<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, 1998

                                       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: (440) 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 May 11, 1998 the Registrant had outstanding 5,069,823 Common
Shares, without par value, and 2,785,378 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>
                                                      MARCH 31,       SEPTEMBER 30,
                                               --------------------   -------------
                                                  1998        1997        1997
                                                  ----        ----        ----
<S>                                            <C>         <C>         <C>     
Assets
------

Current assets:
     Cash and cash equivalents                 $  2,033    $  1,737    $  1,727
     Accounts receivable and other, net          18,679      18,873      25,113
     Inventories:
           Raw materials                          8,031       7,041       7,787
           Work in process                        5,651       4,841       5,671
           Finished products                      3,825       5,073       3,121
                                               --------    --------    --------
             Total inventories                   17,507      16,955      16,579
     Other current assets                         3,507       3,851       3,107
                                               --------    --------    --------
             Total current assets                41,726      41,416      46,526
                                               --------    --------    --------

Property, plant and equipment, at cost           42,552      41,346      41,527
Less-Accumulated depreciation                    25,561      24,148      24,272
                                               --------    --------    --------
Total property, plant and equipment, net         16,991      17,198      17,255
                                               --------    --------    --------

Other assets                                     14,703      13,546      15,332
                                               --------    --------    --------
Total assets                                   $ 73,420    $ 72,160    $ 79,113
                                               ========    ========    ========


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

Current liabilities:
     Short-term debt and current
       installments on long-term debt          $     --    $     47    $     16
     Accounts payable                             8,162       8,675      11,568
     Accrued payroll and related expenses         4,202       4,104       4,698
     Other accrued expenses                       6,495       7,273       6,951
     Income taxes payable                         2,164         756       1,821
                                               --------    --------    --------
           Total current liabilities             21,023      20,855      25,054
                                               --------    --------    --------

Long-term debt                                   13,246      16,682      17,442
Other long-term liabilities                       3,836       3,944       3,934

Shareholders' equity:
     Paid-in-capital                              8,742       7,050       7,489
     Earnings reinvested in the business         27,198      24,248      25,773
     Cumulative translation adjustment              160         252         250
     Unamortized portion of restricted stock       (478)       (680)       (569)
     Common shares held in treasury, at cost       (307)       (191)       (260)
                                               --------    --------    --------
           Total shareholders' equity            35,315      30,679      32,683
                                               --------    --------    --------
Total liabilities and shareholders' equity     $ 73,420    $ 72,160    $ 79,113
                                               ========    ========    ========
</TABLE>

                                       2
<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   FOR THE SIX MONTHS
                                                  ENDED MARCH 31,       ENDED MARCH 31,
                                                 1998       1997        1998       1997
                                                 ----       ----        ----       ----

<S>                                            <C>        <C>         <C>        <C>     
Net sales                                      $ 29,696   $ 28,148    $ 61,319   $ 56,034

Cost of goods sold                               13,008     11,746      26,047     23,500

Selling, general and administrative expenses     11,682     11,878      24,388     24,389

Product development expenses                      3,256      4,410       7,183      8,874

Special charges                                     335        375         335        433

Net financing expenses                              253        203         568        473
                                               --------   --------    --------   --------


Income (loss) before income taxes                 1,162       (464)      2,798     (1,635)

Income taxes (benefit)                              383       (126)        923       (459)
                                               --------   --------    --------   --------


Net income (loss)                              $    779   $   (338)   $  1,875   $ (1,176)
                                               ========   ========    ========   ========


Basic income (loss) per share                  $   0.10   $  (0.04)   $   0.24   $  (0.16)
                                               ========   ========    ========   ========

Diluted income (loss) per share                $   0.10   $  (0.04)   $   0.23   $  (0.16)
                                               ========   ========    ========   ========

Cash dividends per Common Share                $   .031   $   .031    $   .063   $   .063
                                               ========   ========    ========   ========

Cash dividends per Class B
    Common Share                               $   .025   $   .025    $   .050   $   .050
                                               ========   ========    ========   ========
</TABLE>


                                       3
<PAGE>   4


                           KEITHLEY INSTRUMENTS, INC.
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                            (In Thousands of Dollars)
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                          FOR THE THREE MONTHS  FOR THE SIX MONTHS
                                                             ENDED MARCH 31,      ENDED MARCH 31,
                                                            1998       1997       1998       1997
                                                            ----       ----       ----       ----
<S>                                                        <C>        <C>        <C>        <C>     
Cash flows from operating activities:
     Net income (loss)                                     $   779    $  (338)   $ 1,875    $(1,176)
     Expenses not requiring outlay of cash                   1,095      1,273      2,253      2,456
     Changes in working capital                             (1,721)    (2,457)       924     (3,805)
     Other operating activities                                221        (27)       395        801
                                                           -------    -------    -------    -------
     Net cash provided by (used in)
       operating activities                                    374     (1,549)     5,447     (1,724)
                                                           -------    -------    -------    -------

Cash flows from investing activities:
     Payments for property, plant, and equipment              (654)    (1,428)    (1,846)    (4,130)
     Other investing activities-net                             61         14         73         16
                                                           -------    -------    -------    -------
     Net cash used in investing activities                    (593)    (1,414)    (1,773)    (4,114)
                                                           -------    -------    -------    -------

Cash flows from financing activities:
     Net increase (decrease) in short term debt                 --        (16)       (16)       (15)
     Net borrowing (repayment) of long term debt            (1,000)      (400)    (4,044)     3,617
     Cash dividends                                           (255)      (221)      (450)      (440)
     Other transactions-net                                  1,163        754      1,207        774
                                                           -------    -------    -------    -------
     Net cash provided by (used in) financing activities       (92)       117     (3,303)     3,936
                                                           -------    -------    -------    -------

Effect of exchange rate changes on cash                        (37)      (355)       (65)      (356)
                                                           -------    -------    -------    -------

Increase (decrease) in cash and cash equivalents              (348)    (3,201)       306     (2,258)
Cash and cash equivalents at beginning of period             2,381      4,938      1,727      3,995
                                                           -------    -------    -------    -------
Cash and cash equivalents at end of period                 $ 2,033    $ 1,737    $ 2,033    $ 1,737
                                                           =======    =======    =======    =======

Supplemental disclosures of cash flow information
-------------------------------------------------
     Cash paid during the period for:
           Income taxes                                    $   266    $   131    $   511    $ 1,307
           Interest                                            229        273        510        513
</TABLE>

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.

                                       4
<PAGE>   5


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

A.   The consolidated financial statements at March 31, 1998 and 1997 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 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 basic net income per share and diluted net income per share was
     7,798,498 and 8,007,564 for the quarter ended March 31, 1998, respectively,
     and 7,609,919 for the quarter ended March 31, 1997. The weighted average
     number of shares and share equivalents used to determine basic net income
     per share and diluted net income per share was 7,741,379 and 8,015,327, for
     the six months ended March 31, 1998, respectively, and 7,541,830 for the
     six months ended March 31, 1997. Both Common Shares and Class B Common
     Shares are included in calculating the weighted average number of shares
     outstanding.

C.   Special charges of $335 for the second quarter of fiscal 1998 relate to
     cost reductions announced in February 1998 for the company's semiconductor
     business, net of $10 for the reversal of personnel related expenses
     previously accrued for the Keithley MetraByte operation relocation. Special
     charges of $375 for the second quarter of fiscal 1997 relate to the
     relocation of the Keithley MetraByte operation to Cleveland from Taunton,
     Massachusetts, and include the reversal of $200 of expense recorded during
     1996 for accrued lease costs related to the relocation for which the lease
     was subsequently terminated. At March 31, 1998 and 1997, the company had
     accruals of $747 and $3,505 remaining on the Consolidated Balance Sheet,
     respectively, ($197 and $3,164 classified as current, respectively, and
     $550 and $341, respectively, classified as long-term). The accrual
     represents personnel and related costs due to cost reduction actions and
     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 that 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 4 years.


                                       5
<PAGE>   6


ITEM 2. Management's Discussion and Analysis of Financial Condition and Results
------- -----------------------------------------------------------------------
        of Operations.
        --------------

                            (In Thousands of Dollars)

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

Second Quarter 1998 Compared with Second Quarter 1997
-----------------------------------------------------

Net income for the second quarter of fiscal 1998 was $779, or $0.10 per share,
compared with a net loss of $338, or $0.04 per share, in the prior year's second
quarter. Excluding special charges in both periods, net income for the second
quarter of fiscal 1998 was $0.13 per share, versus a net loss of $0.01 per share
in the year-earlier period. The earnings turnaround is principally due to
reduced losses from the company's new businesses as earnings from traditional
businesses were essentially unchanged from last year.

Net sales of $29,696 increased 5 percent from $28,148 in the prior year's second
quarter. Higher instruments shipments accounted for the increase.
Geographically, sales increased in the United States and Europe, but decreased
in the Pacific Basin due to lower sales of the company's semiconductor products.
Orders for the second quarter were $29,641, down 12 percent from $33,655 in the
prior year's quarter. Geographically, orders were down in the U.S., down
significantly in the Pacific Basin region, but up in Europe. The largest decline
was experienced in the Pacific Basin region for the company's capital equipment
products serving the semiconductor industry. Order backlog decreased $1,286 for
the quarter to $14,858 at March 31, 1998.

Cost of goods sold as a percentage of net sales increased 2.1 percentage points
to 43.8 percent from 41.7 percent. This was due to lower margins for the
company's semiconductor products. The effect of the company's hedging activities
on cost of goods sold for the quarter was to decrease cost of goods sold by 0.2
percentage points of net sales versus a decrease of 0.3 percentage points in the
prior year's quarter.

Selling, general and administrative expenses of $11,682 for the second quarter
decreased less than 2 percent from the prior year's quarter.

Product development expenses of $3,256, or 11.0 percent of net sales, decreased
26 percent from $4,410, or 15.7 percent of net sales, in the prior year's
quarter. The decrease was due to completion of several of the company's major
project initiatives including Quantox (R)and the S600 parametric tester, which
were notable expenses last year, and the company's SmartLink(TM) line of
products. Additionally, the company implemented cost reduction actions in
February 1998 affecting the Semiconductor Business Unit in an effort to bring
Quantox to near break-even in the second half of the fiscal year and in response
to the downturn in the semiconductor capital equipment market. (See Note C.)

Special charges of $335 for the second quarter of fiscal 1998 relate to cost
reductions announced in February 1998 for the company's semiconductor business,
net of $10 for the reversal of personnel related expenses previously accrued for
the Keithley MetraByte operation relocation. Special charges of $375 for the
second quarter of fiscal 1997 relate to the relocation of the Keithley MetraByte
operation to Cleveland from Taunton, Massachusetts, and include the reversal of
$200 of expense recorded during 1996 for accrued lease costs related to the
relocation for which the lease was

                                       6
<PAGE>   7


subsequently terminated. At March 31, 1998 and 1997, the company had $747 and
$3,505 remaining on the Consolidated Balance Sheet, respectively, ($197 and
$3,164 classified as current , respectively, and $550 and $341, respectively,
classified as long-term). The accrual represents personnel and related costs due
to cost reduction actions and European operating subleases. (See Note C.)

Lower interest expense, due to lower average debt levels during the quarter, was
offset by lower interest income resulting in an increase to net financing
expenses of $50 from the prior year. The prior year's quarter included interest
income received on a federal income tax refund.


Six Months Ended March 31, 1998 Compared with Six Months Ended March 31, 1997
-----------------------------------------------------------------------------

Net income for the six months ending March 31, 1998, was $1,875, or $.23 per
share on a diluted basis, compared to a net loss of $1,176, or $.16 per share
for the six month period last year. The earnings turnaround was due to higher
sales levels in both traditional and new businesses and significantly lower
losses from the company's new businesses.

Net sales of $61,319 increased $5,285, or 9 percent, from $56,034 reported for
the six month period last year. The increase was due mainly to increased
instruments sales, as well as increased shipments of Quantox and increased
billing to the Navy. Geographically, sales increased in the United States and
the Pacific Basin region, but decreased in Europe. Orders for the six month
period were essentially flat versus last year. Increased orders for the
company's instrument products were offset by decreases for data acquisition
boards. Additionally, last year's six month period included a large order from
the Navy. Geographically, orders were down in the United States and Pacific
Basin region, but up in Europe.

Cost of goods sold as a percentage of net sales increased to 42.5 percent from
41.9 percent for the six month period last year. The company's hedging
activities decreased cost of goods sold by 0.1 percentage points of net sales
and 0.2 percentage points for the six months ended March 31, 1998, and 1997,
respectively.

Selling, general and administrative expenses of $24,388 were flat against
$24,389 in the same period last year. As a percentage of net sales, selling,
general and administrative expenses decreased to 39.8 percent from 43.5 percent
in the prior year's six month period due to higher sales volume this year.

Product development expenses of $7,183, or 11.7 percent of net sales, decreased
19 percent from $8,874, or 15.9 percent of net sales, in the prior year. Again,
the decrease was due to completion of several of the company's major project
initiatives including Quantox and the S600 parametric tester, which were notable
expenses last year, and the company's SmartLink(TM) line of products.
Additionally, the company implemented cost reduction actions in February 1998
affecting the Semiconductor Business Unit in an effort to bring Quantox to near
break-even in the second half of the fiscal year and in response to the downturn
in the semiconductor capital equipment market. (See Note C.)

Net financing expenses of $568 increased $95 from the prior year's period. This
was due primarily to interest income received last year on a federal income tax
refund.

                                       7
<PAGE>   8


The effective tax rate was 33.0 percent for the six month period compared with
28.1 percent last year. During the prior year's six month period, $846 of income
tax related accruals were released to income as circumstances giving rise to the
accruals were no longer present. Also during last year's period, and in response
to a 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 4 years.


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

Cash generated from operations was $374 for the second quarter and $5,447 for
the six months ended March 31, 1998, and was used principally to pay down
long-term debt and purchase fixed assets. Additionally, financing activities for
the second quarter include $1,163 generated from the issuance of company stock
through the company's employee stock purchase plan and the exercise of employee
stock options. Total debt of $13,246 at March 31, 1998, decreased $1,091 during
the quarter and $4,212 from the beginning of the fiscal year. The total
debt-to-capital ratio was 27.3 percent at March 31, 1998 compared with 34.8
percent at September 30, 1997.

The company expects to finance capital spending and working capital requirements
with cash provided by operations. At March 31, 1998, the Company had available
unused lines of credit with domestic and foreign banks aggregating $17,082, of
which $5,328 were short term and $11,754 were long term.


Outlook
-------

The impact of the Asian financial crisis and DRAM over-capacity began to affect
the second quarter's order levels. Management believes that this negative impact
will continue for at least the next several quarters.

Additionally, management feels that earnings from operations will be somewhat
higher on relatively flat sales for the company's second half of fiscal 1998
when compared to the first half results.


Factors That May Affect Future Results
--------------------------------------

Information included above in the production development paragraph of the
Results of Operations section, the last paragraph in the Liquidity and Capital
Resources section and the Outlook section of Management's Discussion and
Analysis of Financial Condition and Results of Operations relating to
expectations as to sales, earnings, gross margins and cash flows, 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 to the semiconductor capital equipment
industry. Growth in demand for semiconductors and new


                                       8
<PAGE>   9


technology drives the demand for new semiconductor capital equipment.
Historically, sales and orders levels for this business have been volatile and
contractions in order levels can adversely affect revenue for the company.

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 48 percent of total revenue for the
first half of fiscal 1998. The company's future results could be adversely
affected by several factors, including the length and severity of the Asian
financial crisis, 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.

The company recognizes the need to ensure that Year 2000 hardware and software
issues will not adversely impact its operations. With regard to the company's
own information systems, a substantial portion of Year 2000 information
technology compliance will be achieved in connection with the company's ongoing
program to upgrade its key financial, information and operational systems. The
company believes that all key systems that are not already Year 2000 compliant
will be modified, upgraded or replaced prior to the year 2000, and that any
related costs will not have a material impact on the results of operations,
financial condition or cash flows of future periods. Certain of the company's
hardware and software products purchased by customers or currently being sold to
customers will require upgrade or other remediation to become Year 2000
compliant. Based on an internal assessment of these products, the company does
not believe that the cost to modify these products for Year 2000 compliance will
have a material effect on the results of operations, financial condition or cash
flows of future periods. Lastly, the company is seeking to determine if the
information systems of its major suppliers (insofar as they relate to the
company's business) comply with Year 2000 requirements. The company has not yet
fully determined the extent to which its business may be impacted by third
parties whose products and services may not be ready for the year 2000. There
can be no assurance that the systems of other companies which the company deals
with will be able to adequately address the Year 2000 issue, or that the failure
to do so will not have an adverse effect on the company's operations.



                                       9
<PAGE>   10


                           PART II. OTHER INFORMATION
                           -------- -----------------


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

(a)        EXHIBITS.  The following exhibits are filed herewith:

<TABLE>
<CAPTION>
          Exhibit
          Number                  Exhibit
          ------                  -------
          <S>           <C>                                           
          11            Statement Re Computation of Per Share Earnings

          27            Financial Data Schedule (EDGAR version only)
</TABLE>



(b)        REPORTS ON FORM 8-K. No reports on Form 8-K were filed during the
              quarterly period ended March 31, 1998.



                                   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.


<TABLE>
<S>                                         <C>
                                                    KEITHLEY INSTRUMENTS, INC.
                                                    (Registrant)






Date:  May 14, 1998                          /s/  Joseph P. Keithley
                                           -------------------------
                                                    Joseph P. Keithley
                                                    Chairman, President and Chief Executive Officer
                                                      (Principal Executive Officer)






Date:  May 14, 1998                          /s/  Ronald M. Rebner
                                           -----------------------
                                                    Ronald M. Rebner
                                                    Vice President and Chief Financial Officer
                                                      (Principal Financial and Accounting Officer)
</TABLE>




                                       10