DREYFUS BASIC GNMA FUND
N-30D, 1999-03-05
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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 BASIC GNMA FUND
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

  We  are pleased to report the performance for Dreyfus BASIC GNMA Fund. For the
12-month  period  ended  December  31,  1998, your Fund produced a total return,
including share price changes and dividend income generated, of 4.71%,* compared
to  6.93%  for  the Lehman Brothers GNMA Index.** Income dividends paid from net
investment  income  amounted  to  approximately $0.971 per share, representing a
distribution rate per share of 6.45%.***

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 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

  During  the  fourth  quarter  of 1998, U.S. interest rates reached new lows in
yield.  This  can  largely be attributed to the tremendous flight to quality, or
maybe  more  appropriately,  the  financial panic that occurred in the worldwide
bond  markets.  With several Japanese-based global financial institutions filing
for  bankruptcy  protection, worldwide liquidity reached dangerously low levels.
This led to widespread demand for U.S. Treasuries, pushing interest rates lower,
and to mass liquidations of many types of fixed income securities.

  As  one  might  expect, the market for mortgage-backed securities faced a very
difficult  time,  especially  in September and October. As shown by the Mortgage
Banker  Association' s Index, homeowner refinancing activity reached an all-time
high  during  the  month of October. That activity is the primary contributor to
mortgage-backed  securities  prepayments;  hence, the prepayment spreads of both
agency  and  non-agency  mortgage-backed  securities reached some of the highest
levels   in   history.   All   this   contributed  to  the  underperformance  of
mortgage-backed securities when compared to U.S. Treasuries for the year.

  The  flight  to  quality  frenzy  that occurred in September and October shook
other  areas  of the mortgage-backed securities market as well. Most notable was
the  liquidation  of  large  holdings of the huge hedge fund, Long Term Capital.
Their  holdings  included  large  quantities  of  high  quality, residential and
commercial  mortgage-backed  securities. Their forced liquidation of billions of
dollars of commercial mortgage-backed securities overwhelmed the market, causing
an  imbalance  in  its  supply and demand. This imbalance resulted in the sudden
widening  of  the  yield  spread  by  over  100  basis  points on AAA commercial
mortgage-backed securities.

  Fortunately,  the Fed saw fit to continue cutting the Fed funds rate. This has
helped  bring  greater liquidity back into the market, and the supply-and-demand
imbalance has begun to normalize.

PORTFOLIO OVERVIEW

  As  might be expected, during this dramatic shift in the fixed-income markets,
we  did  make  some significant changes to the Fund's holdings. Most notably, we
increased  the  Fund' s  average effective duration to be longer than the Lehman
Brothers  GNMA  Index, which helped the performance of the Fund. Consistent with
our  anticipation  of  faster mortgage loan refinancing, we've also continued to
look  for  further  prepayment  protection.  Hence,  we  have  continued  to add
discounted  GNMA  30-year pass-through securities to the portfolio. We have also
continued    to    sell    our    higher    dollar-priced    securities.

  With  the significant shifts in the market discussed above, liquidity has been
at a premium; hence, we have continued to use our existing GNMA adjustable rate,
mortgage-backed  securities  (ARMs)  as  a  highly  liquid, yield-improving cash
substitute. Even though mortgage prepayments have been at extremely high levels,
discount  GNMA  ARMs have continued to add additional yield and liquidity to the
Fund.

  During  the  month  of December, we were able to sell approximately 14% of our
GNMA  project loans at a significant premium to their normal market value into a
Wall  Street  securitization  (also  known  as a FNMA ACES REMIC). We have since
replaced  approximately  6% of these assets at cheaper, higher yields. It is our
conviction  that  GNMA  project loans will continue to add stability to the Fund
and  protection  as it faces the current mortgage-refinancing wave that we think
will continue to challenge the GNMA mortgage-backed securities marketplace.

  Lastly,  we  continue  to  feel  commercial  mortgage-backed securities in the
portfolio  are  among  the  best  opportunities  in the fixed-income marketplace
today. Even though this allocation to CMBS was the primary reason for the Fund's
weaker performance during the months of September and October, we have continued
to hold this position. In the last two months of 1998, the CMBS market began its
return  to  market equilibrium. Spreads on AAA-rated, 10-year CMBS have moved in
dramatically,  from  the  very  depressed  level  of  210 basis points that they
reached  in  the  peak  of the liquidity crisis, to a spread of 130 basis points
(over    the    10-year    Treasury)    today.

               Sincerely,


               [Michael Hoeh signature]


               Michael Hoeh

               Portfolio Manager

January 15, 1999

New York, N.Y.

* Total return includes reinvestment of dividends and any capital gains paid.

**SOURCE:  LEHMAN  BROTHERS--The  Lehman  Brothers GNMA Index is an unmanaged,
total  return  performance  benchmark for the GNMA market, consisting of 15- and
30-year fixed-rate GNMA securities.

***  Distribution rate per share is based upon dividends per share paid from net
investment  income during the period divided by the net asset value per share at
the end of the period, adjusted for capital gain distributions.



DREYFUS BASIC GNMA FUND                                     DECEMBER 31, 1998
- -----------------------------------------------------------------------------

COMPARISON OF CHANGE IN VALUE OF $10,000 INVESTMENT IN DREYFUS BASIC GNMA FUND
                      AND THE LEHMAN BROTHERS GNMA INDEX

                                    Dollars

$24,216

Lehman Brothers GNMA Index*

$21,544

Dreyfus BASIC GNMA Fund

*Source: Lehman Brothers

<TABLE>
Average Annual Total Returns
- -----------------------------------------------------------------------------

                      One Year Ended                   Five Years Ended                  Ten Years Ended

                     December 31, 1998                 December 31, 1998                December 31, 1998
                     ___________________               ___________________              ___________________
<S>                         <C>                              <C>                              <C>
                            4.71%                            6.78%                            7.98%
- ------------------------

Past performance is not predictive of future performance.
</TABLE>

The above graph compares a $10,000 investment made in Dreyfus BASIC GNMA Fund on
12/31/88  to a $10,000 investment made in the Lehman Brothers GNMA Index on that
date. All dividends and capital gain distributions are reinvested.

The  Fund invests primarily in Ginnie Maes and its performance shown in the line
graph  takes into account all applicable fees and expenses. Unlike the Fund, the
Lehman  Brothers  GNMA  Index is an unmanaged total return performance benchmark
for  the  GNMA market, consisting of 15- and 30-year fixed-rate GNMA securities.
All issues have at least one year to maturity and an outstanding par value of at
least $100 million. The Index does not take into account charges, fees and other
expenses.  These  factors  can contribute to the Index potentially outperforming
the  Fund.  Further  information relating to Fund performance, including expense
reimbursements,  if applicable, is contained in the Financial Highlights section
of the Prospectus and elsewhere in this report.

<TABLE>
DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                    DECEMBER 31, 1998

                                                                                                Principal

Bonds and Notes--162.5%                                                                          Amount               Value
- -------------------------------------------------------                                       _____________        ____________
<S>                                                                                            <C>                 <C>
U.S. Government Agencies/Mortgage-Backed Securities--114.0%

Government National Mortgage Association I:

   6%  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $ 16,500,000  (a)   $ 16,360,740

   6.50% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       13,500,000  (a)     13,605,435

   6.50%, 10/15/2010-12/15/2028  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        4,244,859           4,294,995

   6.50%, 4/15/2011-6/15/2011  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,193,989           1,222,718

   7.50%, 12/15/2023 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          350,277  (b)        361,661

   8%, 1/15/2022-4/15/2022 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          408,011             427,748

   8%, 4/15/2008-9/15/2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        2,569,176  (b)      2,671,943

   8.50%, 2/15/2005-3/15/2022  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          927,604             992,279

   8.50%, 1/15/2020  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          291,819  (b)        312,428

   9%, 5/15/2016-11/15/2022  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,162,719           1,247,276

   9.50%, 1/15/2017-12/15/2021 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          548,464             595,424

                                                                                                                  _____________

                                                                                                                     42,092,647

                                                                                                                  _____________

Government National Mortgage Association I;

  Construction Loans;

   6.75% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        6,505,500  (a)      6,601,944

                                                                                                                  _____________

Government National Mortgage Association I,

  Project Loans:

   6.32%, 10/15/2033 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        2,586,899  (b)      2,612,769

   6.375%  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,186,600  (a)      1,205,135

   6.375%, 10/15/2033  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        3,196,307           3,265,219

   6.40%, 10/15/2033 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,846,463           1,894,933

   6.41%, 8/15/2028  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          997,813           1,025,254

   6.43% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,500,000  (a)      1,523,430

   6.45%, 11/15/2033 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        2,998,211  (b)      3,085,340

   6.55%, 12/15/2033 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          703,500             718,667

   6.60%, 5/15/2028  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,934,698           1,972,173

   6.625%  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        5,472,700  (a)      5,590,691

   6.625%, 8/15/2028-1/15/2034 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        9,347,133           9,688,787

   6.70%, 3/15/2028  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          642,887             669,606

   6.75%, 12/15/2023 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        6,872,200           7,091,217

   9.25%, 10/15/2023 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          938,836             939,419

                                                                                                                  _____________

                                                                                                                     41,282,640

                                                                                                                  _____________

Government National Mortgage Association II:

   5%, 4/20/2028 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          487,833  (c)        489,956

   5%, 5/20/2028 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        2,915,599  (b,c)    2,928,341

   9%, 3/20/2016-7/20/2025 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          882,776             937,768

   9.50%, 9/20/2021-12/20/2021 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          184,460             198,826

                                                                                                                  _____________

                                                                                                                      4,554,891

                                                                                                                  _____________

Government National Mortgage Association II,

  Real Estate Mortgage Investment Conduit,

  Collateralized Mortgage Obligations,

   Ser. 1997-2, Cl. K, 7.50%, 1/20/2024  . . . . . . . . . . . . . . . . . . . . . . . . .        2,780,000  (d)      2,843,912

                                                                                                                  _____________

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                        DECEMBER 31, 1998

                                                                                                Principal

Bonds and Notes (continued)                                                                      Amount               Value
- -------------------------------------------------------                                       _____________        ____________

U.S. Government Agencies/Mortgage-Backed Securities (continued)

Federal Home Loan Mortgage Corp.:

  Real Estate Mortgage Investment Conduit,

  Collateralized Mortgage Obligations,

       Ser. 1092, Cl. J, 8.50%, 5/15/2020  . . . . . . . . . . . . . . . . . . . . . . . .     $    176,739  (d)   $    176,666

Federal Home Loan Mortgage Corp. (continued)

  Stripped Securities, Interest Only Class:

       Ser. 1541, Cl. FA, 7%, 5/15/2019  . . . . . . . . . . . . . . . . . . . . . . . . .        4,904,658  (d,e)      658,254

       Ser. 1547, Cl. B, 7%, 2/15/2022 . . . . . . . . . . . . . . . . . . . . . . . . . .        1,750,000  (e)        286,073

       Ser. 1590, Cl. JA, 6.50%, 10/15/2021  . . . . . . . . . . . . . . . . . . . . . . .        6,000,000  (e)      1,070,625

       Ser. 1596, Cl. L, 6.50%, 12/15/2012 . . . . . . . . . . . . . . . . . . . . . . . .        1,800,000  (d,e)      271,800

       Ser. 1916, Cl. PI, 7%, 12/15/2011 . . . . . . . . . . . . . . . . . . . . . . . . .        1,241,033  (d,e)      186,924

       Ser. 1987, Cl. PI, 7%, 9/15/2012  . . . . . . . . . . . . . . . . . . . . . . . . .        1,298,396  (e)        213,911

       Ser. 1999, Cl. PW, 7%, 8/15/2026  . . . . . . . . . . . . . . . . . . . . . . . . .        3,934,384  (d,e)      644,255

       Ser. 2066, Cl. PM, 6.50%, 12/15/2026  . . . . . . . . . . . . . . . . . . . . . . .        3,843,569  (e)        731,479

                                                                                                                  _____________

                                                                                                                      4,239,987

                                                                                                                  _____________

Federal Housing Administration,

  Project Loans:

       7.20%, 2/1/2033 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,121,021           1,164,811

       7.625%, 4/1/2031  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,240,479           1,313,745

                                                                                                                  _____________

                                                                                                                      2,478,556

                                                                                                                  _____________

Federal National Mortgage Association:

   6.94% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        4,269,553  (a)      4,483,030

   Real Estate Mortgage Investment Conduit,

   Stripped Securities, Interest Only Class:

       Ser. 1993-61, Cl. N, 7%, 3/25/2022  . . . . . . . . . . . . . . . . . . . . . . . .        7,218,166  (d)      1,116,217

       Ser. 1993-137, Cl. PT, 7%, 6/25/2022  . . . . . . . . . . . . . . . . . . . . . . .        4,000,000  (d)        641,250

                                                                                                                  _____________

                                                                                                                      6,240,497

                                                                                                                  _____________

Total U.S. Government Agencies/Mortgage-Backed Securities. . . . . . . . . . . . . . . . .                          110,335,074

                                                                                                                  _____________

Asset-Backed Securities--8.6%

Illinois Power Special Purpose Trust,

   Ser. 1998-1, Cl. A-5, 5.38%, 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . .        2,000,000           1,993,375

Nomura Depositor Trust,

  Ser. 1998-ST-1:

       Cl. A-3, 6.127%, 2003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,000,000  (a,f,g)    949,375

       Cl. A-5, 6.80%, 2003  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        3,500,000  (a,f,g)   3,358,906

The Money Store Home Equity Trust,

   Ser. 1997-A, Cl. A-9, 7.235%, 2028  . . . . . . . . . . . . . . . . . . . . . . . . . .        2,000,000           2,055,938

                                                                                                                  _____________

Total Asset-Backed Securities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                            8,357,594

                                                                                                                  _____________

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                        DECEMBER 31, 1998

                                                                                                Principal

Bonds and Notes (continued)                                                                      Amount               Value
- -------------------------------------------------------                                       _____________        ____________

Commercial Mortgage Pass-Through Ctfs.--19.3%

Asset Securitization,

   Ser. 1997-D5, Cl. A1-D, 6.85%, 2041 . . . . . . . . . . . . . . . . . . . . . . . . . .     $  2,250,000  (d)   $  2,349,141

Chase Commercial Mortgage Securities,

   Ser. 1998-SN1, Cl. D, 6.486%, 2001  . . . . . . . . . . . . . . . . . . . . . . . . . .          750,000  (d,f,e)    724,805

CS First Boston Mortgage Securities,

   Ser. 1998-C1, Cl. C, 6.78%, 2009  . . . . . . . . . . . . . . . . . . . . . . . . . . .        2,000,000  (d)      2,061,910

DLJ Commercial Mortgage,

   Ser. 1998-ST1A, Cl. B-1, 6.567%, 2000 . . . . . . . . . . . . . . . . . . . . . . . . .        2,400,000  (d,f,g)   2,352,750

GS Mortgage Securities II:

   Ser. 1998-GL2, Cl. A-2, 6.562%, 2031  . . . . . . . . . . . . . . . . . . . . . . . . .        3,000,000  (d)      3,120,000

   Ser. 1998-GS1:

       Cl. C, 5.854%, 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        3,000,000  (d,f,g)   2,970,938

       Cl. D, 6.154%, 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        1,750,000  (d,f,g)   1,731,406

Merrill Lynch Mortgage Investors,

   Ser. 1997-SD1, Cl. E, 6.280%, 2010  . . . . . . . . . . . . . . . . . . . . . . . . . .        3,500,000  (d)      3,397,188

                                                                                                                  _____________

Total Commercial Mortgage Pass-Through Ctfs. . . . . . . . . . . . . . . . . . . . . . . .                           18,708,138

                                                                                                                  _____________


Residential Mortgage Pass-Through Ctfs.--20.6%

BA Mortgage Securities,

   Ser. 1998-2, Cl. 2B-2, 6.50%, 2013  . . . . . . . . . . . . . . . . . . . . . . . . . .          301,630  (d)        279,008

Chase Mortgage Finance,

  Ser. 1998-S3:

       Cl. B-1, 6.50%, 2013  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          774,697  (d)        756,674

       Cl. B-2, 6.50%, 2013  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          664,025  (d)        648,577

GE Capital Mortgage Services,

   Ser. 1998-16, Cl. B-2, 6.50%, 2013  . . . . . . . . . . . . . . . . . . . . . . . . . .          617,424  (d)        588,096

Norwest Asset Securities:

  Ser. 1997-3:

       Cl. B-1, 7.25%, 2027  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        2,456,485  (d)      2,481,198

       Cl. B-2, 7.25%, 2027  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          982,594  (d)        984,923

   Ser. 1997-7, Cl. B-2, 7%, 2027  . . . . . . . . . . . . . . . . . . . . . . . . . . . .          786,813  (d)        782,422

   Ser. 1997-9, Cl. B-2, 7%, 2012  . . . . . . . . . . . . . . . . . . . . . . . . . . . .          446,746  (d)        430,346

   Ser. 1997-15, Cl. B-2, 6.75%, 2012  . . . . . . . . . . . . . . . . . . . . . . . . . .          648,091  (d)        647,527

   Ser. 1997-20, Cl. B-2, 6.75%, 2012  . . . . . . . . . . . . . . . . . . . . . . . . . .          408,037  (d)        404,348

   Ser. 1998-14, Cl. B-3, 6.50%, 2013  . . . . . . . . . . . . . . . . . . . . . . . . . .          611,629  (d)        569,414

   Ser. 1998-18, Cl. B-3, 6.25%, 2028  . . . . . . . . . . . . . . . . . . . . . . . . . .          872,245  (d)        772,210

PNC Mortgage Securities:

   Ser. 1997-8, Cl. 3B-3, 6.75%, 2012  . . . . . . . . . . . . . . . . . . . . . . . . . .          296,731  (d)        307,553

   Ser. 1998-2:

       Cl. 3B-3, 6.75%, 2013 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          563,879  (d)        581,624

       Cl. 4B-3, 6.75%, 2027 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          398,318  (d)        409,793

   Ser. 1998-11, Cl. 2B-3, 6.25%, 2013 . . . . . . . . . . . . . . . . . . . . . . . . . .          521,897  (d)        475,904

Prudential Home Mortgage Securities,

   Ser. 1995-6, Cl. B-2, 7.50%, 2025 . . . . . . . . . . . . . . . . . . . . . . . . . . .        2,108,448  (d)      2,130,249

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                        DECEMBER 31, 1998

                                                                                                Principal

Bonds and Notes (continued)                                                                      Amount               Value
- -------------------------------------------------------                                       _____________        ____________

Residential Mortgage Pass-Through Ctfs. (continued)

Residential Accredit Loans,

   Ser. 1997-QS6:

   Cl. M-2, 7.50%, 2012  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $  1,001,944  (d)   $  1,031,874

   Cl. M-3, 7.50%, 2012  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          651,259  (d)        670,713

Residential Funding Mortgage Securities I:

   Ser. 1997-S10, Cl. M-3, 7%, 2012  . . . . . . . . . . . . . . . . . . . . . . . . . . .          504,715  (d)        507,016

   Ser. 1997-S11, Cl. M-3, 7%, 2012  . . . . . . . . . . . . . . . . . . . . . . . . . . .          732,860  (d)        745,965

   Ser. 1998-S12, Cl. M-3, 6.75%, 2028 . . . . . . . . . . . . . . . . . . . . . . . . . .        1,044,329  (d)        962,578

   Ser. 1998-S14, Cl. M-3, 6.50%, 2013 . . . . . . . . . . . . . . . . . . . . . . . . . .          840,675  (d)        840,309

   Ser. 1998-S16, Cl. M-3, 6.50%, 2013 . . . . . . . . . . . . . . . . . . . . . . . . . .          755,657  (d)        710,317

   Ser. 1997-S19, Cl. M-3, 6.50%, 2012 . . . . . . . . . . . . . . . . . . . . . . . . . .          664,080  (d)        629,814

   Ser. 1997-S21, Cl. M-3, 6.50%, 2012 . . . . . . . . . . . . . . . . . . . . . . . . . .          383,765  (d)        394,422

   Ser. 1998-NS1:

       Cl. M-2, 6.375%, 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          153,435  (d)        153,367

       Cl. M-3, 6.375%, 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           76,717  (d)         73,181

                                                                                                                  _____________

Total Residential Mortgage Pass-Through Ctfs.. . . . . . . . . . . . . . . . . . . . . . .                           19,969,422
                                                                                                                  _____________

TOTAL BONDS AND NOTES

   (cost $157,996,984) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $157,370,228
                                                                                                                  _____________

Short-Term Investments--.3%
- -------------------------------------------------------

U.S. Treasury Bills:

   5.03%, 1/14/1999  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  $       200,000  (h)   $       199,741

   5.05%, 1/21/1999  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          100,000  (h)         99,755

                                                                                                                  _____________

TOTAL SHORT-TERM INVESTMENTS

   (cost $299,483) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $    299,496
                                                                                                                  _____________

TOTAL INVESTMENTS

   (cost $158,296,467) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           162.8%        $157,669,724

                                                                                                    _______       _____________

LIABILITIES, LESS CASH AND RECEIVABLES . . . . . . . . . . . . . . . . . . . . . . . . . .          (62.8%)      $ (60,823,440)

                                                                                                    _______       _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           100.0%        $ 96,846,284

                                                                                                    _______       _____________

Notes to Statement of Investments:
- -----------------------------------------------------------------------------

(a)  Purchased on a forward commitment basis.

(b)  Held by broker as collateral for open reverse repurchase agreements.

(c)  Adjustable rate mortgage--interest rate subject to change periodically.

(d)  Held  by the custodian in a segregated account as collateral for securities
     purchased on a forward commitment basis.

(e)  Reflects notional face amount.

(f)  Securities exempt from registration under Rule 144A of the Securities Act
     of 1933.  These securities may  be  resold  in  transactions  exempt  from
     registration, normally to qualified institutional buyers.  At December 31,
     1998, these securities amounted to $12,088,180 or 12.5% of net assets.

(g)  Variable rate security--interest rate subject to change periodically.

(h)  Held by the custodian in  a  segregated  account as collateral for open
     financial futures positions.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

  STATEMENT OF FINANCIAL FUTURES                              DECEMBER 31, 1998

                                                                            Market Value                          Unrealized

                                                                               Covered                           Appreciation

Financial Futures Short                                     Contracts       by Contracts        Expiration        at 12/31/98

____________________                                        ________        ____________         _________       ____________
<S>                                                            <C>             <C>               <C>                <C>
U.S. Treasury 5 year notes . . . . . . . . . . . . . . .       69              $7,820,719        March '99          $ 63,156

U.S. Treasury 10 year notes. . . . . . . . . . . . . . .       66               7,864,312        March '99            89,075

                                                                                                                   _________

                                                                                                                    $152,231

                                                                                                                   _________

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

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

STATEMENT OF ASSETS AND LIABILITIES                         DECEMBER 31, 1998

                                                                                                    Cost              Value
                                                                                                 ____________      ____________
<S>                                                                                              <C>               <C>
ASSETS:                          Investments in securities--See Statement of Investments . .     $158,296,467      $157,669,724

                                 Cash  . . . . . . . . . . . . . . . . . . . . . . . . . .                              246,140

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                            1,009,459

                                 Receivable for shares of Beneficial Interest subscribed . .                             41,673

                                 Paydown receivables . . . . . . . . . . . . . . . . . . .                               36,863

                                 Receivable for investment securities sold . . . . . . . .                                4,485

                                 Prepaid expenses  . . . . . . . . . . . . . . . . . . . .                                7,729

                                                                                                                 ______________

                                                                                                                    159,016,073

                                                                                                                 ______________

LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                               44,121

                                 Payable for investment securities purchased . . . . . . .                           44,957,346

                                 Payable for Reverse Repurchase Agreements--Note 5 . . . .                           16,958,000

                                 Payable for shares of Beneficial Interest redeemed  . . .                              121,716

                                 Interest payable--Note 5  . . . . . . . . . . . . . . . .                               17,163

                                 Payable for futures variation margin--Note 4(a) . . . . .                                  300

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                               71,143

                                                                                                                 ______________

                                                                                                                     62,169,789

                                                                                                                 ______________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        $  96,846,284

                                                                                                                 ______________


REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .                        $  97,812,880

                                 Accumulated undistributed investment income--net  . . . .                               11,427

                                 Accumulated net realized gain (loss) on investments . . .                            (503,511)

                                 Accumulated net unrealized appreciation (depreciation)
                                   of investments (including $152,231 net unrealized
                                   appreciation on financial futures)--Note 4(b) . . . . .                            (474,512)

                                                                                                                 ______________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        $  96,846,284
                                                                                                                 ______________

SHARES OUTSTANDING

(UNLIMITED NUMBER OF $.001 PAR VALUE SHARES OF BENEFICIAL INTEREST AUTHORIZED) . . . . . .                            6,453,939

NET ASSET VALUE, offering and redemption price per share . . . . . . . . . . . . . . . . .                               $15.01

                                                                                                                       ________




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

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS                          YEAR ENDED DECEMBER 31, 1998

INVESTMENT INCOME
<S>                                                                                        <C>                    <C>
INCOME                           Interest Income . . . . . . . . . . . . . . . . .                                $ 6,269,499

EXPENSES:                        Management fee--Note 3(a) . . . . . . . . . . . .         $    525,492

                                 Shareholder servicing costs--Note 3(b)  . . . . .              218,728

                                 Interest expense--Note 5  . . . . . . . . . . . .              144,148

                                 Professional fees . . . . . . . . . . . . . . . .               39,592

                                 Trustees' fees and expenses--Note 3(c)  . . . . .               37,041

                                 Registration fees . . . . . . . . . . . . . . . .               34,108

                                 Custodian fees--Note 3(b) . . . . . . . . . . . .               23,658

                                 Prospectus and shareholders' reports  . . . . . .               17,983

                                 Loan commitment fees--Note 2  . . . . . . . . . .                  622

                                 Miscellaneous . . . . . . . . . . . . . . . . . .               13,322

                                                                                            ___________

                                        Total Expenses . . . . . . . . . . . . . .            1,054,694


                                 Less--reduction in management fee due to
                                    undertaking--Note 3(a) . . . . . . . . . . . .             (340,642)

                                                                                            ___________

                                        Net Expenses . . . . . . . . . . . . . . .                                    714,052

                                                                                                                  ___________

INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                  5,555,447

                                                                                                                  ___________

REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS--Note 4:

                                 Net realized gain (loss) on investments
                                    and securities sold short  . . . . . . . . . .          $ 1,267,159

                                 Net realized gain (loss) on financial futures . .           (1,774,271)
                                                                                            ___________

                                        Net Realized Gain (Loss) . . . . . . . . .                                  (507,112)

                                 Net unrealized appreciation (depreciation) on
                                    investments and securities sold short (including
                                    $152,231 net unrealized appreciation
                                    on financial futures)  . . . . . . . . . . . .                                 (1,328,489)
                                                                                                                  ___________

NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS . . . . . . . . . . . . . .                                 (1,835,601)
                                                                                                                  ___________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . .                                $ 3,719,846
                                                                                                                  ___________

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

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

                                                                                              Year Ended        Year Ended

                                                                                          December 31, 1998  December 31, 1997
                                                                                           _________________  _________________
<S>                                                                                         <C>                 <C>
OPERATIONS:

   Investment income--net  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        $   5,555,447       $   4,055,809

   Net realized gain (loss) on investments . . . . . . . . . . . . . . . . . . . . .             (507,112)            954,499

   Net unrealized appreciation (depreciation) on investments . . . . . . . . . . . .           (1,328,489)            776,447

                                                                                            _____________       _____________

       Net Increase (Decrease) in Net Assets Resulting from Operations . . . . . . .            3,719,846           5,786,755
                                                                                            _____________       _____________
DIVIDENDS TO SHAREHOLDERS FROM:

   Investment income--net  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           (5,545,920)         (4,053,909)

   Net realized gain on investments  . . . . . . . . . . . . . . . . . . . . . . . .             (291,592)         (1,027,054)
                                                                                            _____________       _____________

       Total Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           (5,837,512)         (5,080,963)
                                                                                            _____________       _____________

BENEFICIAL INTEREST TRANSACTIONS:

   Net proceeds from shares sold . . . . . . . . . . . . . . . . . . . . . . . . . .           43,371,763          31,673,859

   Dividends reinvested  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .            4,345,234           3,692,556

   Cost of shares redeemed . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          (24,682,862)        (17,807,854)
                                                                                            _____________       _____________

       Increase (Decrease) in Net Assets from Beneficial Interest Transactions . . .           23,034,135          17,558,561
                                                                                            _____________       _____________

          Total Increase (Decrease) in Net Assets  . . . . . . . . . . . . . . . . .           20,916,469          18,264,353

NET ASSETS:

   Beginning of Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           75,929,815          57,665,462
                                                                                            _____________       _____________

   End of Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         $ 96,846,284        $ 75,929,815
                                                                                            _____________       _____________

UNDISTRIBUTED INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . .     $        11,427   $           1,900
                                                                                            _____________       _____________

                                                                                               Shares              Shares
                                                                                            _____________       _____________

CAPITAL SHARE TRANSACTIONS:

   Shares sold   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .            2,827,468           2,070,281

   Shares issued for dividends reinvested  . . . . . . . . . . . . . . . . . . . . .              283,676             241,976

   Shares redeemed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           (1,611,860)         (1,167,399)
                                                                                            _____________       _____________

       Net Increase (Decrease) in Shares Outstanding . . . . . . . . . . . . . . . .            1,499,284           1,144,858
                                                                                            _____________       _____________

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

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

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  . . . . . . . . . .        $15.32       $15.14       $15.42        $14.16       $15.39
                                                                   _______      _______      _______       _______      _______

   Investment Operations:

   Investment income--net  . . . . . . . . . . . . . . . . .          .97           .99          .98          1.03         1.08

   Net realized and unrealized gain (loss) on investments  .          (.26)         .41         (.27)         1.25        (1.23)
                                                                   _______      _______      _______       _______      _______

   TOTAL FROM INVESTMENT OPERATIONS  . . . . . . . . . . . .           .71         1.40          .71          2.28         (.15)
                                                                   _______      _______      _______       _______      _______

   Distributions:

   Dividends from investment income--net . . . . . . . . . .          (.97)        (.99)        (.99)        (1.02)       (1.08)

   Dividends from net realized gain on investments . . . . .          (.05)        (.23)         --           --           --
                                                                   _______      _______      _______       _______      _______

   TOTAL DISTRIBUTIONS . . . . . . . . . . . . . . . . . . .         (1.02)       (1.22)        (.99)        (1.02)       (1.08)
                                                                   _______      _______      _______       _______      _______

   Net asset value, end of period  . . . . . . . . . . . . .        $15.01       $15.32       $15.14        $15.42       $14.16
                                                                   _______      _______      _______       _______      _______

TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . .          4.71%        9.55%        4.81%        16.62%        (.99%)

RATIOS/SUPPLEMENTAL DATA:

   Ratio of operating expenses to average net assets . . . ..          .65%         .65%         .65%          .50%         .06%

   Ratio of interest expense and loan commitment
     fees to average net assets  . . . . . . . . . . . . . .           .17%           --           --           --            --

   Ratio of net investment income to average net assets  . .          6.34%        6.46%        6.50%         6.86%        7.34%

   Decrease reflected in above expense ratios
     due to undertakings by the Manager  . . . . . . . . . .           .39%         .42%         .52%          .78%        1.43%

   Portfolio Turnover Rate   . . . . . . . . . . . . . . . .        388.97%      534.25%      332.96%       254.36%      290.20%

   Net Assets, end of period (000's Omitted)   . . . . . . .       $96,846      $75,930      $57,665      $55,615       $44,937

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

NOTES    TO    FINANCIAL    STATEMENTS

NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:

   Dreyfus  BASIC  GNMA  Fund  (the  "Fund" ) is registered under the Investment
Company Act of 1940, as amended (the "Act") as a diversified open-end management
investment  company.  The  Fund's investment objective is to provide an investor
with as high a level of current income as is consistent with the preservation of
capital  by  investing  principally  in  instruments  issued  by  the Government
National Mortgage Association. The Dreyfus Corporation (the "Manager") serves as
the  Fund' s  investment  adviser.  The Manager is a direct subsidiary of Mellon
Bank,  N.A. ("Mellon"). Premier Mutual Fund Services, Inc. is the distributor of
the Fund's shares, which are sold to the public without a sales charge.

   The  Fund' s  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.

   (A)  PORTFOLIO  VALUATION:  Investments  in  securities (excluding short-term
investments  other  than  U.S.  Treasury Bills and financial futures) are valued
each  business day by an independent pricing service ("Service") approved by the
Board of Trustees. Investments for which quoted bid prices are readily available
and  are  representative  of  the  bid side of the market in the judgment of the
Service are valued at the mean between the quoted bid prices (as obtained by the
Service  from dealers in such securities) and asked prices (as calculated by the
Service  based  upon  its  evaluation  of the market for such securities). Other
investments  (which  constitute  a  majority  of  the  portfolio securities) are
carried  at  fair  value  as  determined  by the Service, based on methods which
include  consideration of: yields or prices of securities of comparable quality,
coupon,  maturity  and  type; indications as to values from dealers; and general
market  conditions.  Short-term  investments, excluding U.S. Treasury Bills, are
carried  at  amortized  cost,  which  approximates  value. Financial futures are
valued  at  the  last  sales  price  on  the  securities  exchange on which such
securities  are  primarily  traded  or  at  the last sales price on the national
securities market on each business day.

   (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
(including,   where   applicable,   amortization   of   discount  on  short-term
investments)  is recognized on the accrual basis. Under the terms of the custody
agreement,  the  Fund  receives  net  earnings  credits  based on available cash
balances left on deposit.

   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)  DIVIDENDS  TO  SHAREHOLDERS:  It  is  the  policy of the Fund to declare
dividends  daily  from  investment  income-net. Such dividends are paid monthly.
Dividends  from  net  realized  capital  gain  are  normally  declared  and paid
annually, but the Fund 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"). To the extent that net realized capital gain can be offset
by  capital  loss  carryovers,  if  any,  it  is  the  policy of the Fund not to
distribute such gain.

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

(D) FEDERAL INCOME TAXES: It is the policy of the Fund 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  Internal  Revenue  Code,  and  to  make  distributions  of  taxable  income
sufficient to relieve it from substantially all Federal income and excise taxes

   The  Fund  has  an  unused  capital  loss carryover of approximately $197,000
available  for  Federal  income  tax  purposes  to be applied against future net
securities  profits,  if  any,  realized  subsequent  to  December 31, 1998. The
carryover  does not include net realized securities losses from November 1, 1998
through December 31, 1998 which are treated, for Federal income tax purposes, as
arising in fiscal 1999. If not applied, the carryover expires in fiscal 2006.

NOTE 2--BANK LINE OF CREDIT:

   The  Fund  participates  with  other  Dreyfus-managed funds in a $600 million
redemption  credit  facility  (" Facility" ) to  be  utilized  for  temporary or
emergency  purposes,  including  the  financing  of  redemptions.  In connection
therewith, the Fund has agreed to pay commitment fees on its pro rata portion of
the  Facility.  Interest  is  charged  to  the Fund at rates based on prevailing
market  rates  in  effect  at  the  time  of borrowings. During the period ended
December 31, 1998, the Fund did not borrow under the Facility.

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

   (A)  Pursuant  to a management agreement with the Manager, the management fee
is  computed  at the annual rate of .60 of 1% of the value of the Fund's average
daily net assets and is payable monthly. The Manager has undertaken from January
1,  1998  through December 31, 1998, and thereafter, until such time as it gives
shareholders  at least 90 days' notice to the contrary, to reduce the management
fee  paid  by  the  Fund,  to  the  extent  that  the Fund's aggregate expenses,
exclusive  of  taxes,  brokerage,  interest  on  borrowings, commitment fees and
extraordinary  expenses,  exceed an annual rate of .65 of 1% of the value of the
Fund' s  average  daily net assets. The reduction in management fee, pursuant to
the undertaking, amounted to $340,642 during the period ended December 31, 1998

   The  undertaking  may  be  extended,  modified  or terminated by the Manager,
provided  that  the  resulting  expense reimbursement would not be less than the
amount required pursuant to the Agreement.

   (B)  Under the Shareholder Services Plan, the Fund 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 the Fund's 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  Fund was charged $134,372 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 Fund was charged $30,649 pursuant to the transfer
agency agreement.

The Fund compensates Mellon under a custody agreement for providing custodial
services  for  the Fund. During the period ended December 31, 1998, the Fund was
charged $23,658 pursuant to the custody agreement.

   (C)  Each  trustee  who  is  not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $250 per
meeting.  The  Chairman  of  the  Board  receives  an  additional  25%  of  such
compensation.

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

NOTE 4--SECURITIES TRANSACTIONS:

  (A)  The  following  summarizes  the  aggregate  amount of purchases and sales
(including  paydowns)  of  investment  securities  and  securities  sold  short,
excluding  short-term  securities and financial futures, during the period ended
December 31, 1998:
<TABLE>

                                                                                            Purchases              Sales
                                                                                          _____________        _____________
<S>                                                                                        <C>                  <C>
Long transactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           $515,977,078         $446,258,944

Short sale transactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .              2,046,875             --
                                                                                          _____________        _____________

   TOTAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           $518,023,953         $446,258,944
                                                                                          _____________        _____________
</TABLE>

  The  Fund  may  engage  in short-selling which obligates the Fund to replace a
security  borrowed  by purchasing the security at current market value. The Fund
would  incur  a  loss if the price of the security increases between the date of
the  short  sale  and the date on which the Fund replaces the borrowed security.
The  Fund  would  realize  a  gain if the price of the security declines between
those  dates.  Until  the  Fund  replaces  the  borrowed security, the Fund will
maintain  daily,  a  segregated account with the custodian, of cash and /or U.S.
Government  securities  sufficient  to cover its short position. At December 31,
1998, there were no securities sold short outstanding.

  The  Fund  may invest in financial futures contracts in order to gain exposure
to  or protect against changes in the market. The Fund is exposed to market risk
as  a  result of changes in the value of the underlying instruments. Investments
in financial futures require the Fund to "mark to market" on a daily basis, this
represents  the  change in the market value of the contract at the close of each
day' s  trading.  Accordingly, variation margin payments are received or made to
reflect  daily  unrealized  gains  or losses. When the contracts are closed, the
Fund  recognizes  a  realized  gain  or  loss. These investments require initial
margin  deposits with a custodian, which consist of cash or cash equivalents, up
to  approximately  10%  of  the contract amount. The amount of these deposits is
determined by the exchange or Board of Trade on which the contract is traded and
is  subject to change. Contracts open at December 31, 1998, are set forth in the
Statement of Financial Futures.

   (B)  At  December  31,  1998,  accumulated  net  unrealized  depreciation  on
investments  and  financial futures was $474,512, consisting of $1,847,467 gross
unrealized appreciation and $2,321,979 gross unrealized depreciation.

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

NOTE 5--REVERSE REPURCHASE AGREEMENTS:

  The  Fund  may enter into reverse repurchase agreements with banks, brokers or
dealers.  This  form  of  borrowing  involves  the  transfer  by  the Fund of an
underlying  debt instrument in return for cash proceeds based on a percentage of
value  of  the  security.  The  Fund  retains  the right to receive interest and
principal  payments  on  the  security.  At an agreed upon future date, the Fund
repurchases  the security at principal plus accrued interest. Reverse repurchase
agreements  may  subject the Fund to interest rate risk and counter party credit
risk.

  As  of  December  31,  1998,  the  Fund  had  entered  into reverse repurchase
agreements  in  the  amount of $16,958,000. The average daily amount outstanding
during  the  period ended December 31, 1998 was approximately $2,498,000, with a
related weighted average annualized interest rate of 5.77%.

DREYFUS BASIC GNMA FUND
- -----------------------------------------------------------------------------

REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF TRUSTEES

DREYFUS BASIC GNMA FUND

  We  have  audited  the  accompanying  statement  of  assets and liabilities of
Dreyfus  BASIC  GNMA Fund, including the statements of investments and financial
futures,  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 verification by
examination  of  securities  held  by  the custodian as of December 31, 1998 and
confirmation  of  securities  not  held  by the custodian by correspondence with
others.  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
Dreyfus  BASIC GNMA Fund at December 31, 1998, the results of its operations for
the  year then ended, the changes in its 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 BASIC GNMA FUND
- -----------------------------------------------------------------------------

IMPORTANT TAX INFORMATION (UNAUDITED)

  For  Federal  tax  purposes,  the Fund hereby designates $.0023 per share as a
long-term  capital  gain distribution of the $.0499 per share paid on August 31,
1998.


                                   [reg.tm logo]

                                   (reg.tm)

DREYFUS BASIC

GNMA FUND

200 Park Avenue

New York, NY 10166

MANAGER

The Dreyfus Corporation

200 Park Avenue

New York, NY 10166

CUSTODIAN

Mellon Bank, N.A.

One Mellon Bank Center

Pittsburgh, PA 15258

TRANSFER AGENT &

DIVIDEND DISBURSING AGENT

Dreyfus Transfer, Inc.

P.O. Box 9671

Providence, RI 02940










Printed in U.S.A.                                             080AR9812

BASIC

GNMA

Fund

Annual Report

December 31, 1998


COMPARISON OF CHANGE IN VALUE OF $10,000
INVESTMENT IN DREYFUS BASIC GNMA FUND AND
THE LEHMAN BROTHERS GNMA INDEX

EXHIBIT A:


              LEHMAN BROTHERS
 PERIOD           GNMA             DREYFUS BASIC
                 INDEX *             GNMA FUND

12/31/88           10,000               10,000
12/31/89           11,569               10,842
12/31/90           12,792               11,772
12/31/91           14,845               13,336
12/31/92           15,945               14,272
12/31/93           16,994               15,521
12/31/94           16,738               15,367
12/31/95           19,593               17,921
12/31/96           20,677               18,784
12/31/97           22,648               20,576
12/31/98           24,216               21,544


*Source: Lehman Brothers



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