<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 JUNE 30, 1997

                                       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 August 1, 1997 the Registrant had outstanding 4,850,561 Common
Shares, without par value, and 2,786,278 Class B Common Shares, without par
value.


<PAGE>   2

                          PART I. FINANCIAL INFORMATION
                          -----------------------------

ITEM 1.  Financial Statements.
------------------------------
<TABLE>
                           KEITHLEY INSTRUMENTS, INC.
                           CONSOLIDATED BALANCE SHEET
                            (In Thousands of Dollars)
                                   (Unaudited)
<CAPTION>
                                                         JUNE 30,             SEPTEMBER 30,
                                                  -----------------------     -------------
                                                   1997             1996          1996
                                                   ----             ----          ----

<S>                                               <C>            <C>            <C>     
Assets
------

Current assets:
     Cash and cash equivalents                    $  2,018       $  3,969       $  3,995
     Accounts receivable and other, net             21,038         19,370         18,538
     Inventories:
           Raw materials                             7,585          8,017          8,255
           Work in process                           5,508          5,704          4,880
           Finished products                         3,800          4,711          4,291
                                                  --------       --------       --------
             Total inventories                      16,893         18,432         17,426
     Other current assets                            3,016          2,631          3,781
                                                  --------       --------       --------
             Total current assets                   42,965         44,402         43,740
                                                  --------       --------       --------
Property, plant and equipment, at cost              41,822         36,592         37,873
Less-Accumulated depreciation                       24,896         24,259         22,531
                                                  --------       --------       --------
Total property, plant and equipment, net            16,926         12,333         15,342
                                                  --------       --------       --------
Intangible assets, net                               1,877          7,973          2,064
Other assets                                        12,712          9,548         12,688
                                                  --------       --------       --------
Total assets                                      $ 74,480       $ 74,256       $ 73,834
                                                  ========       ========       ========


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

Current liabilities:
     Short-term debt and current
       installments on long-term debt             $     31       $     84       $     61
     Accounts payable                                9,089          7,032          8,162
     Accrued payroll and related expenses            4,141          5,232          4,525
     Other accrued expenses                          7,336          5,246          9,358
     Income taxes payable                            1,244          1,956          2,955
                                                  --------       --------       --------
           Total current liabilities                21,841         19,550         25,061
                                                  --------       --------       --------

Long-term debt                                      17,865         11,308         13,308
Other long-term liabilities                          3,531          3,125          3,709

Shareholders' equity:
     Paid-in-capital                                 7,076          5,074          5,479
     Earnings reinvested in the business            24,787         34,911         25,865
     Cumulative translation adjustment                 218            399            562
     Unamortized portion of restricted stock          (625)            (3)           (14)
     Common shares held in treasury, at cost          (213)          (108)          (136)
                                                  --------       --------       --------
           Total shareholders' equity               31,243         40,273         31,756
                                                  --------       --------       --------
Total liabilities and shareholders' equity        $ 74,480       $ 74,256       $ 73,834
                                                  ========       ========       ========
</TABLE>


                                       2

<PAGE>   3


<TABLE>
                           KEITHLEY INSTRUMENTS, INC.
                     CONSOLIDATED STATEMENT OF INCOME (LOSS)
               (In Thousands of Dollars Except for Per Share Data)
                                   (Unaudited)
<CAPTION>
                                                 FOR THE THREE MONTHS        FOR THE NINE MONTHS
                                                     ENDED JUNE 30,            ENDED JUNE 30,
                                                    1997        1996          1997          1996
                                                    ----        ----          ----          ----
<S>                                             <C>          <C>           <C>           <C>    
Net sales                                         $32,410      $29,403       $88,444       $89,245

Cost of goods sold                                 13,896       11,376        37,396        34,178

Selling, general and administrative expenses       12,842       11,985        37,117        36,263

Product development expenses                        3,878        4,664        12,752        13,096

Special charges                                       306           --           739            --

Amortization of intangible assets                      56          171           170           462

Net financing expenses                                344          201           817           536
                                                  -------      -------      --------       -------


Income (loss) before income taxes (benefit)         1,088        1,006          (547)        4,710

Income taxes (benefit)                                327          245          (132)        1,319
                                                  -------      -------      --------       -------


Net income (loss)                                 $   761      $   761      $   (415)      $ 3,391
                                                  =======      =======      ========       =======


Net income (loss) per share                       $  0.10      $  0.10      $  (0.05)      $  0.43
                                                  =======      =======      ========       =======

Cash dividends per Common Share                   $  .031      $  .031      $   .094       $  .094
                                                  =======      =======      ========       =======

Cash dividends per Class B
  Common Share                                    $  .025      $  .025      $   .075       $  .075
                                                  =======      =======      ========       =======
</TABLE>




                                       3
<PAGE>   4


<TABLE>
                           KEITHLEY INSTRUMENTS, INC.
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                            (In Thousands of Dollars)
                                   (Unaudited)
<CAPTION>
                                                        FOR THE THREE MONTHS              FOR THE NINE MONTHS
                                                           ENDED JUNE 30,                    ENDED JUNE 30,
                                                         1997          1996                1997         1996
                                                         ----          ----                ----         ----
<S>                                                  <C>          <C>                  <C>            <C>
Cash flows from operating activities:               
     Net income (loss)                                  $   761       $   761              $  (415)      $ 3,391
     Expenses not requiring outlay of cash                  732         1,213                3,188         3,415
     Changes in working capital                            (290)       (2,061)              (4,095)       (5,850)
     Other operating activities                          (1,278)         (958)                (477)         (281)
                                                        -------       -------              -------       -------
     Net cash provided by (used in)
         operating activities                               (75)       (1,045)              (1,799)          675
                                                        -------       -------              -------       -------

Cash flows from investing activities:
     Payments for property, plant, and equipment           (828)         (964)              (4,958)       (4,419)
     Acquisitions (excluding cash of $11)                    --            --                   --        (1,408)
     Other investing activities-net                         103             2                  119             5
                                                        -------       -------              -------       -------
     Net cash used in investing activities                 (725)         (962)              (4,839)       (5,822)
                                                        -------       -------              -------       -------

Cash flows from financing activities:
     Net increase (decrease) in short-term debt             (15)           12                  (30)           13
     Net borrowing (repayment) of long-term debt          1,303         1,686                4,920         5,373
     Cash dividends                                        (222)         (215)                (662)         (637)
     Other transactions-net                                   4           257                  778           606
                                                        -------       -------              -------       -------
     Net cash provided by financing activities            1,070         1,740                5,006         5,355
                                                        -------       -------              -------       -------

Effect of exchange rate changes on cash                      11           (53)                (345)         (129)
                                                        -------       -------              -------       -------

Increase (decrease) in cash and cash equivalents            281          (320)              (1,977)           79
Cash and cash equivalents at beginning of period          1,737         4,289                3,995         3,890
                                                        -------       -------              -------       -------
Cash and cash equivalents at end of period              $ 2,018       $ 3,969              $ 2,018       $ 3,969
                                                        =======       =======              =======       =======

Supplemental disclosures of cash flow information 
--------------------------------------------------
  Cash paid during the period for:
           Income taxes                                 $   399       $   857              $ 1,706       $ 1,543
           Interest                                         306           158                  819           505

Supplemental schedule of noncash investing activities
-----------------------------------------------------
     The company's acquisitions included the following
noncash transactions (See Notes E and F):
           Fair value of assets acquired                     --            --                   --       $ 2,525
           Cash paid                                         --            --                   --        (1,408)
           Common Shares issued                              --            --                   --          (201)
                                                        -------       -------              -------       -------
                 Liabilities assumed                         --            --                   --       $   916
                                                        =======       =======              =======       =======

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>


                                       4
<PAGE>   5



                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                   ------------------------------------------

A.   The consolidated financial statements at June 30, 1997 and 1996 and for the
     three month periods then ended have not been examined by independent
     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 (loss) 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 outstanding used in determining net
     income per share was 7,877,808 for the quarter ended June 30, 1997 and
     7,867,335 for the quarter ended June 30, 1996. For the nine months ended
     June 30, 1997 and June 30, 1996, the weighted average number of shares
     outstanding was 7,570,062 and 7,804,342, respectively. Both Common Shares
     and Class B Common Shares are included in calculating the weighted average
     number of shares outstanding. Fully diluted net income per share is not
     materially different than net income per share.

C.   Special charges of $306 for the third quarter of fiscal 1997 include $706
     for the relocation of the Keithley MetraByte operation to Cleveland from
     Taunton, Massachusetts and a reversal of $400 of expense recorded during
     1996 for accrued lease costs. $224 of special charges in the third quarter
     were non-cash. At June 30, the moving of the operation was substantially
     complete and any additional expenses recorded in the fourth quarter of
     fiscal 1997 are expected to be nominal. At June 30, 1997, the company had
     $2,026 remaining on the Consolidated Balance Sheet ($1,685 in the caption
     "Other accrued expenses" and $341 in the caption "Other long-term
     liabilities") for the closing of the Taunton facility and certain European
     operating subleases.

D.   During the first quarter of fiscal 1997, $846 of income tax related
     accruals were released to income as circumstances giving rise to the
     accruals were no longer present. Also during the first quarter, and in
     response to a recent tax law change, the company decided to terminate
     existing corporate owned life insurance policies and a deferred tax charge
     of $888 was recorded, reflecting the tax on the excess of cash surrender
     value over premiums paid on the policies. The tax is payable over four
     years.

E.   On February 15, 1996, the company consummated the purchase of certain
     assets of Turner Engineering Technology (Turner) of Roanoke, Texas. Turner
     specializes in accelerated test methods for determining the quality of
     semiconductor wafers at various stages of manufacturing. These test methods
     are designed to save semiconductor manufacturers money by providing process
     control feedback to allow optimization and continued semiconductor process
     improvement.

F.   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
---------------------

Third Quarter 1997 Compared with Third Quarter 1996
---------------------------------------------------

The third quarter of 1997 marked the return to profitability for the company,
and represented the first quarter of positive earnings since the third quarter
of fiscal 1996. Earnings before income taxes and special charges related to the
Keithley MetraByte relocation were $1,394, up 39 percent from last year's third
quarter. Net income for the quarter was $761, or $.10 per share, which is the
same as last year's third quarter.

Record net sales of $32,410 for the third quarter of fiscal 1997 were up 10
percent from $29,403 in the same period last year. The increase was due mostly
to high demand for the company's recently introduced products designed
specifically for the telecommunications industry and the ramp-up in sales for
the Quantox(R) Silicon Oxide Monitoring System, offset somewhat by lower sales
for Keithley MetraByte's PC board products and lower sales of parametric test
products serving the semiconductor industry. Orders for the third quarter of
$35,806 increased 30 percent from the prior year's third quarter and represent
the fourth consecutive quarterly increase. Geographically, orders were up
significantly in the United States and down in the Pacific Basin and Europe.
Backlog increased $1,857 during the quarter to a record $18,835 at June 30,
1997.

Cost of goods sold as a percentage of net sales increased 4.2 percentage points
to 42.9 percent from 38.7 percent. This was due to expected lower margins and
start up costs of the company's new business initiatives, and higher fixed costs
resulting from the expansion of manufacturing facilities. The effect of the
company's hedging activities on cost of goods sold was a decrease of 0.2
percentage points of net sales in both this year's and the prior year's quarter.

Selling, general and administrative expenses of $12,842 for the third quarter
increased $857, or 7 percent from the prior year's quarter, but decreased as a
percentage of net sales to 39.6 percent from 40.8 percent. The increase in
dollars was due mainly to higher commissions and higher sales promotion
expenses.

Product development expenses of $3,878 decreased 17 percent from $4,664 in the
prior year's quarter. Higher development costs for the company's instrument
products were more than offset by lower product development expenses for
Keithley MetraByte due to that operation's relocation. Additionally, last year's
quarter contained high development expenses for the S600 parametric tester which
is essentially complete.

Special charges of $306 for the third quarter of fiscal 1997 include $706 for
the relocation of the Keithley MetraByte operation to Cleveland from Taunton,
Massachusetts and a reversal of $400 of expense recorded during 1996 for accrued
lease costs. $224 of special charges were non-cash. At June 30, the moving of
the operation was substantially complete and any additional expenses recorded in
the fourth quarter of fiscal 1997 are expected to be nominal. At June 30, 1997,
the company had



                                        6
<PAGE>   7
$2,026 remaining on the Consolidated Balance Sheet ($1,685 in the caption "Other
accrued expenses" and $341 in the caption "Other long-term liabilities") for the
closing of the Taunton facility and certain European operating subleases.

Amortization expense of $56 for the quarter decreased from the prior year's
quarter due to the September 1996 write-off of the remaining goodwill associated
with Keithley MetraByte.

Net financing expenses of $344 increased $143 or 71 percent from last year's
third quarter due to higher average debt levels during the quarter.

Nine Months Ended June 30, 1997 Compared with Nine Months Ended June 30, 1996
-----------------------------------------------------------------------------

The company recorded a net loss of $415, or $.05 per share, for the nine months
ended June 30, 1997, compared with net income of $3,391, or $.43 per share, for
the prior year. Excluding special charges for the nine month period in fiscal
1997, net income was $112, or $.01 per share.

Net sales of $88,444 decreased less than 1 percent, from $89,245 reported for
the nine month period last year. The decrease was due to decreased sales of
parametric testers serving the semiconductor industry and of the company's data
acquisition boards, offset by increased sales of Quantox and of the company's
instrument products. Orders for the nine month period were up 12 percent from
last year. The majority of the increase was due to orders for Quantox and strong
demand for the company's instrument products. Geographically, orders for the
nine months were up in the United States and Pacific Basin, while down in
Europe.

Cost of goods sold as a percentage of net sales increased to 42.3 percent from
38.3 percent for the nine month period last year. This was due to expected lower
margins and start up costs of the company's new business initiatives and higher
fixed costs resulting from the expansion of manufacturing facilities. The effect
of the company's hedging activities on cost of goods sold was a decrease of 0.1
percentage points of net sales for the nine months ended June 30, 1997, versus
no effect on cost of goods sold in last year's nine month period.

Selling, general and administrative expenses of $37,117, or 42.0 percent of net
sales, were up $854, or 2 percent, from $36,263, or 40.6 percent of net sales,
in the same period in the prior year due to higher marketing costs. Decreased
expenses related to Keithley MetraByte's relocation, were offset by increased
costs for the company's new business initiatives.

Product development expenses of $12,752, or 14.4 percent of net sales, for the
first nine months of fiscal 1997, decreased 3 percent from $13,096 , or 14.7
percent of net sales in the same period last year. Higher development costs for
the company's instrument products and new business initiatives were more than
offset by lower product development expenses for Keithley MetraByte due to that
operation's relocation. Additionally, last year's nine month period contained
high development expenses for the S600 parametric tester which was essentially
completed during fiscal 1997.

Special charges of $739 for the nine month period during fiscal 1997 include
$1,339 for the relocation of the Keithley MetraByte operation to Cleveland from
Taunton, Massachusetts and a reversal of $600 of expense recorded during 1996
for accrued lease costs. $224 of special charges were non-cash. At June 30, the
moving of the operation was substantially complete and any additional expenses


                                       7

<PAGE>   8
recorded in the fourth quarter of fiscal 1997 are expected to be nominal. At
June 30, 1997, the company had $2,026 remaining on the Consolidated Balance
Sheet ($1,685 in the caption "Other accrued expenses" and $341 in the caption
"Other long-term liabilities") for the closing of the Taunton facility and
certain European operating subleases.

Net financing expenses of $817 increased $281, or 52 percent, due to higher
average debt levels during the period.

The effective tax rate was 24.0 percent for the nine month period compared with
28.0 percent for the prior year's period. The effective rate is less than the
statutory rate of 34 percent due to the utilization of foreign sales corporation
(FSC) benefits.

Liquidity and Capital Resources
-------------------------------

Cash used in operations was $75 for the third quarter and $1,799 for the nine
months ended June 30, 1997. Total debt of $17,896 at June 30, 1997 increased
$4,527 from the beginning of the fiscal year. The increase in debt and decrease
in cash during the nine month period were used primarily to pay current
liabilities, purchase fixed assets, and fund the expansion of the company's
Semiconductor and Radiation Measurements facilities. The facilities expansion
was substantially completed by the end of the second quarter. The total
debt-to-capital ratio was 36.4 percent at June 30, 1997 compared with 29.6
percent at September 30, 1996.

During the second quarter of fiscal 1997, the company amended its $25,000
unsecured, multi-currency debt facility. The agreement was extended until March
2002, and generally includes lower overall borrowing costs than the previous
agreement. The company expects to finance capital spending and working capital
requirements with cash provided by operations and its available lines of credit.
At June 30, 1997, the Company had available unused lines of credit with domestic
and foreign banks aggregating $13,118, of which $5,983 were short term and
$7,135 were long term.

Outlook
-------

Based on expected order levels and the company's backlog, fourth quarter sales
and earnings are expected to be somewhat better than those reported in the third
quarter. However, a prolonged strike by the Teamsters at UPS could impact the
company's ability to meet its fourth quarter shipment estimate. Additionally,
the company's new business initiatives are entering the phase in their
commercialization where revenues are beginning to ramp up and the challenge
ahead is to manage them profitability. The company expects that by the middle of
fiscal 1998, the current new businesses will be close to break even and that
fiscal year 1998's profits will be better than 1997's.

Gross margins, however, are not expected to improve over the next several
quarters due to higher fixed costs resulting from the expansion of manufacturing
facilities, increased shipments of Quantox which carry lower margins, and the
potential continued strengthening of the U.S. dollar.



                                       8
<PAGE>   9
Factors That May Affect Future Results
--------------------------------------

Information included above in the Outlook section of Management's Discussion and
Analysis of Financial Condition and Results of Operations relating to the
expectations for sales, earnings, new business initiatives and gross margins,
constitute "forward-looking" statements, as that term is defined in the Private
Securities Litigation Reform Act of 1995. Such statements are subject to certain
risks and uncertainties that could cause actual results to differ materially
from those projected. Some of the factors that may affect future results are
discussed below.

Although the company operates in a single industry segment, certain of its
products and product lines including the Quantox unit and the company's line of
parametric test systems, are sold into the semiconductor capital equipment
industry. Growth in demand for semiconductors and new technology drives the
demand for new semiconductor capital equipment. Although order growth in this
industry has recently increased, the sustainability of this trend cannot be
predicted.

In September 1996, the company announced its intention to relocate its Keithley
MetraByte operation to Cleveland, Ohio from Taunton, Massachusetts, and form a
new business. This relocation is now complete; however, sales of the company's
personal computer plug-in boards have declined somewhat. The business decline
could be protracted for several reasons, including the continuation of hiring
and training qualified personnel to assume duties of employees who did not
relocate from Taunton, and assimilation and establishment of sales support and
manufacturing processes in Cleveland to sell and produce the plug-in board
products.

The company's business relies on the development of new high technology products
and services to provide solutions to customer's complex measurement needs. This
requires anticipation of customers' changing needs and emerging technology
trends. The company must make long-term investments and commit significant
resources before knowing whether its predictions will eventually result in
products that achieve market acceptance. The company incurs significant expenses
developing new business opportunities that may or may not result in significant
sources of revenue and earnings in the future.

In many cases the company's products compete directly with those offered by
other manufacturers. If any of the company's competitors were to develop
products or services that are more cost-effective or technically superior,
demand for the company's product offerings could slow.

The company currently has ten subsidiaries or sales offices located outside the
United States, and non-U.S. sales made up 47 percent of total revenue for the
first nine months of fiscal 1997. The company's future results could be
adversely affected by several factors, including changes in foreign currency
exchange rates, changes in a country's or region's political or economic
conditions, trade protection measures, import or export licensing requirements,
unexpected changes in regulatory requirements and natural disasters.



                                       9


<PAGE>   10
                           PART II. OTHER INFORMATION
                           --------------------------

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

(a)      Exhibits.  The following exhibits are filed herewith:
         --------

         Exhibit
         Number                     Exhibit
         -------                    -------

         11               Statement Re Computation of Per Share Earnings

         27               Financial Data Schedule (EDGAR version only)


(b)      REPORTS ON FORM 8-K. No reports on Form 8-K were filed during the 
         quarterly period ended June 30, 1997.

                                   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:  August 13, 1997     /s/  Joseph P. Keithley
                           -------------------------
                           Joseph P. Keithley
                           Chairman, President and Chief Executive Officer
                             (Principal Executive Officer)

Date:  August 13, 1997     /s/  Ronald M. Rebner
                           -----------------------
                           Ronald M. Rebner
                           Vice President and Chief Financial Officer
                             (Principal Financial and Accounting Officer)


                                       10