UNITED STATES
               SECURITIES AND EXCHANGE COMMISSION
                     WASHINGTON, D.C.  20549
                            FORM 10-Q
                           __________
[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
SECURITIES EXCHANGE ACT OF 1934

For the quarterly period ended June 30, 1998

                                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 1-8782

                       GLEASON CORPORATION
   (Exact name of registrant as specified in its charter)

             DELAWARE                     16-1224655
   (State or other jurisdiction of     (I.R.S. Employer
    incorporation or organization)      Identification No.)

    1000 University Avenue, Rochester, New York        14692
   (Address of principal executive offices)           (Zip Code)


Registrant's telephone number, including area code:   (716) 473-1000

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 ( ).

The number of shares outstanding of the registrant's Common
stock, par value $1 per share, at June 30, 1998 was 10,524,815
shares.

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

                    GLEASON CORPORATION AND SUBSIDIARIES
                         CONSOLIDATED BALANCE SHEETS
                                 (Unaudited)
<CAPTION>

                                                      (Dollars in thousands)
                                                       JUNE 30   DECEMBER 31
Assets                                                   1998        1997
<S>                                                   <C>          <C>
Current assets
  Cash and equivalents                                $ 20,488     $ 12,478
  Trade accounts receivable                             93,049      101,024
  Inventories                                           57,331       55,991
  Other current assets                                  13,538       13,367
    Total current assets                               184,406      182,860

Property, plant and equipment, at cost                 251,528      242,399
  Less accumulated depreciation                        126,818      118,026
                                                       124,710      124,373

Goodwill                                                17,737       18,036
Other assets                                            16,918       20,384

Total assets                                          $343,771     $345,653

Liabilities and Stockholders' Equity

Current liabilities
  Short-term borrowings                               $  5,475     $  5,760
  Current portion of long-term debt                         94        1,613
  Trade accounts payable                                33,082       30,810
  Income taxes                                           7,907       13,640
  Other current liabilities                             63,209       70,614
    Total current liabilities                          109,767      122,437

Long-term debt                                          35,907       38,244
Pension plans and other retiree benefits                60,587       60,235
Other liabilities                                       11,670       10,516

  Total liabilities                                    217,931      231,432

Stockholders' equity
  Common stock                                          11,594       11,594
  Additional paid-in capital                            12,291       12,061
  Retained earnings                                    118,255      107,797
  Accumulated other comprehensive income:
    Cumulative foreign currency translation 
     adjustment                                         (3,882)      (3,889)
    Minimum pension liability adjustment                  (901)        (901)
                                                       137,357      126,662
  Less treasury stock, at cost                          11,517       12,441

  Total stockholders' equity                           125,840      114,221

Total liabilities and stockholders' equity            $343,771     $345,653

<FN>
See notes to consolidated financial statements.
</FN>
</TABLE>
<PAGE>
<PAGE>

<TABLE>
                   GLEASON CORPORATION AND SUBSIDIARIES
                    CONSOLIDATED STATEMENTS OF OPERATIONS
                                 (Unaudited)
<CAPTION>
                                                (Dollars in thousands, except
                                                     per share amounts)
                                                     THREE MONTHS ENDED
                                                           JUNE 30
                                                      1998         1997
<S>                                                <C>          <C>
Net sales                                            $108,171     $ 62,384

Costs and expenses
  Cost of products sold                                75,766       42,683
  Selling, general and
    administrative expenses                            17,920        9,759
  Research and development expenses                     2,692        1,660
  Loss on settlement of pension plan                    2,031           --
  Interest (income) expense -- net                        275         (120)
  Other (income) -- net                                   (82)        (285)


Income before income taxes                              9,569        8,687

Provision for income taxes                              4,010        3,110

Net income                                           $  5,559     $  5,577


Earnings per common share:
  Basic                                              $    .53     $    .56
  Diluted                                            $    .51     $    .54

Weighted average number of common shares outstanding:
  Basic                                            10,501,250    9,922,136
  Diluted                                          10,922,179   10,306,354

Cash dividends declared per common share             $  .0625     $  .0625

<FN>
See notes to consolidated financial statements.
</FN>
</TABLE>
<PAGE>
<PAGE>
                                     
<TABLE>
                   GLEASON CORPORATION AND SUBSIDIARIES
                    CONSOLIDATED STATEMENTS OF OPERATIONS
                                 (Unaudited)

<CAPTION>

                                                (Dollars in thousands, except
                                                       per share amounts)
                                                        SIX MONTHS ENDED
                                                            JUNE 30
                                                        1998       1997
<S>                                                <C>          <C>
Net sales                                            $203,568     $122,719

Costs and expenses
  Cost of products sold                               141,740       83,699
  Selling, general and
    administrative expenses                            34,530       19,622
  Research and development expenses                     4,906        3,634
  Loss on settlement of pension plan                    2,031           --
  Interest (income) expense -- net                        642         (121)
  Other (income) -- net                                   (71)        (825)


Income before income taxes                             19,790       16,710

Provision for income taxes                              8,021        5,939

Net income                                           $ 11,769     $ 10,771


Earnings per common share:
  Basic                                              $   1.12     $   1.08
  Diluted                                            $   1.08     $   1.04

Weighted average number of common shares 
  outstanding:
  Basic                                            10,483,704    9,944,966
  Diluted                                          10,896,833   10,316,908

Cash dividends declared per common share             $   .125     $   .125

<FN>
See notes to consolidated financial statements.
</FN>
</TABLE>
<PAGE>
<PAGE>
<TABLE>
                   GLEASON CORPORATION AND SUBSIDIARIES
                  CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (Unaudited)
<CAPTION>                        
                                                     (Dollars in thousands)
                                                          SIX MONTHS ENDED
                                                               JUNE 30
                                                          1998         1997
<S>                                                    <C>          <C>
Cash flows from operating activities:
  Net income                                           $ 11,769     $ 10,771
  Adjustments to reconcile net income
    to net cash provided by operating activities:
    Loss on settlement of pension plan                    2,031           --
    Depreciation and amortization                        10,659        5,535
    (Gain) on disposals of property, plant
      and equipment                                          (5)        (462)
    Provision for deferred income taxes                     617          278
    Changes in operating assets and liabilities:
       Decrease in accounts receivable                    7,622        6,068
      (Increase) in inventories                          (1,668)      (4,201)
      (Increase) decrease in other current assets           263         (617)
      Increase (decrease) in trade accounts payable        (578)         797
      Increase (decrease) in income taxes payable        (5,265)       1,166
      Increase (decrease) in all other current 
        operating liabilities                            (3,932)         478
      Other, net                                          1,449          (59)

  Net cash provided by operating activities              22,962       19,754

Cash flows from investing activities:
  Capital expenditures                                  (10,608)      (5,424)
  Proceeds from asset disposals                             144        1,554
  Proceeds from collection of notes receivable               18           36

   Net cash (used in) investing activities              (10,446)      (3,834)

Cash flows from financing activities:
  Proceeds from (repayments of) short-term 
   borrowings                                              (291)       1,820
  Net (repayments) under revolving credit agreements     (2,021)      (1,795)
  Net proceeds from (repayment of) long-term debt        (1,561)         128
  Purchase of treasury stock                                 (5)      (1,360)
  Net stock issues                                          701           26
  Dividends paid                                         (1,311)      (1,242)

   Net cash (used in) financing activities               (4,488)      (2,423)

Effect of exchange rate changes on cash
  and equivalents                                           (18)        (259)
Increase in cash and equivalents                          8,010       13,238
Cash and equivalents, beginning                          12,478        7,199

Cash and equivalents, ending                           $ 20,488     $ 20,437

<FN>
See notes to consolidated financial statements.
</FN>
</TABLE>
<PAGE>
<PAGE>
   
            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                           JUNE 30, 1998
                            (Unaudited)
                                

1.   In the opinion of management, the accompanying unaudited
     consolidated financial statements contain all adjustments
     necessary to present fairly (a) the results of operations
     for the three and six-month periods ended June 30, 1998 and
     1997,  (b) the financial position at June 30, 1998 and
     December 31, 1997, and (c) the cash flows for the six-month
     periods ended June 30, 1998 and 1997, of Gleason Corporation
     and subsidiaries.

2.   The results of operations for the six-month period ended
     June 30, 1998 are not necessarily indicative of the results
     to be expected for the full year.

3.   All significant intercompany transactions are eliminated in
     consolidation.

4.   The components of inventories were as follows:
     (In thousands)             6/30/98  12/31/97
     Raw materials and
       purchased parts         $ 11,047  $ 11,215
     Work in process             35,423    34,491
     Finished goods              10,861    10,285
                               $ 57,331  $ 55,991


5.   Net cash payments for income taxes were $12,882,000 and
     $4,158,000 for the six months ended June 30, 1998 and 1997,
     respectively.  Interest payments were $1,147,000 and $79,000 for
     the six months ended June 30, 1998 and 1997, respectively.

6.   Effective January 1, 1998, the Company adopted Statement of
     Financial Standards No. 130, "Reporting Comprehensive Income"
     (FAS No. 130).  FAS No. 130 establishes standards for the
     reporting and display of comprehensive income and its components.
     The adoption of FAS No. 130 does not impact the calculation of
     net earnings or earnings per share nor does it impact reported
     assets, liabilities or total stockholders' equity.  Application
     of this Statement will result in the presentation of the
     components of comprehensive income within the annual financial
     statements, which must be displayed with the same prominence as
     other financial statements.

<PAGE>
<PAGE>
     
     The components of the Company's total comprehensive income
     were:
<TABLE>
<CAPTION>
     
                                  Three Months Ended        Six Months Ended
                                       June 30,                  June 30,
     
    (in thousands)                    1998      1997         1998       1997
     <S>                            <C>       <C>         <C>        <C>
     Net income                     $5,559    $5,577      $11,769    $10,771
     Foreign currency translation
       adjustments                     (82)     (116)           7     (1,499)
     Total comprehensive income     $5,477    $5,461      $11,776    $ 9,272
</TABLE>

7.   In February 1998, the Financial Accounting Standards Board
     issued Statement of Financial Accounting Standards No. 132,
     "Employers' Disclosures about Pension and Other Postretirement
     Benefits".  This Statement revises employers' disclosures of
     pensions and other postretirement benefits, requires additional
     information on changes in benefit obligations and fair value of
     plan assets and eliminates certain disclosures.  Restatement of
     disclosures for earlier periods is required.  This Statement is
     effective for the Company's consolidated financial statements for
     the year ending December 31, 1998.

8.   In June 1998, the Financial Accounting Standards Board
     issued Statement of Financial Standards No. 133, "Accounting for
     Derivative Instruments and Hedging Activities" which provides new
     guidelines for accounting for derivative instruments.  The
     Company is currently analyzing what impact the new guideline will
     have on the Company.  This statement is effective for fiscal
     periods beginning after June 15, 1999.

<PAGE>
<PAGE>
               GLEASON CORPORATION AND SUBSIDIARIES

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

The following are management's comments relating to significant
changes in the results of operations for the three and six-month
periods ended June 30, 1998 and 1997 and in the Company's
financial condition during the six months ended June 30, 1998.

Results of Operations

All references to earnings per share reflect diluted earnings per
share.  Basic and diluted earnings per share for prior periods
have been restated to reflect the Company's two-for-one stock
split which occurred in September 1997.

Net income for the second quarter ended June 30, 1998 was $5.6
million, or $.51 per share, compared to $5.6 million, or $.54 per
share, for the 1997 second quarter.  Net income for the quarter
included a $2.0 million ($1.2 million after-tax), or $.11 per
share, non-cash charge, which the Company had previously
disclosed, for the write-off of a prepaid pension asset
associated with the settlement of the Company's U.S. defined
benefit retirement plan.  Excluding the pension charge, earnings
per share for the 1998 second quarter would have increased 15%,
compared to the 1997 second quarter, to $.62 per share.

Net income for the six months ended June 30, 1998 was $11.8
million, or $1.08 per share, compared to $10.8 million, or $1.04
per share, for the 1997 first half.  Excluding the pension charge,
earnings per share for the first half of 1998 would have
increased 14%, compared to the 1997 first half, to $1.19 per
share.  This increase in net income was primarily attributable to 
the inclusion of the Company's Pfauter operations, which were acquired 
on July 31, 1997.

New orders totaled $85.7 million for the second quarter compared
to $74.6 million in the 1997 second quarter.  Order levels for
the 1998 six-month period were $181.5 million compared to $130.0
million in the 1997 first half.  Order levels, excluding Pfauter
operations, decreased 42% and 20%, respectively, compared to the
1997 periods due to lower incoming orders for both bevel and
cylindrical gear production machines.  This decline was primarily
due to a lack of significant orders from automotive customers in
1998 and lower demand from customers in the Asian region.  In
the first half of 1997, the Company received large orders for
both bevel and cylindrical gear production machines tied to major
automotive capital investment programs, including a $14.0 million
order for cylindrical gear production machines from a European
automotive transmission producer.

The Company expects demand for its products in the Americas and
Europe to remain reasonably strong, but due to the economic
crisis in the Asian markets, new orders for the second half of
1998 are expected to be only slightly higher than for the first
half.   Approximately 20% of the Company's normal sales volume
comes from customers in Asia, but given the economic conditions
in that region, the Company anticipates this level will account
for only about 5% of total new orders in 1998.

<PAGE>
<PAGE>

Consolidated backlog was $155.6 million at June 30,1998 compared
to $177.7 million at December 31, 1997 and $130.1 million at June
30,1997.  Backlog at June 30, 1998, excluding Pfauter
operations, totaled $87.0 million, compared to $108.9 million at
December 31, 1997.

Net sales were $108.2 million and $203.6 million for the three
and six-month periods ended June 30, 1998 compared to $62.4
million and $122.7 million in the prior year periods. Sales for
these same periods, excluding Pfauter, increased 6% and 3%
respectively, compared to the prior year.  Higher shipments of
cylindrical gear machine products offset lower sales of bevel
gear production machines in both the second quarter and first
half.  Sales of tooling and aftermarket products were flat for
the second quarter and down 4% for the first half compared to the
1997 periods.  On a regional basis (excluding Pfauter), shipments
in the 1998 first half were higher to customers in the United
States and Europe, but were significantly lower to customers in
Asia.  Sales to the Asia-Pacific region declined to represent
only 13% of sales in the 1998 first half, compared to 26% in the
prior year first half.  Sales to customers in Europe increased
54% and 22%, respectively, for the second quarter and first half
compared to the 1997 periods.

Cost of products sold as a percentage of sales was 70.0% and
69.6% for the three and six-month periods ended June 30, 1998
compared to 68.4% and 68.2% for the comparable 1997 periods.
Margins are heavily impacted by the mix of products sold.  For
example, machines, in general, tend to carry higher cost of sales
percentages than tooling and other products.  Consolidated
margins were lower in the 1998 second quarter and first half
primarily due to a higher level of machine sales.  Margins on
machine products were lower in 1998 due to higher cylindrical
gear production machine sales, including Pfauter machines.

Selling, general and administrative expenses for the second
quarter were $17.9 million, or 16.6% of sales,  compared to $9.8
million, or 15.6% of sales, in the 1997 second quarter.   For the
first half of 1998, these expenses totaled $34.5 million, or
17.0% of sales, compared to $19.6 million, or 16.0% of sales, for
the prior year period.  These expenses as a percentage of sales
for the first half increased due to the inclusion of the Pfauter
operations in the 1998 results.  Excluding Pfauter, spending as a
percentage of sales for the first half equaled the 1997 level of
16.0% of sales.

Research and development expenses were $2.7 million and $4.9
million in the three and six-month periods of 1998, compared to
$1.7 million and $3.6 million in the respective prior year
periods.   For the first half of 1998, excluding Pfauter, these
expenses approximated the 1997 level.  Research and development
spending in 1998 included new product development programs for
both bevel and cylindrical gear machine products.

<PAGE>
<PAGE>

Other income was $.1 million for both the second quarter and
first half of 1998 compared to $.3 million and $.8 million in the
1997 periods.  Other income in the first half of 1997 included a
$.4 million gain on the sale of property associated with one of
the Company's former businesses.  The property had been leased to
the purchaser of that operation since its sale in 1992.

Net interest expense totaled $.3 million and $.6 million for the
three and six-month periods ended June 30, 1998 compared to $.1
million of net interest income for the 1997 second quarter and
first half.  The increase in interest expense was due to the
higher outstanding debt associated with the acquisition of
Pfauter, partially offset by lower average borrowing rates.

The Company's provision for income taxes as a percentage of
income before taxes was 41.9% for the 1998 second quarter and
40.5% for the first half, compared to 35.8% and 35.5% for the
respective 1997 periods.  The level of income generated within
taxing jurisdictions can impact the Company's consolidated
effective tax rate.  The second quarter rate was higher due to a
greater percentage of income from the Company's European
operations that have higher effective tax rates.  The effective
tax for the 1997 period was lower primarily due the availability
of certain foreign tax credit carryforwards.  The Company expects
its effective tax rate to be higher in 1998 than in 1997 due to a
decrease in available tax credit carryforwards.

<PAGE>
<PAGE>

Liquidity and Capital Resources

Cash and cash equivalents increased $8.0 million in the first
half of 1998 to $20.5 million.   Borrowings under the Company's
term loan and revolving credit facilities decreased to $35.7
million at June 30, 1998 from $38.0 million at December 31, 1997.
Available unused short and long-term credit lines with banks,
including revolving credit facilities, totaled $79.5 million at
June 30, 1998.  As of July 1998, the Company reduced the total
amount of the facility from $135 million to $110 million, with
the elimination of the term loan portion of the facility (which
was reduced from $25 million at December 31, 1997).  All other
terms and conditions remain the same.  Dividend payments to
stockholders totaled $1.3 million in the first half.

Operating activities provided cash of $23.0 million in the first
half of 1998 versus $19.8 million in the comparable 1997 period.
Operating cash flows were higher in the 1998 first half due to
higher operating earnings before non-cash items including
depreciation, amortization and the pension charge.  Operating
cash flows were negatively impacted by higher income tax payments
during the first half of 1998 compared to the 1997 period.

Investing activities used $10.5 million of cash in the 1998 first
half versus $3.8 million in the comparable prior year period.
Capital expenditures totaled $10.6 million compared to $5.4
million in the 1997 first half.  Capital expenditures for the
1998 full year are expected to exceed depreciation expense with
spending planned for investments in information technology and
equipment to upgrade existing production facilities.  Cash flows
from investing activities in the 1997 first half also included
$1.5 million in cash from the sale of the property of a former
business which was sold in 1992.

Financing activities in the 1998 first half included $.7 million
of cash provided from stock issuances compared to $1.3 million of
cash used in stock repurchases in the 1997 first half.

Management believes that the Company's cash balances, borrowing
capacity under its lines of credit, and anticipated funds from
operations will be sufficient to meet its near-term operating and
investing activities and that it will be able to obtain
additional long-term financing if such financing is required.

Forward looking statements related to the level and timing of
incoming orders is subject to a number of risk factors which
could cause actual results to differ materially from those
expected.  These risk factors include, but are not limited to,
actions taken by competitors, the stability of customers' capital
spending plans and changes in general economic conditions in the
world markets the Company serves.

<PAGE>
<PAGE>
PART II - OTHER INFORMATION

Item 1.  Legal Proceedings

             Not applicable.


Item 2.  Changes in Securities

             Not applicable.

Item 3.  Defaults Upon Senior Securities

             Not applicable.


Item 4.  Submission of Matters to a Vote of Security Holders

             Not applicable.


Item 5.  Other Information
 
         The Company's By-laws provide that in order to properly bring
         business before an annual meeting of stockholders, a
         stockholder must give timely notice thereof in writing to the
         Secretary of the Company.  Generally, to be timely, a
         stockholder's notice must be delivered to or mailed and
         received at the principal executive offices of the Company not
         less than 60 days prior nor more than 90 days prior to
         scheduled date of the annual meeting.  Such a notice must also
         comply with a number of procedural requirements, which are set
         forth in Article I, Section 11 of the Company's By-laws.
  

Item 6.  Exhibits and Reports on Form 8-K

         (a)  Exhibits
                  Exhibit 10 (a):  Gleason Corporation Supplemental
                                   Retirement Plan, restated as of 
                                   July 1, 1998.

                  Exhibit 10 (b):  Form of Executive Agreement between the
                                   Company and its executive officers.

                  Exhibit 10 (c):  Trust Agreement for Gleason Corporation
                                   Executive Compensation Arrangements. 

                  Exhibit 27 (a):  Financial Data Schedule - Six Months 
                                   Ended June 30, 1998

                  Exhibit 27 (b):  Financial Data Schedule - Six Months 
                                   Ended June 30, 1997 Restated


         (b)   Reports on Form 8-K

                  Not applicable.

<PAGE>
<PAGE>
                             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.






                                        GLEASON CORPORATION
                                        Registrant




DATE:  August 12, 1998                        John J. Perrotti
                                              John J. Perrotti
                                          Vice President - Finance
                                          (Chief Financial Officer)