition included the following
noncash transactions (See Note C):
          Liabilities assumed                                                    $  557                 --
          Remaining purchase obligation                                             819                 --
                                                                                  -----             ------
                Total noncash transactions                                        1,376                 --
                                                                                  -----             ------
          Cash paid                                                                 200                 --
                                                                                 ------             ------
          Fair value of assets acquired                                          $1,576                 --
                                                                                 ======             ======

Disclosure of accounting policy 
-------------------------------
        
        For purposes of this statement, the Company considers all highly liquid investments with maturities of three months or less
when purchased to be cash equivalents.

</TABLE>





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<PAGE>   5
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                (In thousands of dollars, except for share data)


A.   The consolidated financial statements at December 31, 1995 and 1994 and
     for the three month periods then ended have not been examined by
     independents accountants, but in the opinion of the management of Keithley
     Instruments, Inc., all adjustments necessary to a fair statement of the
     consolidated balance sheet, consolidated statement of income and
     consolidated statement of cash flows for those periods have been
     included.  All adjustments included are of a normal recurring nature.

B.   The weighted average number of shares and share equivalents used in
     determining net income per share was 7,787,927 for the quarter ended
     December 31, 1995 and 7,104,876 for the quarter ended December 31, 1994. 
     The weighted average number of shares and share equivalents used in
     determining fully  diluted net income per share was 7,834,149 for the
     quarter ended December 31, 1995, and 7,104,876 for the quarter ended
     December 31, 1995.  Prior to the quarter ended June 30, 1995, fully
     diluted net income per share had not been materially different from net
     income per share.  Both Common Shares and Class B Common Shares are
     included in calculating the weighted average number of shares outstanding.

C.   On December 5, 1995, the company consummated the purchase of the principal
     assets of International Sensor Technology, Inc. (IST) of Pullman,
     Washington. IST pioneered the development of laser heating technology in
     thermoluminescence dosimetry (TLD) systems for personal radiation
     protection. The technology has potential uses in radiation therapy,
     nuclear waste management, radiation processing, environmental and
     radiation-hard electronics applications in government, medicine and the
     nuclear industry.





                                       5
<PAGE>   6
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS.

                           (In Thousands of Dollars)

Results of Operations
---------------------

First Quarter 1996 Compared with First Quarter 1995
---------------------------------------------------

Net income for the first quarter of fiscal 1996 was $1,145, or $.15 per share,
up from $346 or $.05 per share reported in the first quarter of 1995.  The
increase in earnings resulted from increased net sales.

Record net sales of $29,823, increased 27 percent from $23,525 in the prior
year's first quarter.  Double-digit sales increases were noted across all
geographies and in all divisions, except Keithley MetraByte, where net sales
were flat versus the prior year.  Orders for the first quarter of 1996 also set
a new record high.  First quarter orders of $34,036 increased 22 percent from
the prior year's first quarter and 19 percent from the fourth quarter of fiscal
1995.  $1,662 was recorded in initial orders for Quantox(TM), the company's
first product based on the process monitoring technology purchased from IBM in
1994.  The Quantox orders were included in the company's backlog at December
31, 1995, which was at a new record level of $15,680.

Cost of goods sold as a percentage of net sales increased to 39.7 percent from
38.7 percent.  This was the result of Quantox start-up costs and product and
customer sales mix.  The effect of foreign exchange hedging on cost of goods
sold was to increase cost of goods sold as a percentage of net sales by 0.3
percentage points in the first quarter of 1996, compared with an increase of
0.2 percentage points in 1995.

Selling, general and administrative expenses increased $1,530 or 15 percent
from the prior year's quarter, but decreased as a percentage of net sales to
40.1 percent from 44.2 percent.  The increase was due to higher marketing costs
related to the market development and introduction of Quantox, increased
personnel and related costs and a seven percent weaker U.S. dollar.

Product development expenses of $4,096 for the quarter increased $891 or 28%.
This was due to increased costs associated with the development of the
company's next generation of parametric test systems, the development of its
new instrument products and the exploration of other new business
opportunities.

Financing expenses (net of investment income) of $159, decreased $55 from last
year's quarter.  This was due to lower average interest rates on lower average
debt levels.

The effective tax rate was 31.0 percent for the quarter compared with 28.0
percent last year.  The effective rate is less than the statutory rate of 34
percent due to the utilization of foreign tax credits and foreign sales
corporation (FSC) benefits.  The effective tax rate was higher in 1996 than in
1995 because most of the foreign tax credit carryforwards were used in 1995.





                                       6
<PAGE>   7
Liquidity and Capital Resources
-------------------------------

Cash provided by operations for the first quarter was $2,803, and was used
primarily to purchase fixed assets, pay down long term debt and pay dividends.
Total debt of $5,535 at December 31, 1995, decreased $578 during the quarter.
The total debt-to-capital ratio was 12.7 percent at December 31, 1995 compared
to 14.2 percent at September 30, 1995.

The company currently expects to increase capital spending during 1996 and
estimates capital spending will total approximately $9,000 for the year. The 
incremental spending will be to expand production capacity and facilities. 
This level of spending is subject to change based upon the company's operations
during the remainder of the fiscal year.  The Company expects to finance
capital spending through cash provided by operations as well as utilizing its
available lines of credit. At December 31, 1995, the Company had available
unused lines of credit with domestic and foreign banks aggregating $26,138 of
which $6,530 were short term and $19,608 were long term.





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<PAGE>   8
                          PART II.   OTHER INFORMATION
                          --------   -----------------

Item 6.  Exhibits and Reports on Form 8-K.
         ---------------------------------
 
        (a)  Exhibit 27 - Financial Data Schedule

        (b)  No reports on Form 8-K were filed during the quarterly period ended
             December 31, 1995.


                                   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.


                                KEITHLEY INSTRUMENTS, INC.
                                (Registrant)





Date:  February 9, 1996         /s/  Joseph P. Keithley
                                -----------------------------------------------
                                Joseph P. Keithley
                                Chairman, President and Chief Executive Officer 
                                 (Principal Executive Officer)





Date:  February 9, 1996         /s/  Ronald M. Rebner 
                                -----------------------------------------------
                                Ronald M. Rebner
                                Vice President and Chief Financial Officer 
                                  (Principal Financial and Accounting Officer)





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