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               March 31, 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 March 31, 1998 was 10,498,625
shares.

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PART I - FINANCIAL INFORMATION
   Item 1. Financial Statements

<TABLE>

                    GLEASON CORPORATION AND SUBSIDIARIES
                         CONSOLIDATED BALANCE SHEETS
                                 (Unaudited)
<CAPTION>
                                                     (Dollars in thousands)
                                                      MARCH 31  DECEMBER 31
Assets                                                    1998         1997
<S>                                                   <C>          <C>
Current assets
  Cash and equivalents                                $ 10,948     $ 12,478
  Trade accounts receivable                             93,613      101,024
  Inventories                                           55,667       55,991
  Other current assets                                  13,317       13,367
    Total current assets                               173,545      182,860

Property, plant and equipment, at cost                 247,629      242,399
  Less accumulated depreciation                        122,318      118,026
                                                       125,311      124,373

Goodwill                                                17,780       18,036
Other assets                                            20,389       20,384

Total assets                                          $337,025     $345,653

Liabilities and Stockholders' Equity

Current liabilities
  Short-term borrowings                               $  8,691     $  5,760
  Current portion of long-term debt                         75        1,613
  Trade accounts payable                                29,768       30,810
  Income taxes                                          13,974       13,640
  Other current liabilities                             62,774       70,614
    Total current liabilities                          115,282      122,437

Long-term debt                                          30,431       38,244
Pension plans and other retiree benefits                59,745       60,235
Other liabilities                                       10,833       10,516

  Total liabilities                                    216,291      231,432

Stockholders' equity
  Common stock                                          11,594       11,594
  Additional paid-in capital                            12,263       12,061
  Retained earnings                                    113,352      107,797
  Cumulative foreign currency translation 
    adjustment                                          (3,800)      (3,889) 
  Minimum pension liability adjustment                    (901)        (901)
                                                       132,508      126,662
  Less treasury stock, at cost                          11,774       12,441

  Total stockholders' equity                           120,734      114,221

Total liabilities and stockholders' equity            $337,025     $345,653

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

                   GLEASON CORPORATION AND SUBSIDIARIES
                    CONSOLIDATED STATEMENTS OF OPERATIONS
                                 (Unaudited)
<CAPTION>
                                                 (Dollars in thousands, except
                                                        per share amounts)
                                                        THREE MONTHS ENDED
                                                              MARCH 31
                                                          1998        1997
<S>                                                 <C>          <C>  
Net sales                                              $95,397      $60,335

Costs and expenses
  Cost of products sold                                 65,974       41,016
  Selling, general and
    administrative expenses                             16,610        9,863
  Research and development expenses                      2,214        1,974
  Interest (income) expense -- net                         367           (1)
  Other (income) expense -- net                             11         (540)

Income before income taxes                              10,221        8,023

Provision for income taxes                               4,011        2,829

Net income                                             $ 6,210      $ 5,194


Earnings per common share:
  Basic                                                $   .59      $   .52
  Diluted                                              $   .57      $   .50

Weighted average number of common shares 
  outstanding:
  Basic                                             10,465,962    9,968,050
  Diluted                                           10,892,080   10,305,854

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

<FN>

See notes to consolidated financial statements.

</FN>
</TABLE>
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<TABLE>
                                     
                   GLEASON CORPORATION AND SUBSIDIARIES
                   CONSOLIDATED STATEMENTS OF CASH FLOWS
                                (Unaudited)
                                                       (Dollars in thousands)
                                                         THREE MONTHS ENDED
                                                              MARCH 31
                                                           1998        1997
<S>                                                     <C>         <C>
Cash flows from operating activities:
  Net income                                            $ 6,210     $ 5,194
  Adjustments to reconcile net income
    to net cash provided by operating activities:
    Depreciation and amortization                         5,334       2,901
    Loss (gain) on disposals of property, plant
      and equipment                                           6        (428)
    Provision  for deferred income taxes                    188          29
    Changes in operating assets and liabilities:
      (Increase) decrease in accounts receivable          6,513      (3,352)
      (Increase) in inventories                            (793)     (2,858)
      (Increase) in other current assets                    (21)         (9)
      Increase (decrease) in trade accounts payable      (2,191)        208
      (Decrease) in all other current operating 
         liabilities                                     (4,552)     (1,463)
      Other, net                                            222         228

  Net cash provided by operating activities              10,916         450

Cash flows from investing activities:
  Capital expenditures                                   (6,729)     (2,127)
  Proceeds from asset disposals                             105       1,520
  Proceeds from collection of notes receivable               --          18

  Net cash (used in) investing activities                (6,624)       (589)

Cash flows from financing activities:
  Proceeds from short-term borrowings                     3,080         310
  Net (repayments) under term loan and revolving
    credit agreements                                    (7,006)       (550)
  Net proceeds from (repayment of) long-term debt        (1,537)         31
  Purchase of treasury stock                                 (3)       (609)
  Net stock issues                                          415          26
  Dividends paid                                           (655)       (622)

  Net cash (used in) financing activities                (5,706)     (1,414)

Effect of exchange rate changes on cash
  and equivalents                                          (116)       (252)
(Decrease) in cash and equivalents                       (1,530)     (1,805)
Cash and equivalents, beginning                          12,478       7,199

Cash and equivalents, ending                            $10,948     $ 5,394

<FN>

See notes to consolidated financial statements.

</FN>
</TABLE>
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           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                          MARCH 31, 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-month periods ended March 31, 1998 and 1997
     (b) the financial position at March 31, 1998 and December
     31, 1997, and (c) the cash flows for the three-month periods
     ended March 31, 1998 and 1997, of Gleason Corporation and
     subsidiaries.

2.   The results of operations for the three-month period ended
     March 31, 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)            3/31/98  12/31/97
     
     Raw materials and
       purchased parts        $ 10,335  $ 11,215
     Work in process            35,443    34,491
     Finished goods              9,889    10,285
                              $ 55,667  $ 55,991


5.   Net cash payments for income taxes were $2,681,000 and
     $788,000 for the three months ended March 31, 1998 and 1997,
     respectively.  Interest payments were $617,000 and $24,000
     for the three months ended March 31, 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.  This
     Statement will result in the presentation of the components of
     comprehensive income within the annual financial statement, which
     must be displayed with the same prominence as other financial
     statements.

<PAGE>
<PAGE>

     The components of the Company's total comprehensive income
     were:
     
                                       Three Months Ended
                                            March 31,
     (in thousands)                     1998           1997
     Net income                       $6,210         $5,194
     Foreign currency translation
       adjustments                        89         (1,383)
     Total comprehensive income       $6,299         $3,811

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 financial statements for the year ending December
     31, 1998.

<PAGE>
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               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-month periods
ended March 31, 1998 and 1997 and in the Company's financial
condition during the three months ended March 31, 1998.

Results of Operations

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

Net income for the first quarter ended March 31, 1998 increased
20% to $6.2 million, or $.59 per share, compared to $5.2 million,
or $.52 per share, for the 1997 first quarter.  Operating income
(earnings before interest and taxes) increased 32% in the first
quarter to $10.6 million, or 11.1% of sales, compared to $8.0
million, or 13.3% of sales, in the 1997 first quarter.

New orders totaled $95.8 million for the first quarter compared
to $55.4 million in the 1997 first quarter.  Orders for the 1998
first quarter by product type were split 57% for machine products
and 43% for tooling and aftermarket products.  Order levels,
excluding the Pfauter operations which the Company acquired in
July 1997, increased 10% compared to the 1997 first quarter to
$60.7 million.  The increase in orders on a comparable basis with
the prior year was primarily attributable to the continued
strength of the U.S. market.  The Company experienced lower
orders in the Asian market, which accounted for only 10% of the
1998 first quarter order intake.  The Company expects continued
weaker demand from the Asian market for the balance of 1998, but
that effect should be offset by more favorable market conditions
in the U.S. and Europe.

Consolidated backlog was $178.1 million at March 31,1998 compared
to $177.8 million at December 31, 1997 and $117.9 million at
March 31,1997.  Backlog at March 31, 1998, excluding Pfauter
operations, totaled $109.0 million.

Net sales were $95.4 million for the first quarter, 58% higher
than the 1997 first quarter.  Sales, excluding Pfauter, were
$60.6 million compared to $60.3 million in the prior year first
quarter.  Higher shipments of cylindrical gear machine products
were offset by lower sales of tooling and aftermarket products.
On a regional basis, higher shipments to the United States were
offset by lower shipments to Asia.  Sales, excluding Pfauter, to
customers in the United States accounted for 50% of total sales
in the 1998 first quarter compared to 35% in the first quarter of
1997.  Sales to the Asia-Pacific region declined to represent
only 16% of sales in the first quarter, compared to 28% in the
prior year first quarter.


<PAGE>
<PAGE>

Cost of products sold as a percentage of sales was 69.2% for the
three-month period ended March 31, 1998 compared to 68.0% for the
comparable 1997 period.   Margins can be heavily impacted by the
mix of products sold.  For example, machines, in general, tend to
carry higher cost of sales percentages than tooling or other
products.  Margins were lower in the 1998 first quarter primarily
due to higher machine sales.  Margins on machine products in the
first quarter were down slightly on a comparable basis with the
first quarter of 1997.  Tooling margins were lower in the 1998
first quarter with the inclusion of Pfauter cylindrical gear
cutting tool products.

Selling, general and administrative expenses were $16.6 million,
or 17.4% of sales, for the first quarter of 1998 compared to $9.9
million, or 16.3% of sales, in the 1997 first quarter.  Spending
as a percentage of sales increased with the inclusion of the
Pfauter operations in the 1998 first quarter.  Excluding Pfauter,
spending as a percentage of sales decreased due to lower
commission expense as a result of lower shipments to Korea where
the Company is represented by an independent machine dealer.

Research and development spending in the first quarter of 1998
was $2.2 million, or 2.3% of sales, compared to $2.0 million, or
3.3% of sales in the 1997 period.  The Company expects
development spending to be higher in 1998 than in 1997 with the
inclusion of the Pfauter operations for the full year.
Development spending included new product development programs
for both bevel and cylindrical gear products.

Other income was $0.5 million lower in the first quarter of 1998
compared to the prior year's first quarter. Other income in the
1997 first quarter included a $0.4 million gain on the sale of
property associated with one of the Company's former Components
Group businesses.  The property had been leased to the purchaser
of that operation since its sale in 1992.

The Company's provision for income taxes as a percentage of
income before taxes was 39.2% in the first quarter of 1998
compared to 35.3% in the 1997 first quarter.  The effective tax
rate for the 1997 period was lower primarily due to the
availability of certain foreign tax credit carryforwards.  The
Company expects the 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 decreased $1.5 million in the first
three months of 1998 to $11.0 million.  Borrowings under the
Company's term loan and revolving credit facilities decreased to
$30.2 million at March 31, 1998 from $38.0 million at December
31, 1997.  In the first quarter, the Company reduced the total
amount of the facility from $135 million to $120 million, with
the term loan portion decreasing from $25 million to $10 million.
All other terms and conditions remain the same.  Available unused
short and long-term credit lines with banks, including the term
loan and revolving credit facilities, totaled $77.6 million at
March 31, 1998.  Dividend payments to stockholders totaled $0.7
million in the first quarter.

Operating activities in the first quarter provided cash of $10.9
million compared $0.5 million in the comparable 1997 period.
Operating cash flows were significantly higher in the 1998 first
quarter due to higher operating earnings before depreciation and
amortization and smaller increases in working capital. Working
capital cash requirements were $6.4 million lower in the 1998
first quarter compared to the 1997 first quarter primarily due to
decreases in trade accounts receivable.

Investing activities used $6.6 million of cash in the 1998 first
quarter versus $.6 million in the comparable prior year period.
Capital expenditures totaled $6.8 million in the 1998 first
quarter compared to $2.1 million in the 1997 first quarter.
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 quarter also included $1.5 million in cash from
the sale of the property of one of the Company's former
businesses.

Financing activities in the 1998 first quarter included $.4
million of net stock issues compared to $.6 million of treasury
share repurchases in the 1997 first quarter.

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 are 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,
general economic conditions in the world markets the Company
serves, currency fluctuations, the success of new product
introductions, competitors' actions, and the stability of
customers' capital spending plans.

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PART II - OTHER INFORMATION

Item 1.  Legal Proceedings

                  None.


Item 2.  Changes in Securities

                  None.

Item 3.  Defaults Upon Senior Securities

                  None.


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

         The Corporation's Annual Meeting of Stockholders
         was held on May 5, 1998.  At the meeting, proxies for
         approximately 94% of the 10,497,796 outstanding shares were
         represented.  Matters voted at the meeting were as
         follows:

                                                   For              Withheld
         (1)  Election of directors:
                For three-year terms
                  Martin L. Anderson            9,841,003             17,040
                  John W. Guffey, Jr.           9,841,017             17,026
                  William P. Montague           9,841,007             17,036
                For a one-year term:
                  Robert L. Smialek             9,840,817             17,226


                                                   For     Against   Abstain
        (2) Appointment of Ernst & Young LLP
            as Independent Auditors for 1998.   9,830,950   18,097     8,996

Item 5.  Other Information

                 None.


Item 6.  Exhibits and Reports on Form 8-K

         (a)  Exhibits

                Exhibit 27 (a):  Financial Data Schedule - Three
                                 Months Ended March 31, 1998

                Exhibit 27 (b):  Financial Data Schedule - Three
                                 Months Ended March 31, 1997
                                 Restated

         (b)   Reports on Form 8-K

                      None




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                             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:  May 13, 1998
                                             John J. Perrotti 
                                             John J. Perrotti
                                         Vice President - Finance
                                         (Chief Financial Officer)