DREYFUS INSTITUTIONAL MONEY MARKET FUND INC
N-30D, 1999-03-02
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YEAR 2000 ISSUES (UNAUDITED)

  The  fund  could  be  adversely  affected  if the computer systems used by The
Dreyfus  Corporation  and  the  fund' s  other service providers do not properly
process  and  calculate date-related information from and after January 1, 2000.
The  Dreyfus  Corporation  is working to avoid Year 2000-related problems in its
systems  and  to  obtain  assurances  from other service providers that they are
taking  similar  steps.  In  addition,  issuers  of securities in which the fund
invests may be adversely affected by Year 2000-related problems. This could have
an impact on the value of the fund's investments and its share price.

DREYFUS INSTITUTIONAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

  We  are  pleased  to  report  the  performance for Dreyfus Institutional Money
Market  Fund  for  the  12-month  period ended December 31, 1998 as shown in the
following table:
<TABLE>
<CAPTION>
                                                                           YIELD                      EFFECTIVE YIELD*
                                                                       ______________                   _____________
        <S>                                                                 <C>                             <C>
        Money Market Series  . . . . . . . . . . . . . . . . .              5.02%                           5.14%

        Government Securities Series . . . . . . . . . . . . .              4.76%                           4.87%
</TABLE>

ECONOMIC REVIEW

  During  1998,  the  main  regions  of  the  world  had very different economic
fundamentals.  The  U.S.  entered  the  year  with  a  strong  economy near full
employment, with unemployment only slightly above 4%. The tight labor market led
the  Federal  Reserve Board to contemplate a rise in interest rates early in the
year,  but  world  economic  weakness  generated powerful enough disinflationary
forces  that  the Fed acted instead to ease credit beginning in September. After
many  years of subpar economic growth, continental Europe moved into a sustained
economic  expansion. The overall European economy benefited as interest rates in
peripheral  countries such as Spain and Italy fell, approaching the lower levels
established  by  Germany,  on  the eve of currency unification. Unlike the U.S.,
Europe  has  substantial excess capacity of productive plant and labor. In Asia,
weak  economies  were  pervasive  as  a  result of a financial crisis. The Latin
American  economies weakened in turn as the financial stresses spread throughout
that  region. On balance, there was a substantial weakening of the world economy
over  the  course  of  1998  moderated mainly by the American consumer's role as
"spender of last resort."

A main influence on the U.S. economy during the year was the foreign financial
crisis  and  consequent  cooling  of the world economy. The positive effects hit
first.  Actual  inflation  and  expected inflation dropped, causing a decline in
long-term  Treasury  bond  yields  and  mortgage  rates.  This  caused a boom in
housing.  The  fall in inflation left more of the growth in consumer income with
which to buy goods and services. Thus, consumers benefited from a combination of
good  growth  in income after inflation, a strong labor market, and increases in
the  prices  of assets they owned, including bonds, stocks and real estate. In a
sense,  1998  was  a  year  of  disinflationary boom in the U.S., as above-trend
economic growth coincided with negligible inflation.

  The  negative  effect of Asian weakness was felt in the industrial sector more
than  in  the consumer sector. Corporate profits weakened, especially in sectors
affected  by  the Asian crisis such as world-traded commodities (oil, metals and
paper)    and    exports.

  Evidence  of  a  weaker world economy accumulated during 1998 as the financial
stresses  continued.  A  worsened  financial crisis occurred between the Russian
default  in  mid-August  and  the  fallout from the Long Term Capital Management
hedge  fund crisis through early October. However, energetic steps were taken to
stabilize the Japanese banks, design a support package for Brazil, ease monetary
policy,   and  help  overinvested  financial  institutions  rebuild  their  cash
reserves.  Indications of a calming of financial fears were evident in the final
months  of  the  year.  In  any  case, there appears to have been a shift in the
priorities   of   key   policymakers   from   fighting  potential  inflation  to
restimulating future world economic growth.

  The  global  economy  survived  a  triple financial crisis in 1998 from Japan,
emerging  market  countries  and  overextended  financial  institutions.  Excess
capacity  persists  in  many  worldwide  industries  after years of high capital
spending  followed by the onset of a worldwide weakening in demand. Fortunately,
the  U.S.  has  led  the  world  in  making  the  transition  away  from the old
manufacturing  industries  to  the new growth industries, such as biotechnology,
software,  computer hardware and the Internet. This contributed to the favorable
combination  of low unemployment and low inflation in the U.S., and may yet lead
toward more efficient allocation of capital elsewhere in the world.

  As  1998 ended, interest rates set by central banks remained in a downtrend in
most  parts  of the world including Europe and the U.S. A similar trend had even
begun in many emerging countries, as the stresses of financial crisis relaxed.

MARKET ENVIRONMENT/PORTFOLIO FOCUS

  The  economic  forces described above drove down interest rates in late summer
and  early  fall. Later in the year there was a modest increase in rates. One of
its  effects  was to change the yield curve from one that had been negative to a
positive,  sloping  structure.  In this normal configuration, longer-term yields
exceeded those of the shorter-term instruments.

  A  flight  to  safety  by  global  investors  was  the  force  that drove down
longer-term  U.S.  yields  last  fall. In recent weeks, investors appear to have
become  more  confident about the economic outlook. One factor has been the rise
in  interest rates in Japan, which brought about some repatriation of investment
funds to that country. In addition, the introduction of the Euro currency at the
start  of  the  new year, which was well received, put some downward pressure on
the U.S. dollar.

Investor fears of worldwide financial turmoil seemed to have receded recently.
Currently,  prices  and  rates in the money market appear to be reacting more to
underlying  economic  forces  than  to  such market psychology factors. This, of
course,   can   be   constructive  for  investors  in  short-term  money  market
instruments.

The fact that the Federal Reserve Open Market Committee lowered interest rates
three   times   between   late   September   and  year-end  has  been  a  strong
confidence-building  factor  in  the  markets.  Currently,  we expect the Fed to
remain in a "wait and see" mode for a while.

  During  the reporting period, we lengthened the average portfolio maturity, as
we  deemed appropriate in order to take advantage of possible declining interest
rates.  We  will  continue  to  monitor the market, including interest rates, in
seeking investment opportunities for the Fund.

               Sincerely,

               [Patricia A. Larkin signature]

               Patricia A. Larkin

               Senior Portfolio Manager

January 13, 1999

New York, N.Y.

* Effective yield based upon dividends declared daily and reinvested monthly.

<TABLE>
<CAPTION>
DREYFUS INSTITUTIONAL MONEY MARKET FUND, MONEY MARKET SERIES
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                    DECEMBER 31, 1998

                                                                                                  Principal

Negotiable Bank Certificates of Deposit--7.1%                                                      Amount            Value
- -------------------------------------------------------                                         _____________     _____________

Branch Bank & Trust Co.
  <S>                                                                                           <C>               <C>
  5.04%, 1/10/00 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  18,000,000     $  17,994,685

LaSalle National Bank

  5.67%, 4/13/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        20,000,000

                                                                                                                  _____________

TOTAL NEGOTIABLE BANK CERTIFICATES OF DEPOSIT

  (cost $37,994,685) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        $  37,994,685

                                                                                                                  _____________


Commercial Paper--55.9%
- -------------------------------------------------------

Bear Stearns Companies Inc.

  5.67%, 1/14/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  20,000,000     $  19,960,278

Canadian Imperial Holdings Inc.

  5.04%, 6/28/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,513,961

Chrysler Financial Corp.

  5.12%, 3/15/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,795,194

Ciesco L.P.

  5.24%, 2/3/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,904,483

Den Danske Corp.

  5.66%, 1/4/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,990,833

Finova Capital Corp.

  5.32%, 3/19/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        24,721,410

Ford Motor Credit Corp.

  4.90%, 1/4/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         15,000,000        14,993,875

General Electric Capital Corp.

  5.49%, 1/28/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,919,300

General Motors Acceptance Corp.

  5.24%, 1/27/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        24,906,833

Goldman Sachs Group L.P.

  5.14%, 4/20/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        24,621,528

Merrill Lynch & Co. Inc.

  5.06%-5.71%, 1/14/99-3/26/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        24,735,239

Paine Webber Group Inc.

  5.75%, 1/7/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        24,976,583

Swedbank Inc.

  5.08%, 4/14/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        24,645,938

Toronto-Dominion Holdings USA Inc.

  5.40%, 1/15/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,958,233

                                                                                                                  _____________

TOTAL COMMERCIAL PAPER

  (cost $302,643,688)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $302,643,688

                                                                                                                  _____________


DREYFUS INSTITUTIONAL MONEY MARKET FUND, MONEY MARKET SERIES
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                        DECEMBER 31, 1998

                                                                                                  Principal

Corporate Notes--19.2%                                                                             Amount            Value
- -------------------------------------------------------                                         _____________      ____________
_

Bankers Trust New York Co.

  4.90%-4.95%, 1/8/99-4/30/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  22,000,000     $  21,999,508

CIT Group Holdings Inc.

  4.87%, 9/21/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,995,780

Heller Financial Inc.

  5.00%-5.05%, 4/13/99-9/8/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . .         22,000,000        22,000,000

Morgan (J.P) & Co. Inc.

  4.86%, 2/24/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,998,760

Salomon Smith Barney Holdings Inc.

  5.00%, 10/28/99 (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        20,000,000

                                                                                                                  _____________

TOTAL CORPORATE NOTES

  (cost $103,994,048)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $103,994,048

                                                                                                                  _____________


Short-Term Bank Notes--13.0%
- -------------------------------------------------------

Bank of America FSB

  5.13%, 3/29/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  25,000,000     $  25,000,000

First Union National Bank

  5.21%, 9/24/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         25,000,000        25,000,000

Key Bank N.A.

  4.87%, 2/24/99 (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        19,997,988

                                                                                                                  _____________

TOTAL SHORT-TERM BANK NOTES

  (cost $69,997,988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        $  69,997,988
                                                                                                                  _____________

Time Deposit--3.6%
- -------------------------------------------------------

Republic National Bank of New York (London)

 2.88%, 1/4/99

  (cost $19,067,000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  19,067,000     $  19,067,000
                                                                                                                  _____________

Repurchase Agreement--.5%
- -------------------------------------------------------

SBC Warburg Dillon Read Inc.

 3.00% dated 12/31/98, due 1/4/99 in the amount of $2,655,855 (fully
collateralized
 by $2,762,000 U.S. Treasury Bills, due 6/3/99, value $2,709,659)

  (cost $2,655,000)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $    2,655,000    $    2,655,000
                                                                                                                  _____________

</TABLE>
<TABLE>
<CAPTION>
TOTAL INVESTMENTS
   <S>                                                                               <C>                           <C>
   (cost $536,352,409) . . . . . . . . . . . . . . . . . . . . . . . . . . .         99.3%                         $536,352,409
                                                                                   _______                        _____________


CASH AND RECEIVABLES (NET) . . . . . . . . . . . . . . . . . . . . . . . . .           .7%                       $    3,929,796
                                                                                   _______                        _____________

NET ASSETS     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        100.0%                         $540,282,205
                                                                                   _______                        _____________
</TABLE>
<TABLE>
<CAPTION>
Notes to Statement of Investments:
- -------------------------------------------------------

(a)  Variable interest rate-subject to periodic change.

                      SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS INSTITUTIONAL MONEY MARKET FUND, GOVERNMENT SECURITIES SERIES
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                    DECEMBER 31, 1998

                                              Annualized

                                               Yield on

                                                Date of  Principal

U.S. Treasury Bills--18.9%                                                     Purchase            Amount             Value
- ----------------------------------------------------------------------------  ___________        ____________      ____________

   1/21/99
   <S>                                                                          <C>               <C>               <C>
   (cost $12,968,005)  . . . . . . . . . . . . . . . . . . . . . . . . . .      4.44%             $13,000,000       $12,968,005
                                                                                                                   ____________


U.S. Treasury Notes--45.4%
- ----------------------------------------------

   5%, 2/15/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      5.89%            $  4,000,000      $  3,997,375

   5.875%, 2/28/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . .      4.38               10,000,000        10,020,742

   6.375%, 7/15/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . .      5.25                5,000,000         5,021,392

   5.875%, 8/31/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . .      4.81                5,000,000         5,032,712

   5.625%, 11/30/99  . . . . . . . . . . . . . . . . . . . . . . . . . . .      4.45                5,000,000         5,043,992

   5.625%, 12/31/99  . . . . . . . . . . . . . . . . . . . . . . . . . . .      4.58                2,000,000         2,017,094

                                                                                                                   ____________

TOTAL U.S. TREASURY NOTES

   (cost $31,133,307)  . . . . . . . . . . . . . . . . . . . . . . . . . .                                          $31,133,307
                                                                                                                   ____________

Repurchase Agreements--34.6%
- ----------------------------------------------

Bear, Stearns & Co.

  dated 12/31/98, due 1/4/99 in the amount of $6,003,100
  (fully collateralized by $6,165,000 U.S. Treasury Bills, due

   4/29/99, value $6,075,683)  . . . . . . . . . . . . . . . . . . . . . .     4.65%             $  6,000,000      $  6,000,000

Donaldson, Lufkin & Jenrette Securities, Inc.

  dated 12/31/98, due 1/4/99 in the amount of $5,002,694
  (fully collateralized by $4,907,000 U.S. Treasury Notes 7.75%, due

   12/31/99, value $5,052,677) . . . . . . . . . . . . . . . . . . . . . .      4.85                5,000,000         5,000,000

Morgan Stanley Dean Witter & Co.

  dated 12/31/98, due 1/4/99 in the amount of $6,003,080
  (fully collateralized by $5,875,000 U.S. Treasury Notes 7.875%, due

   11/15/99, value $6,088,567) . . . . . . . . . . . . . . . . . . . . . .      4.62                6,000,000         6,000,000

SBC Warburg Dillon Read Inc.

  dated 12/31/98, due 1/4/99 in the amount of $6,748,623
  (fully collateralized by $7,004,000 U.S.Treasury Bills, due

   5/20/99, value $6,884,199)  . . . . . . . . . . . . . . . . . . . . . .      3.50                6,746,000         6,746,000

                                                                                                                   ____________

</TABLE>
<TABLE>
<CAPTION>
TOTAL REPURCHASE AGREEMENTS
   <S>                                                                <C>                                           <C>
   (cost $23,746,000)  . . . . . . . . . . . . . . . . . . . . . . . . . .                                          $23,746,000
                                                                                                                   ____________

TOTAL INVESTMENTS

   (cost $67,847,312)  . . . . . . . . . . . . . . . . . . . . .      98.9%                                         $67,847,312
                                                                    _______                                        ____________


CASH AND RECEIVABLES (NET) . . . . . . . . . . . . . . . . . . .       1.1%                                       $     767,604
                                                                    _______                                        ____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . .     100.0%                                         $68,614,916
                                                                    _______                                        ____________

</TABLE>

<TABLE>
<CAPTION>
                      SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS INSTITUTIONAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF ASSETS AND LIABILITIES                         DECEMBER 31, 1998

                                                                                                  Money            Government

                                                                                                  Market           Securities

                                                                                                   Series            Series
                                                                                                _____________     _____________

ASSETS:                          Investments in securities--See Statement of Investments
                                   (including repurchase agreements
                                   of $2,655,000 and $23,746,000
                                   for the Money Market Series and the Government
                                   Securities Series, respectively)--Note 2(b) . . . . . .       $536,352,409     $  67,847,312
                                 <S>                                                                <C>                 <C>
                                 Cash  . . . . . . . . . . . . . . . . . . . . . . . . . .          1,746,510           248,402

                                 Interest receivable . . . . . . . . . . . . . . . . . . .          2,490,541           564,611

                                 Prepaid expenses  . . . . . . . . . . . . . . . . . . . .             16,963             9,278
                                                                                                _____________     _____________

                                                                                                  540,606,423        68,669,603
                                                                                                _____________     _____________

LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .            233,909            28,147

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .             90,309            26,540
                                                                                                _____________     _____________

                                                                                                      324,218            54,687

                                                                                                _____________     _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $540,282,205     $  68,614,916
                                                                                                _____________     _____________

REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .       $540,316,560     $  68,614,916

                                 Accumulated net realized gain (loss) on investments . . .            (34,355)          ---
                                                                                                _____________     _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $540,282,205     $  68,614,916
                                                                                                _____________     _____________

SHARES OUTSTANDING

(UNLIMITED NUMBER OF $.001 PAR VALUE SHARES OF BENEFICIAL INTEREST AUTHORIZED) . . . . . .        540,316,560        68,614,916

NET ASSET VALUE, offering and redemption price per share . . . . . . . . . . . . . . . . .              $1.00             $1.00
                                                                                                       ______            ______


                                                SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS INSTITUTIONAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS                          YEAR ENDED DECEMBER 31, 1998

                                                                                                  Money            Government

                                                                                                  Market           Securities

                                                                                                   Series            Series
                                                                                                _____________     _____________
INVESTMENT INCOME

INCOME                           Interest Income . . . . . . . . . . . . . . . . . . . . .        $30,174,110      $  4,559,239
                                                                                                 ____________      ____________

EXPENSES--Note 2(c):             Management fee--Note 3(a) . . . . . . . . . . . . . . . .       $  2,701,351     $     418,907

                                 Shareholder servicing costs--Note 3(b)  . . . . . . . . .            135,009            34,762

                                 Custodian fees  . . . . . . . . . . . . . . . . . . . . .             66,824            32,044

                                 Trustees' fees and expenses--Note 3(c)  . . . . . . . . .             66,050             9,134

                                 Professional fees . . . . . . . . . . . . . . . . . . . .             37,037            28,535

                                 Registration fees . . . . . . . . . . . . . . . . . . . .             24,958            32,595

                                 Prospectus and shareholders' reports  . . . . . . . . . .              9,184             9,599

                                 Miscellaneous . . . . . . . . . . . . . . . . . . . . . .             31,420             1,543
                                                                                                 ____________      ____________

                                              Total Expenses . . . . . . . . . . . . . . .          3,071,833           567,119
                                                                                                 ____________      ____________

INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         27,102,277         3,992,120

NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 2(b) . . . . . . . . . . . . . . . . . . . .           (27,774)            10,367
                                                                                                 ____________      ____________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . . . . . .        $27,074,503      $  4,002,487
                                                                                                 ____________      ____________

</TABLE>
<TABLE>
<CAPTION>

                      SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS INSTITUTIONAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

                                                               Money Market Series             Government Securities Series
                                                          ________________________________    ________________________________

                                                          Year Ended         Year Ended        Year Ended        Year Ended
                                                         December 31,       December 31,      December 31,      December 31,
                                                             1998               1997              1998              1997
                                                         ________________   _______________   ________________   _______________

OPERATIONS:
  <S>                                                      <C>             <C>               <C>               <C>
  Investment income--net . . . . . . . . . . . . . . .     $   27,102,277  $     26,296,105  $     3,992,120   $      7,308,145

  Net realized gain (loss) on investments  . . . . . .           (27,774)            5,095            10,367            60,691
                                                         ________________   _______________   ________________   _______________

    Net Increase (Decrease) in Net Assets
       Resulting from Operations . . . . . . . . . . .         27,074,503        26,301,200        4,002,487          7,368,836
                                                         ________________   _______________   ________________   _______________

DIVIDENDS TO SHAREHOLDERS FROM:

  Investment income--net . . . . . . . . . . . . . . .        (27,102,277)      (26,296,105)        (3,992,120)       (7,308,145)

  Net realized gain on investments . . . . . . . . . .         ---                ---                 (10,396)          ---
                                                         ________________   _______________   ________________   _______________

    Total Dividends  . . . . . . . . . . . . . . . . .        (27,102,277)      (26,296,105)        (4,002,516)       (7,308,145)
                                                         ________________   _______________   ________________   _______________

BENEFICIAL INTEREST TRANSACTIONS:

 ($1.00 per share):

  Net proceeds from shares sold  . . . . . . . . . . .      3,374,356,270     4,633,185,786        579,548,799       954,131,576

  Dividends reinvested . . . . . . . . . . . . . . . .          2,871,717         3,514,763          1,501,989         1,378,967

  Cost of shares redeemed  . . . . . . . . . . . . . .     (3,368,354,264)   (4,588,425,068)      (620,130,251)     (950,602,391)
                                                         ________________   _______________   ________________   _______________

    Increase (Decrease) in Net Assets from
       Beneficial Interest Transactions  . . . . . . .          8,873,723        48,275,481        (39,079,463)        4,908,152

                                                         ________________   _______________   ________________   _______________
    Total Increase (Decrease) in Net Assets . . . .             8,845,949        48,280,576        (39,079,492)        4,968,843

NET ASSETS:

  Beginning of Period  . . . . . . . . . . . . . . . .        531,436,256       483,155,680        107,694,408       102,725,565

                                                         ________________   _______________   ________________   _______________

  End of Period  . . . . . . . . . . . . . . . . . . .  $     540,282,205  $    531,436,256  $      68,614,916  $    107,694,408
                                                         ________________   _______________   ________________   _______________


</TABLE>
<TABLE>
<CAPTION>
                      SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS INSTITUTIONAL MONEY MARKET FUND, MONEY MARKET SERIES
- -----------------------------------------------------------------------------

FINANCIAL HIGHLIGHTS

   Contained  below  is  per  share  operating  performance  data for a share of
Beneficial  Interest outstanding, total investment return, ratios to average net
assets  and  other supplemental data for each period indicated. This information
has been derived from the Fund's financial statements.


                                                                                     Year Ended December 31,
                                                                        ______________________________________________________

PER SHARE DATA:                                                     1998         1997          1996         1995         1994
                                                                   _______      _______      _______       _______      _______
   <S>                                                             <C>          <C>          <C>           <C>          <C>
   Net asset value, beginning of period  . . . . . . . . . .       $  1.00      $  1.00      $  1.00       $  1.00      $  1.00
                                                                   _______      _______      _______       _______      _______

   Investment Operations:

   Investment income--net  . . . . . . . . . . . . . . . . .          .050         .051         .049         .054          .036
                                                                   _______      _______      _______       _______      _______

   Distributions:

   Dividends from investment income--net . . . . . . . . . .         (.050)       (.051)       (.049)        (.054)       (.036)
                                                                   _______      _______      _______       _______      _______

   Net asset value, end of period  . . . . . . . . . . . . .       $  1.00      $  1.00      $  1.00       $  1.00      $  1.00
                                                                   _______      _______      _______       _______      _______

TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . .          5.14%        5.17%        5.03%         5.57%        3.65%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . . . . . . . .           .57%         .57%         .58%          .62%         .63%

   Ratio of net investment income
       to average net assets . . . . . . . . . . . . . . . .          5.02%        5.06%        4.91%         5.43%        3.59%

   Net Assets, end of period (000's Omitted) . . . . . . . .      $540,282      $531,436     $483,156      $402,032     $362,825

</TABLE>
<TABLE>
<CAPTION>

                      SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS INSTITUTIONAL MONEY MARKET FUND, GOVERNMENT SECURITIES SERIES
- -----------------------------------------------------------------------------

FINANCIAL HIGHLIGHTS (CONTINUED)

   Contained  below  is  per  share  operating  performance  data for a share of
Beneficial  Interest outstanding, total investment return, ratios to average net
assets  and  other supplemental data for each period indicated. This information
has been derived from the Fund's financial statements.


                                                                                     Year Ended December 31,
                                                                        ______________________________________________________

PER SHARE DATA:                                                     1998         1997          1996         1995         1994
                                                                   _______      _______      _______       _______      _______

   <S>                                                             <C>          <C>          <C>           <C>          <C>
   Net asset value, beginning of period  . . . . . . . . . .       $  1.00      $  1.00      $  1.00       $  1.00      $  1.00
                                                                   _______      _______      _______       _______      _______

   Investment Operations:

   Investment income--net  . . . . . . . . . . . . . . . . .          .048         .048         .047          .052         .034
                                                                   _______      _______      _______       _______      _______

   Distributions:

   Dividends from investment income--net . . . . . . . . . .         (.048)       (.048)       (.047)        (.052)       (.034)
                                                                   _______      _______      _______       _______      _______

   Net asset value, end of period  . . . . . . . . . . . . .       $  1.00      $  1.00      $  1.00       $  1.00      $  1.00
                                                                   _______      _______      _______       _______      _______

TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . .          4.87%        4.95%        4.84%         5.36%        3.49%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . . . . . . . .           .68%         .61%         .63%          .65%         .69%

   Ratio of net investment income
       to average net assets . . . . . . . . . . . . . . . .          4.76%        4.84%        4.74%         5.23%        3.40%

   Net Assets, end of period (000's Omitted) . . . . . . . .       $68,615      $107,694     $102,726      $123,171    $ 120,281

</TABLE>

                      SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS INSTITUTIONAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS

NOTE 1--GENERAL:

   Dreyfus  Institutional Money Market Fund (the "Fund") is registered under the
Investment  Company  Act  of  1940,  as  amended  (the  "Act"), as a diversified
open-end  management investment company and operates as a series company issuing
two  classes  of Beneficial Interest: the Money Market Series and the Government
Securities  Series. The Fund accounts separately for the assets, liabilities and
operations  of  each  series.  The  Fund' s  investment  objective is to provide
investors  with  as  high  a  level  of current income as is consistent with the
preservation   of   capital  and  the  maintenance  of  liquidity.  The  Dreyfus
Corporation (the "Manager") serves as the Fund's investment adviser. The Manager
is  a  direct subsidiary of Mellon Bank, N.A. Premier Mutual Fund Services, Inc.
is  the distributor of the Fund's shares, which are sold to the public without a
sales charge.

It is the Fund's policy to maintain a continuous net asset value per share of
$1.00  for  each  series;  the  Fund  has  adopted certain investment, portfolio
valuation and dividend and distribution policies to enable it to do so. There is
no assurance, however, that the Fund will be able to maintain a stable net asset
value    per    share    of    $1.00    for    each    series.

   The  Funds'  financial  statements  are prepared in accordance with generally
accepted accounting principles which may require the use of management estimates
and assumptions. Actual results could differ from those estimates.

NOTE 2--SIGNIFICANT ACCOUNTING POLICIES:

   (A)  PORTFOLIO  VALUATION:  Investments in securities are valued at amortized
cost, which has been determined by the Fund's Board of Trustees to represent the
fair value of the Fund's investments.

   (B)  SECURITIES  TRANSACTIONS  AND INVESTMENT INCOME: Securities transactions
are  recorded  on  a  trade  date  basis. Realized gain and loss from securities
transactions  are  recorded  on  the  identified  cost basis. Interest income is
recognized  on the accrual basis. Cost of investments represents amortized cost.
Under  the  terms  of  the  custody  agreements,  the Fund receives net earnings
credits  based  on  available  cash  balances left on deposit. During the period
ended  December 31, 1998, the Government Securities Series received net earnings
credits  of $2,359. Income earned under this arrangement is included in interest
income.

   The  Fund  may  enter into repurchase agreements with financial institutions,
deemed  to  be  creditworthy  by  the  Fund' s  Manager, subject to the seller's
agreement  to repurchase and the Fund's agreement to resell such securities at a
mutually   agreed   upon  price.  Securities  purchased  subject  to  repurchase
agreements are deposited with the Fund's custodian and, pursuant to the terms of
the  repurchase  agreement,  must have an aggregate market value greater than or
equal  to  the repurchase price plus accrued interest at all times. If the value
of  the underlying securities falls below the value of the repurchase price plus
accrued  interest,  the  Fund  will  require  the  seller  to deposit additional
collateral by the next business day. If the request for additional collateral is
not met, or the seller defaults on its repurchase obligation, the Fund maintains
the  right  to  sell the underlying securities at market value and may claim any
resulting loss against the seller.

   (C)  EXPENSES:  Expenses  directly attributable to each series are charged to
that  series'  operations;  expenses  which  are  applicable  to both series are
allocated between them.

   (D)  DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund, with respect to
both  series,  to  declare dividends from investment income-net on each business
day;  such dividends are paid monthly. Dividends from net realized capital gain,
with  respect  to both series, are normally declared and paid annually, but each
series  may  make  distributions  on  a  more  frequent basis to comply with the
distribution  requirements of the Internal Revenue Code of 1986, as amended (the
" Code" ). However,  to  the  extent  that a net realized capital gain of either
series can be reduced by a capital loss carryover of that series, such gain will
not be distributed.

 DREYFUS INSTITUTIONAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

   (E)  FEDERAL  INCOME  TAXES:  It  is the policy of each series to continue to
qualify  as a regulated investment company, if such qualification is in the best
interests  of  its  shareholders, by complying with the applicable provisions of
the  Code,  and to make distributions of taxable income sufficient to relieve it
from substantially all Federal income and excise taxes.

The Money Market Series has an unused capital loss carryover of approximately
$34,500  available  for Federal income tax purposes to be applied against future
net securities profits, if any, realized subsequent to December 31, 1998. If not
applied,  $6,500  of the carryover expires in fiscal 2002 and $28,000 expires in
fiscal 2006.

   At  December  31,  1998,  the  cost of investments of each series for Federal
income  tax  purposes  was  substantially  the  same  as  the cost for financial
reporting purposes (see the Statements of Investments).

NOTE 3--MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:

   (A)  Pursuant  to a management agreement with the Manager, the management fee
for  each series is computed at the annual rate of .50 of 1% of the value of the
average daily net assets of each series and is payable monthly.

   (B)  Under  the  Shareholder  Services  Plan,  each series reimburses Dreyfus
Service  Corporation, a wholly-owned subsidiary of the Manager, an amount not to
exceed  an  annual  rate of .25 of 1% of the value of each series' average daily
net  assets for certain allocated expenses of providing personal services and/or
maintaining  shareholder  accounts.  The  services provided may include personal
services  relating  to  shareholder  accounts,  such  as  answering  shareholder
inquiries  regarding  the  Fund and providing reports and other information, and
services  related  to the maintenance of shareholder accounts. During the period
ended  December  31, 1998, the Money Market Series and the Government Securities
Series   were  charged  $35,966  and  $10,135,  respectively,  pursuant  to  the
Shareholder Services Plan.

The Fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager,   under  a  transfer  agency  agreement  for  providing  personnel  and
facilities  to  perform transfer agency services for the Fund. During the period
ended  December  31, 1998, the Money Market Series and the Government Securities
Series  were  charged $72,118 and $3,578, respectively, pursuant to the transfer
agency agreement.

   (C)  Each  trustee  who  is  not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $4,500 and an attendance fee of $500 per
meeting.  The  Chairman  of  the  Board  receives  an  additional  25%  of  such
compensation.


DREYFUS INSTITUTIONAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF TRUSTEES

DREYFUS INSTITUTIONAL MONEY MARKET FUND

   We  have  audited  the  accompanying  statement  of  assets  and liabilities,
including  the  statements of investments, of Dreyfus Institutional Money Market
Fund  (comprising,  respectively,  the  Money  Market  Series and the Government
Securities  Series)  as  of  December  31,  1998,  and  the related statement of
operations  for  the year then ended, the statement of changes in net assets for
each  of  the  two  years in the period then ended, and financial highlights for
each  of  the  years indicated therein. These financial statements and financial
highlights  are  the responsibility of the Fund's management. Our responsibility
is  to express an opinion on these financial statements and financial highlights
based on our audits.

   We  conducted  our  audits  in  accordance  with  generally accepted auditing
standards.  Those standards require that we plan and perform the audit to obtain
reasonable  assurance  about  whether  the  financial  statements  and financial
highlights  are free of material misstatement. An audit includes examining, on a
test  basis,  evidence  supporting  the amounts and disclosures in the financial
statements  and  financial  highlights.  Our procedures included confirmation of
securities  owned  as  of December 31, 1998 by correspondence with the custodian
and brokers. An audit also includes assessing the accounting principles used and
significant  estimates  made  by  management,  as well as evaluating the overall
financial   statement  presentation.  We  believe  that  our  audits  provide  a
reasonable basis for our opinion.

In our opinion, the financial statements and financial highlights referred to
above  present  fairly, in all material respects, the financial position of each
of the respective series constituting Dreyfus Institutional Money Market Fund at
December  31, 1998, the results of their operations for the year then ended, the
changes  in their net assets for each of the two years in the period then ended,
and the financial highlights for each of the indicated years, in conformity with
generally accepted accounting principles.





New York, New York

February 4, 1999



DREYFUS INSTITUTIONAL MONEY MARKET FUND, GOVERNMENT SECURITIES SERIES
- -----------------------------------------------------------------------------

IMPORTANT TAX INFORMATION (UNAUDITED)

   For  State  individual  income tax purposes, the Government Securities Series
hereby designates 34.56% of the ordinary income dividends paid during its fiscal
year  ended  December  31,  1998  as attributable to interest income from direct
obligations  of  the  United  States.  Such  dividends are currently exempt from
taxation  for individual income tax purposes in most states, including New York,
California and the District of Columbia.


                                   [reg.tm logo]

                                   (reg.tm)

DREYFUS INSTITUTIONAL

MONEY MARKET FUND

200 Park Avenue

New York, NY 10166

MANAGER

The Dreyfus Corporation

200 Park Avenue

New York, NY 10166

CUSTODIAN

The Bank of New York

90 Washington Street

New York, NY 10286

TRANSFER AGENT &

DIVIDEND DISBURSING AGENT

Dreyfus Transfer, Inc.

P.O. Box 9671

Providence, RI 02940










Printed in U.S.A.                                         179/195AR9812

Institutional

Money Market

Fund

Annual Report


December 31, 1998



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