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, 1999

                                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, 1999 was 9,575,807
shares.

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<TABLE>
PART I - FINANCIAL INFORMATION
   Item 1. Financial Statements
                    GLEASON CORPORATION AND SUBSIDIARIES
                         CONSOLIDATED BALANCE SHEETS
                                 (Unaudited)

<CAPTION>
                                                      (Dollars in thousands)
                                                      MARCH 31    DECEMBER 31
                                                        1999         1998
<S>                                                   <C>         <C>
Assets

Current assets
  Cash and equivalents                                $  8,473    $ 13,229
  Trade accounts receivable                             85,904      89,095
  Inventories                                           63,673      58,614
  Other current assets                                  16,014      16,094
    Total current assets                               174,064     177,032

Property, plant and equipment, at cost                 258,417     265,790
  Less accumulated depreciation                        134,586     133,468
                                                       123,831     132,322

Goodwill                                                18,541      16,682
Other assets                                            15,474      14,433

Total assets                                          $331,910    $340,469

Liabilities and Stockholders' Equity

Current liabilities
  Short-term borrowings                               $  7,737    $  1,853
  Current portion of long-term debt                        250           8
  Trade accounts payable                                31,263      33,421
  Income taxes                                           7,145       6,790
  Other current liabilities                             56,624      62,485
    Total current liabilities                          103,019     104,557

Long-term debt                                          26,270      28,906
Pension plans and other retiree benefits                65,227      66,163
Other liabilities                                       13,483      12,872

  Total liabilities                                    207,999     212,498

Stockholders' equity
  Common stock                                          11,594      11,594
  Additional paid-in capital                            12,001      12,443
  Retained earnings                                    135,290     131,323
  Accumulated other comprehensive income                (6,971)     (5,688)

                                                       151,914     149,672
  Less treasury stock, at cost                          28,003      21,701

  Total stockholders' equity                           123,911     127,971

Total liabilities and stockholders' equity            $331,910    $340,469

<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
                                                          1999       1998
<S>                                                  <C>         <C>
Net sales                                              $ 85,716    $ 95,397

Costs and expenses
  Cost of products sold                                  59,673      65,974
  Selling, general and
    administrative expenses                              16,572      16,610
  Research and development expenses                       2,572       2,214
  Interest expense --net                                    158         367
  Other (income) expense --net                             (946)         11

Income before income taxes                                7,687      10,221

Provision for income taxes                                3,097       4,011

Net income                                             $  4,590    $  6,210


Earnings per common share:
  Basic                                                $    .47    $    .59
  Diluted                                              $    .46    $    .57

Weighted average number of common shares 
  outstanding:
  Basic                                               9,793,291  10,465,962
  Diluted                                            10,043,601  10,892,080

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

<FN>
See notes to consolidated financial statements.
</FN>
</TABLE>
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<PAGE>
<TABLE>
                                     
                   GLEASON CORPORATION AND SUBSIDIARIES
                               CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (Unaudited)
<CAPTION>       
                                                        (Dollars in thousands)
                                                           THREE MONTHS ENDED
                                                                MARCH 31
                                                             1999      1998
<S>                                                        <C>       <C>
Cash flows from operating activities:
  Net income                                               $ 4,590   $ 6,210
  Adjustments to reconcile net income
    to net cash provided by operating activities:
    Depreciation and amortization                            5,843     5,334
    (Gain) loss on disposals of property, plant
      and equipment                                         (1,024)        6
    Provision for deferred income taxes                      1,008       188
    Changes in operating assets and liabilities:
      Decrease in accounts receivable                        4,817     6,513
      (Increase) in inventories                             (2,846)     (793)
      (Increase) decrease in other current assets              296       (21)
      (Decrease) in trade accounts payable                  (3,324)   (2,191)
      (Decrease) in all other current operating 
         liabilities                                        (8,896)   (4,552)
      Other, net                                               636       222

  Net cash provided by operating activities                  1,100    10,916

Cash flows from investing activities:
  Capital expenditures                                      (2,985)   (6,729)
     Acquisition of business, net of cash acquired             365        --
  Proceeds from asset disposals                              4,729       105

  Net cash provided by (used in) investing activities        2,109    (6,624)

Cash flows from financing activities:
  Proceeds from short-term borrowings                          797     3,080
  Net (repayments) under term loan and
     revolving credit agreements                            (1,273)   (7,006)
  Net proceeds from (repayment of) long-term debt              407    (1,537)
  Purchase of treasury stock                                (7,193)       (3)
  Net stock issues                                             449       415
  Dividends paid                                              (623)     (655)

  Net cash (used in) financing activities                   (7,436)   (5,706)

Effect of exchange rate changes on cash
  and equivalents                                             (529)     (116)

(Decrease) in cash and equivalents                          (4,756)   (1,530)
Cash and equivalents, beginning                             13,229    12,478

Cash and equivalents, ending                               $ 8,473   $10,948

<FN>
See notes to consolidated financial statements.
</FN>
</TABLE>
<PAGE>
<PAGE>
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                          MARCH 31, 1999
                            (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, 1999 and 1998,
     (b) the financial position at March 31, 1999 and December
     31, 1998, and (c) the cash flows for the three-month periods
     ended March 31, 1999 and 1998, of Gleason Corporation and
     subsidiaries.

2.   The results of operations for the three-month period ended
     March 31, 1999 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)                  3/31/99    12/31/98
     Raw materials and
       purchased parts              $ 11,864    $ 12,626
     Work in process                  35,420      33,508
     Finished goods                   16,389      12,480
                                    $ 63,673    $ 58,614


5.   Net cash payments for income taxes were $674,000 and
     $2,681,000 for the three months ended March 31, 1999 and
     1998, respectively.  Interest payments were $303,000 and
     $617,000 for the three months ended March 31, 1999 and 1998,
     respectively.

6.   Comprehensive income includes all changes in equity during a
     period except those resulting from transactions with owners of
     the Company.  The components of the Company's comprehensive
     income  for the three-month periods ended March 31, 1999 and 1998
     were as follows:
        
                                      Three Months Ended
                                           March 31,
     (In thousands)                    1999        1998
     
     Net income                      $ 4,590     $ 6,210
     Foreign currency translation
       adjustments                    (1,311)         89
     Minimum pension liability
       adjustments                        28          --
     Comprehensive income            $ 3,307     $ 6,299

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<PAGE>


     The components of accumulated other comprehensive income
     shown on the balance sheet were as follows:
     
     
     (In thousands)                  3/31/99    12/31/98
     Cumulative foreign currency
       adjustments                  $ (4,746)   $ (3,435)
     Minimum pension liability 
       adjustments                    (2,225)     (2,253)
     Accumulated other comprehen-
       sive income                  $ (6,971)   $ (5,688)


7.   The Company adopted Statement of Financial Accounting
     Standards No. 131, "Disclosure about Segments of an
     Enterprise and Related Information" (FAS No. 131), at
     December 31, 1998. The Company's operations are treated as
     one operating segment.  The principal activity within this
     operating segment is the design, manufacture and sale of
     machinery and equipment for the production of gears.  As a
     result, the financial information disclosed herein
     materially represents all of the financial information
     related to the Company's principal operating segment.

8.   The Company has not yet adopted Statement of Financial
     Accounting Standards No. 133, "Accounting for Derivative
     Instruments and Hedging Activities" (FAS No. 133), which
     provides new guidelines for accounting for derivative
     instruments.  FAS No. 133 requires companies to recognize
     all derivatives on the balance sheet at fair value.  Gains
     or losses resulting from changes in the values of the
     derivatives would be accounted for depending on the use of
     the derivative and whether it qualifies for hedge
     accounting.  The Company is currently analyzing what impact
     the new guidelines will have on the Company.  This Statement
     is effective for fiscal years 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-month periods
ended March 31, 1999 and 1998 and in the Company's financial
condition during the three months ended March 31, 1999.

Results of Operations

All references to earnings per share reflect diluted earnings per
share.

Net income for the first quarter ended March 31, 1999 was $4.6
million, or $.46 per share, compared to $6.2 million, or $.57 per
share, for the 1998 first quarter.  The decline in net income in
the first quarter compared to the prior year quarter was largely
attributable to lower sales volumes and decreased operating
margins.

Net orders levels for the first quarter totaled $83.4 million, or
13% lower compared to the 1998 first quarter.  Orders for the
quarter for machines, tooling and aftermarket products were lower
compared to the 1998 quarter.  The comparative decline in orders
occurred principally in the Americas and European regions.  Net
order levels for the 1999 first quarter were negatively impacted
by foreign exchange translation effects of $5.1 million due to
the stronger U.S. dollar versus the major European currencies.

Consolidated backlog was $137.6 million at March 31, 1999
compared to $132.5 million at December 31, 1998 and $178.1
million at March 31,1998.   The Company assumed a backlog of $7.4
million with its purchase of OGA Corporation, the Company's sales
and service representative in Japan and Taiwan, in the first
quarter of 1999.

Net sales were $85.7 million for the 1999 first quarter, 10%
lower than the 1998 first quarter primarily due to lower sales of
machine products.  Total machine sales decreased 13% in the 1999
first quarter compared to the 1998 first quarter mainly due to a
significant decline in sales to customers in the United States
partially offset by a smaller increase in machine sales to
European customers.  Sales of machine products to customers in
the United States accounted for 21% of total machine sales in the
1999 quarter compared to 41% in the prior year first quarter.
Combined sales of tooling and aftermarket products for the
quarter were slightly lower than in the 1998 first quarter.
Because of its lower backlog, the Company expects that sales for
the full year 1999 will be lower than in 1998.

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<PAGE>

Cost of products sold as a percentage of sales was 69.6% for the
three-month period ended March 31, 1999 compared to 69.2% for the
comparable 1998 period.  Gross margins were negatively impacted
by lower production volumes, which resulted in less coverage of
fixed operating costs.  The Company is taking actions to improve
operating margins, including closing its two Italian
manufacturing plants located in Bologna and Porretta Terme within
this year.  These plants, which manufacture cylindrical gear
machinery, have combined employment of approximately 150 persons
and were acquired as part of the Company's Pfauter acquisition in
1997.   The expected closure costs should be covered by the
restructuring costs accrued by the Company in connection with the
Pfauter acquisition.  The Company expects these actions will
result in a decrease in fixed operating costs and improvement in
operating margins.

Selling, general and administrative expenses were $16.6 million,
or 19.3% of sales, for the first quarter of 1999 compared to
$16.6 million, or 17.4% of sales, in the 1998 first quarter.
Spending as a percentage of sales increased due to a similar
level of expense in the 1999 quarter compared to the prior year
quarter on a lower sales base in the 1999 period.  With the
acquisition of OGA Corporation the Company has experienced an
increase in fixed selling costs and a decrease in variable
commission costs.  In prior years sales to customers in Japan and
Taiwan would have resulted in a variable commission expense.

Research and development spending in the first quarter of 1999
was $2.6 million, or 3.0% of sales, compared to $2.2 million, or
2.3% of sales in the 1998 period.  Development spending in the
1999 first quarter included new product development programs for
bevel and cylindrical machine products which were demonstrated at
a European (EMO) machine and tooling trade show in 1999.  The
Company expects that development spending will be slightly lower
for the 1999 full year compared to 1998.

Other income in the first quarter of 1999 was $1.0 million higher
than the prior year quarter.  The 1999 amount included a combined
net gain on the sale of certain assets, including real estate, of
$.8 million.  The after-tax effect on income of this net gain was
$.5 million, or $.05 per share.

The Company's provision for income taxes as a percentage of
income before taxes was 40.3% in the first quarter of 1999
compared to 39.2% in the 1998 first quarter.  The levels of
income generated in different taxing jurisdictions can impact the
Company's consolidated effective tax rate.  The effective tax
rate for the 1999 period increased compared to the 1998 first
quarter due to a higher percentage of income from Germany, which
has higher statutory tax rates compared to other taxing
jurisdictions in which the Company has operations.

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<PAGE>

Liquidity and Capital Resources

Cash and cash equivalents decreased $4.8 million in the first
three months of 1999 to $8.5 million.   Borrowings under the
Company's revolving credit facilities decreased to $25.3 million
at March 31, 1999 from $28.7 million at December 31, 1998.
Available unused short and long-term credit lines with banks,
including the revolving credit facilities, totaled $88.5 million
at March 31, 1999.  Dividend payments to stockholders totaled
$0.6 million in the first quarter of 1999.

Operating activities in the first quarter provided cash of $1.1
million compared $10.9 million in the comparable 1998 period.
Operating cash flows were lower in the 1999 first quarter due to
lower operating earnings before depreciation and amortization and
increases in working capital.  Working capital levels were higher
in the 1999 first quarter due to increases in inventories and
decreases in advance payments received from customers.

Investing activities provided $2.1 million of cash in the 1999
first quarter and used  $6.6 million of cash in the comparable
prior year period.  Capital expenditures totaled $3.0 million in
the 1999 first quarter compared to $6.7 million in the 1998 first
quarter.  Capital expenditures for the 1999 full year are
expected to be approximately equal to depreciation expense with
spending planned for equipment to upgrade existing production
facilities and investments in information technology, including
costs for hardware, software and consulting services to support
the implementation of the Company's global enterprise resource
planning (ERP) system.  The Company paid cash of $3.4 million to
acquire the remaining 80% of OGA Corporation in the first quarter
of 1999 and $3.7 million of cash was assumed as part of this
acquisition.  Other investing activities in 1999 included the
receipt of $4.7 million related to the sale of certain assets,
including real estate.

In the first quarter of 1999 the Company used $7.2 million to
repurchase 431,500 shares of Common Stock.  In October 1998, the
Company's Board of Directors authorized the repurchase of up to
10% of the Company's outstanding shares, of which 318,334 shares
remained available for purchase as of March 31, 1999.

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.



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<PAGE>

Year 2000 Readiness Disclosure

State of Readiness

Since 1997, the Company has undertaken a Year 2000 Program to
ensure that the Company's business critical computer systems will
be able to function without significant disruption because of the
use in the Year 2000 of computer date systems which were designed
using only two digits to identify the year in the date field and
without considering the effect of a change in the century
designation.  The Company's Program addresses major information
technology and non-information technology (embedded chips) areas
including: business computer systems (such as financial,
manufacturing and sales and marketing systems); manufacturing,
warehousing and servicing equipment (such as manufacturing
execution systems and shop floor controls); technical
infrastructure (such as workstations, mainframes, servers and
operating systems); end-user computing (personal computers); the
readiness of suppliers, agents and service providers; facilities;
research and development test facilities; and the Company's
products.  The Program includes the following phases: inventory /
identification; impact analysis / risk evaluation; remediation;
testing; and implementation.

The Company is in the process of remediating and testing those of
its major business information systems which are believed to be
non-compliant.  Other major equipment, processes and systems have
also been evaluated.  Those systems, equipment and processes
which have been identified as non-compliant are being upgraded,
modified or replaced so that they will properly process dates
beyond December 31, 1999. The Company's schedule is for all
mission critical systems, processes and equipment to be Year 2000
compliant by June 30, 1999.   All mission critical systems are
expected to be remediated and tested prior to June 30, 1999 with
the exception of a certain number of inventory control and
warehousing systems at one of the Company sites where remediation
and testing is expected to be completed by the end of the third
quarter.

The Company also is in the process of contacting its significant
suppliers and other third parties with whom the Company has
relationships in order to determine whether their operations and
the products and services they provide are Year 2000 compliant.
The Company has sent surveys to its suppliers and is in the
process of confirming their progress with Year 2000 readiness
efforts.  While the actions of these entities are largely outside
the Company's control, where practical, the Company will attempt
to mitigate its risks with respect to the failure of these
parties to be Year 2000 ready.  However, such failures remain a
possibility and could have an adverse impact on the Company's
results of operations or financial condition.  The Company will

<PAGE>
<PAGE>

continue to evaluate the nature of these risks, but is unable to
determine the probability that any such risk will occur, or if it
does, what the nature, length or other effect, if any, it may
have on the Company.

The Company has evaluated the products it has sold and is
currently selling, to determine if any potential Year 2000 issues
exist.  The Company believes, based on its own testing and/or
information received from its suppliers, that all of the products
it currently sells are compliant and that products formerly sold
are either compliant or can be made compliant at a minimal cost.


Cost:

The Company estimates that the cumulative costs of its Year 2000
Program will be approximately $1.0 million, of which
approximately $.6 million was incurred through March 31, 1999.
These costs, which are primarily for modifying and upgrading
software programs, are being funded from internally-generated
funds, are being expensed as incurred and are not expected to be
material to the Company's financial condition.  The Company does
not separately track its internal costs, principally payroll and
related expenses of certain information systems personnel, for
the Year 2000 Program.


Risks:

The Company believes that the activities it is undertaking in
connection with its Year 2000 Program should satisfactorily
reduce the risk of or resolve Year 2000 issues.  However, as is
true for most companies, the Year 2000 issue creates a risk for
the Company.  If date information is not correctly recognized or
processed for years after 1999, there could be an adverse impact
on the Company's operations and financial results.  Thus, if
necessary modifications and upgrades to the Company's systems and
equipment are not operationally effective on a timely basis, the
Year 2000 issue could have a material impact on the operations
and financial results of the Company.    Likewise, if a
significant number of suppliers or key vendors of the Company are
not Year 2000 compliant, the ability of the Company to obtain
necessary materials or to manufacture, deliver or sell the
Company's products could be impaired.  Disruption of the
Company's or its suppliers' and vendors' information technology
systems and embedded chips, as well as the cost of avoiding such
disruption, could have a material adverse effect upon the
Company's financial condition and results of operations.

The Company is uncertain as to its most reasonably likely worst
case Year 2000 scenario.  However, customers not satisfied with
the Company's timetable for its Year 2000 Program or the
Company's efforts to remediate any failure to be Year 2000
compliant may choose to delay or cancel orders for the Company's
products, which could have a material adverse effect on the

<PAGE>
<PAGE>
Company's business, financial condition or results of operations.
To date, there has been no indication that any customer has
chosen to delay or cancel orders due to Year 2000 concerns.


Contingency Plans:

The Company believes its Year 2000 Program is designed to
safeguard the interests of the Company and its customers.  The
Company believes that this Program will minimize the risk of a
Year 2000 issue serious enough to cause significant operational
problems.  However, a failure to timely identify all Year 2000
dependencies in the Company's systems, equipment or processes, or
those of its suppliers or other third parties, or a delay or
failure to remediate any Year 2000 defects, could have material
adverse consequences.  The Company is in the process of
considering contingency plans for continuing operations in the
event such problems arise, but there can be no assurance that any
such contingency plans will successfully address all
contingencies that may arise.


Euro Conversion

The Company sells products and has operations in several European
countries which have begun conversion in 1999 to the new common
currency (the Euro) used by members of the European Union.  The
Company does not anticipate any significant risk to its
operations as a result of the conversion.


Market Risk Disclosures

The Company is exposed to market risk arising form its global
operating and financing activities.  The Company's results of
operations could be adversely impacted by fluctuations in foreign
exchange rates and interest rates.  The Company does not use
derivative financial instruments for speculative or trading
purposes.

The Company manufactures its products in the United States,
Germany, the United Kingdom, Italy, Switzerland and India and
sells its products to customers in over 35 countries.  The
Company's results of operations could be significantly impacted
by such factors as changes in foreign currency exchange rates or
weak economic conditions in foreign markets.  The Company's
operating results are exposed to fluctuations between the U.S.
dollar and European currencies.  In an attempt to mitigate the
short-term effect of currency fluctuations, the Company enters
into forward exchange contracts to hedge specific foreign
currency transactions entered into in the ordinary course of
business.  Gains and losses on such forward contracts offset the
gains and losses on the transactions being hedged.  The Company
performed sensitivity analysis assuming a hypothetical 10%
adverse movement in foreign exchange rates applied to forward
exchange contracts outstanding at March 31, 1999 and 1998.  This
analysis indicated that such an adverse movement in exchange

<PAGE>
<PAGE>

rates would have resulted in losses on outstanding contracts at
March 31, 1999 and 1998 of $1.5 million and $.9 million,
respectively.  However, these losses would have been
substantially offset by gains from the revaluation or settlement
of the underlying positions hedged.

The Company is exposed to interest rate risk related to its
outstanding debt.  The Company utilizes both U.S. dollar
denominated and foreign currency denominated borrowings under its
revolving credit facility and various short-term credit lines to
fund its working capital needs.  The revolving credit facility
provides for the Company to borrow on a spread over LIBOR as
determined by certain financial ratios which are adjusted on a
quarterly basis.  A hypothetical 50 basis point increase in the
worldwide weighted average borrowing rate in the first quarter
1999 and 1998 would not have had a material impact on the
Company's results of operations or cash flows for the respective
periods.  The Company does not currently invest in derivative
instruments such as interest rate swaps or options to hedge its
exposure to interest rate fluctuations.


Forward Looking Statements

This report and other documents or oral statements which have
been and will be prepared or made in the future contain or may
contain forward-looking statements by or on behalf of the
Company.  Forward-looking statements are subject to a number of
factors that could cause actual results to differ materially from
those expected.  Risk factors associated with future sales
include, but are not limited to, less favorable economic
conditions in the markets the Company serves, currency
fluctuations, the success of new product introductions and
competitors actions which may effect the Company's ability to
obtain orders.  Factors which may affect future benefits from
restructuring and cost savings activities include, but are not
limited to, the risk of not realizing fully the anticipated cost
reductions, unplanned delays in completing such activities and
the ability to implement changes in a manner that does not unduly
disrupt business operations or demand for the Company's products.

Risk factors associated with the Company's Year 2000 Program
include, but are not limited to, unforeseen Year 2000 issues
affecting the Company's systems, infrastructure, embedded
technologies and products, including issues arising from any
inaccuracy in the inventory, assessment, remediation or testing
done by the Company, and the failure of third parties with whom
the Company has relationships to effectively address their Year
2000 issues.

Risk factors associated with the adoption of the Euro currency
include, but are not limited to, delays, or unforeseen
difficulties in transitioning the Company's business information
systems to be made Euro compliant.  Such delays or difficulties
could result in the Company incurring significant costs or may
impact the Company's ability to obtain and process customer
orders.

<PAGE>
<PAGE>

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 4, 1999.  At the meeting, proxies for
         approximately 91% of the 9,608,135 outstanding shares were
         represented.  Matters voted at  the meeting were as
         follows:

                                                   For           Withheld
         (1)  Election of directors:
                 Silas L. Nichols               8,566,678          186,503
                 Robert L. Smialek              8,568,481          184,700



                                                    For    Against  Abstain
         (2) Appointment of Ernst & Young LLP
             as Independent Auditors for 1999.  8,727,107   19,628   6,446


Item 5.  Other Information

              None.


Item 6.  Exhibits and Reports on Form 8-K

         (a)  Exhibits

              Exhibit 27 :    Financial Data Schedule - Three Months
                              Ended March 31, 1999



         (b)  Reports on Form 8-K

                 None.



<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:  May 14, 1999
                                                 John J. Perrotti
                                                 John J. Perrotti
                                             Vice President - Finance
                                              (Chief Financial Officer)