DREYFUS BASIC MUNICIPAL MONEY MARKET FUND INC /MD/
N-30D, 1998-10-30
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DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

  We  are  pleased  to  report  the  performance  for  Dreyfus  BASIC New Jersey
Municipal  Money  Portfolio  for the 12-month period ended August 31, 1998. Your
Portfolio produced a yield of 2.97% and, after taking into account the effect of
compounding, the effective yield was 3.01%.*

The Economy

  Having   consistently   viewed   inflation   as  the  primary  threat  to  our
strong-growth,  low-unemployment  economy, the Federal Reserve Board (the "Fed")
now  has another factor to ponder in setting monetary policy: the risk of global
recession.  The wave of economic uncertainty that shook stock markets and caused
currencies  to devalue begun in Thailand on July 2, 1997 (the onset of the Asian
financial crisis) and has since spread through Asia and around the world. By the
end  of  the reporting period, Russia had devalued its ruble. All this financial
tumult  has  underscored  just how economically interrelated the world's nations
are. In fact, the fragility of global financial markets has been a key factor in
the  Fed' s  reluctance to raise interest rates in an economy now in its seventh
year  of  economic  expansion. It feared that a rise in rates might threaten the
stability of other currencies.

  There  were  additional economic factors that stayed the Fed's hand. Inflation
has remained tame, comfortably below 2% on the consumer level, and is minimal at
the  production  level  of the economy as well. One reason for the low inflation
rate  is  the  strong  dollar, which keeps imports cheap; domestic producers are
constrained  from raising prices by competition from cheaper foreign goods. This
has all been good news for consumers, who account for two thirds of all economic
activity. Bolstered by solid wage gains and abundant jobs, consumers have been a
driving  positive  force  in  the  economy.  By the end of the reporting period,
however,  there  were  hints  that this could change. The political and economic
instability  in  Russia jolted the U.S. stock market in August. The stock market
sell-off could cause consumers to grow less confident and curtail spending, even
though the larger-scale economic fundamentals for consumers remain positive: low
inflation and plentiful jobs (unemployment remains near its 28-year low of 4.5%)
 . In response to the markets' uncertainty, short-term rates moved sharply lower.
In  addition,  second-quarter economic growth lessened to 1.6%, the slowest rate
in  three  years  and  dramatically  below  the 5.5% rate reported for the first
quarter.  Many  market participants indicated that an ease by the Fed might be a
strong probabilty given the recent changes in economic conditions.

Market Environment/Portfolio

  While  the  Fed  has  left  interest rates unchanged since March, 1997, market
technicals  nevertheless  created  fluctuations in rates on short-term municipal
securities  in  this  reporting  period.  During the first weeks of January, the
demand  in  the municipal money market was particularly strong due to large cash
inflows,  although the market remained in a trading range throughout most of the
first quarter of 1998. However, in April, money funds were tapped for income tax
payments,  placing  upward  pressure  on rates as funds experienced redemptions.
Supply  conditions  in  late  May reversed this trend as municipal fund managers
anticipated  the  effect  of  several billion dollars worth of notes leaving the
market at the end of June. July brought rate stability back to the market as new
supply eased the demand pressure that had existed.

  Unlike  previous summer financing periods, this year's late summer calendar of
municipal  notes  (consisting mainly of California-exempt paper) was drastically
reduced  by  a  combination  of  factors. Due to the strength of local and state
economies,  several  issuers  reduced the amount of short-term borrowing needed.
Additionally,  many  issuers  came  to  market  with  maturities  outside of the
13-month maximum maturity allowable for money funds. In prior years, such issues
had  shorter maturities and could be purchased by money funds. Other issues were
converted  to a synthetic structure that is not currently permitted for purchase
in your Fund. The overall result was a lower yield for most one-year paper, both
national  and  state-specific.  While  we did participate in the one-year market
when  attractive  yield  opportunities  became  available, we often utilized the
commercial   paper   market   to   keep   average   maturities  from  shortening
significantly.  As  the  Fall  approaches,  we  hope  to  have additional buying
opportunities in the New Jersey note market (for example, the recent addition of
the  State  of  New Jersey commercial paper program to the market). We expect to
choose  selectively  among  these  issues  and  to structure the portfolio in an
attempt  to  maximize  current  yield  while  maintaining our commitment to high
quality tax-exempt investments.

  Included  in  this report is a series of detailed statements about your Fund's
holdings  and its financial condition. We hope they are informative. Please know
that  we  appreciate  greatly  your continued confidence in this Fund and in The
Dreyfus Corporation.

               Very truly yours



               [Richard J. Moynihan logo signature]


               Richard J. Moynihan

               Director, Municipal Portfolio Management

               The Dreyfus Corporation

September 18, 1998

New York, N.Y.

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


<TABLE>
DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                      AUGUST 31, 1998

                                                                                                  Principal

Tax Exempt Investments--99.5%                                                                       Amount            Value
- -------------------------------------------------------                                         _____________      ____________
<S>                                                                                           <C>               <C>
New Jersey--97.1%

Atlantic City, GO Notes 4%, 8/15/99 (Insured; AMBAC) . . . . . . . . . . . . . . . . . . .    $     2,250,000   $     2,258,317

Atlantic County Improvement Authority, Revenue, VRDN (Pooled Government Loan
Program)

  2.65% (LOC; Kredietbank) (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          4,000,000         4,000,000

Burlington County, BAN 4%, 6/11/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . .          3,724,000         3,734,018

East Brunswick Township, BAN 4%, 1/7/99. . . . . . . . . . . . . . . . . . . . . . . . . .          3,000,000         3,003,545

Essex County Improvement Authority, Revenue, VRDN (Pooled Government Loan
Program)

  2.50% (LOC; Banco Santander) (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . .          4,200,000         4,200,000

City of Fort Lee, TAN 4%, 2/2/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,007,309

Hudson County Improvement Authority, VRDN (Essential Purpose Pooled Government)

  3.20% (LOC: Comerica Bank and Fuji Bank) (a) . . . . . . . . . . . . . . . . . . . . . .          4,700,000         4,700,000

Jersey City, BAN 4.25%, 1/15/99. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,500,000         1,502,592

Monmouth County Improvement Authority, Revenue, VRDN (Pooled Government Loan
Program)

  2.90% (LOC; Union Bank of Switzerland) (a) . . . . . . . . . . . . . . . . . . . . . . .          7,000,000         7,000,000

New Jersey Economic Development Authority:

  SWDR (Newark Recycling) 3.95%, 12/15/98 (LOC; Societe Generale)  . . . . . . . . . . . .          3,000,000         3,000,000

  VRDN:

    Dock Facility Revenue, Refunding (Bayonne/ IMTT Project)

       3.15%, Series A (LOC; First Chicago Corp.) (a)  . . . . . . . . . . . . . . . . . .          4,950,000         4,950,000

    EDR, Refunding (Dow Chemical-El Dorado Terminal)

       2.80%, Series 1984A (LOC; Dow Chemical Co.) (a) . . . . . . . . . . . . . . . . . .         10,000,000        10,000,000

    Industrial and EDR (Merck and Co.)

       3.45%, Series A and B (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,700,000         1,700,000

    Revenue (U.S. Golf Association Project)

       3.25%, Series A (LOC; PNC Bank) (a) . . . . . . . . . . . . . . . . . . . . . . . .          2,400,000         2,400,000

    Thermal Energy Facilities, Revenue (Thermal Energy Limited Partnership)

       3.10% (LOC; First Chicago Corp.) (a)  . . . . . . . . . . . . . . . . . . . . . . .          3,000,000         3,000,000

New Jersey Health Care Facilities Financing Authority, Revenue, VRDN

 (Hospital Capital Asset Financing):

    3.05%, Series A (LOC; Chase Manhattan Bank) (a)  . . . . . . . . . . . . . . . . . . .          5,500,000         5,500,000

    3.05%, Series D (LOC; Chase Manhattan Bank) (a)  . . . . . . . . . . . . . . . . . . .          6,000,000         6,000,000

    Refunding (Christian Health) 2.77%, Series 97B (LOC; Valley National Bank) (a) . . . .          3,700,000         3,700,000

New Jersey Sports and Exposition Authority, VRDN (State Contract)

  3%, Series C (Insured; MBIA and Liquidity; Credit Suisse) (a)  . . . . . . . . . . . . .          9,945,000         9,945,000

New Jersey Turnpike Authority, Turnpike Revenue, Refunding, VRDN

  2.90%, Series D (Insured; FGIC and SBPA; Societe Generale) (a) . . . . . . . . . . . . .          1,900,000         1,900,000

Port Authority of New York and New Jersey, Special Obligation Revenue, VRDN

 (Versatile Structure Obligation):

    3.20%, Series 2 (LOC; Morgan Guaranty Trust Co.) (a) . . . . . . . . . . . . . . . . .          1,000,000         1,000,000

    3.35%, Series 3 (BPA; Morgan Guaranty Trust Co.) (a) . . . . . . . . . . . . . . . . .          5,700,000         5,700,000

    3.35%, Series 5 (Liquidity; Bayerische Landesbank) (a) . . . . . . . . . . . . . . . .          5,300,000         5,300,000

    3.30%, Series 6 (BPA; Bank of Nova Scotia) (a) . . . . . . . . . . . . . . . . . . . .          1,000,000         1,000,000

DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                          AUGUST 31, 1998

                                                                                                   Principal

Tax Exempt Investments (continued)                                                                  Amount            Value
- -------------------------------------------------------                                          ____________      ____________

New Jersey (continued)

Salem County Pollution Control Financing Authority, PCR, Refunding, VRDN

 (Public Service Electric and Gas)

  2.95% (BPA; Union Bank of Switzerland and Insured; MBIA) (a) . . . . . . . . . . . . . .    $     6,500,000   $     6,500,000

Somerset County Industrial Pollution Control Financing Authority, Revenue,
Refunding,

  VRDN (American Cyanamid) 2.65% (LOC; American Home Products) (a) . . . . . . . . . . . .          4,400,000         4,400,000

Woodbridge Township, BAN 4%, 7/1/99. . . . . . . . . . . . . . . . . . . . . . . . . . . .          3,820,450         3,834,214

U.S. Related--2.4%

Commonwealth of Puerto Rico Government Development Bank, Refunding, VRDN

  2.50% (BPA; Credit Suisse and Insured; MBIA) (a) . . . . . . . . . . . . . . . . . . . .          2,800,000         2,800,000

                                                                                                                  _____________

TOTAL INVESTMENTS (cost $118,034,995). . . . . . . . . . . . . . . . . . . . . . . . . . .              99.5%      $118,034,995

                                                                                                      =======     =============


CASH AND RECEIVABLES (NET) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                .5%   $       587,496

                                                                                                      =======     =============


NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             100.0%      $118,622,491

                                                                                                      =======     =============


Summary of Abbreviations
- -----------------------------------------------------------------------------

AMBAC       American Municipal Bond Assurance Corporation           MBIA        Municipal Bond Investors Assurance

BAN         Bond Anticipation Notes                                                Insurance Corporation

BPA         Bond Purchase Agreement                                 PCR         Pollution Control Revenue

EDR         Economic Development Revenue                            SBPA        Standby Bond Purchase Agreement

FGIC        Financial Guaranty Insurance Company                    SWDR        Solid Waste Disposal Revenue

GO          General Obligation                                      TAN         Tax Anticipation Notes

LOC         Letter of Credit                                        VRDN        Variable Rate Demand Notes

Summary of Combined Ratings (Unaudited)
- -----------------------------------------------------------------------------

Fitch                or            Moody's             or            Standard & Poor's              Percentage of Value

____                               ________                          _________________              ___________________

F1+/F1                             VMIG1/MIG1, P1                    SP1+/SP1, A1+/A1                      86.1%

AAA/AA (b)                         Aaa/Aa (b)                        AAA/AA (b)                             1.9

Not Rated (c)                      Not Rated (c)                     Not Rated (c)                         12.0

                                                                                                         _______

                                                                                                          100.0%

                                                                                                         _______

                                                                                                         _______

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

(a)  Securities payable on demand. Variable interest rate-subject to change.
(b)  Notes which are not MIG, SP or F rated are represented by bond ratings of
     the issuers.

(c)  Securities which, while  not rated by Fitch, Moody's or Standard & Poor's
     have been determined by the Manager to be of comparable quality to those
     rated securities in which the Fund may invest.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

STATEMENT OF ASSETS AND LIABILITIES                           AUGUST 31, 1998

                                                                                                     Cost             Value
                                                                                                _____________     _____________
<S>                                                                                              <C>               <C>
ASSETS:                          Investments in securities--See Statement of Investments . .     $118,034,995      $118,034,995

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                              690,602

                                 Prepaid expenses  . . . . . . . . . . . . . . . . . . . .                                3,623

                                                                                                                  _____________

                                                                                                                    118,729,220

                                                                                                                  _____________

LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                               26,746

                                 Cash overdraft due to Custodian . . . . . . . . . . . . .                               43,073

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                               36,910

                                                                                                                  _____________

                                                                                                                        106,729

                                                                                                                  _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $118,622,491

                                                                                                                  =============


REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .                         $118,625,970

                                 Accumulated net realized gain (loss) on investments . . .                              (3,479)

                                                                                                                  _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $118,622,491

                                                                                                                  =============

SHARES OUTSTANDING

(1 BILLION SHARES OF $.001 PAR VALUE COMMON STOCK AUTHORIZED). . . . . . . . . . . . . . .                          118,625,970

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

                                                                                                                         ======


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS                            YEAR ENDED AUGUST 31, 1998

INVESTMENT INCOME

<S>                                                                                                  <C>             <C>
INCOME                           Interest Income . . . . . . . . . . . . . . . . . . . . .                           $4,398,875


EXPENSES:                        Management fee--Note 2(a) . . . . . . . . . . . . . . . .           $642,288

                                 Shareholder servicing costs--Note 2(b)  . . . . . . . . .            128,106

                                 Professional fees . . . . . . . . . . . . . . . . . . . .             18,008

                                 Custodian fees  . . . . . . . . . . . . . . . . . . . . .             13,339

                                 Registration fees . . . . . . . . . . . . . . . . . . . .              9,510

                                 Prospectus and shareholders' reports  . . . . . . . . . .              8,697

                                 Directors' fees and expenses--Note 2(c) . . . . . . . . .              2,652

                                 Miscellaneous . . . . . . . . . . . . . . . . . . . . . .              4,588

                                                                                                  ___________


                                        Total Expenses . . . . . . . . . . . . . . . . . .            827,188


                    Less--reduction in management fee due to

                                    undertaking--Note 2(a) . . . . . . . . . . . . . . . .           (247,828)

                                                                                                  ___________


                                        Net Expenses . . . . . . . . . . . . . . . . . . .                              579,360

                                                                                                                    ___________


INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                            3,819,515


NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b) . . . . . . . . . . . . . . . . . . . .                               (3,479)

                                                                                                                    ___________


NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . . . . . .                           $3,816,036

                                                                                                                    ===========


                                                SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------


STATEMENT OF CHANGES IN NET ASSETS

                                                                                              Year Ended        Year Ended

                                                                                           August 31, 1998    August 31, 1997

                                                                                             _______________   _______________

OPERATIONS:
<S>                                                                                           <C>               <C>
  Investment income--net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      $    3,819,515    $    3,798,419

  Net realized gain (loss) on investments  . . . . . . . . . . . . . . . . . . . . . . .              (3,479)              --

                                                                                               _____________     _____________

    Net Increase (Decrease) in Net Assets Resulting from Operations  . . . . . . . . . .           3,816,036         3,798,419

                                                                                               _____________     _____________

DIVIDENDS TO SHAREHOLDERS FROM:

  Investment income--net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          (3,819,515)       (3,798,419)

                                                                                               _____________     _____________

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

  Net proceeds from shares sold  . . . . . . . . . . . . . . . . . . . . . . . . . . . .          79,800,472       111,644,558

  Dividends reinvested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .           3,709,795         3,698,562

  Cost of shares redeemed  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        (101,437,681)      (79,037,487)

                                                                                               _____________     _____________

    Increase (Decrease) in Net Assets from Capital Stock Transactions  . . . . . . . . .         (17,927,414)       36,305,633

                                                                                             _____________     _____________

       Total Increase (Decrease) in Net Assets . . . . . . . . . . . . . . . . . . . . .         (17,930,893)       36,305,633

NET ASSETS

  Beginning of Period  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         136,553,384       100,247,751

                                                                                               _____________     _____________

  End of Period  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        $118,622,491      $136,553,384

                                                                                               =============     =============


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

FINANCIAL HIGHLIGHTS

  Contained  below is per share operating performance data for a share of Common
Stock  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 August 31,

                                                                                            ___________________________________
PER SHARE DATA:                                                                                1998          1997        1996(1)
                                                                                              ______        ______       ______
<S>                                                                                          <C>           <C>          <C>
   Net asset value, beginning of period  . . . . . . . . . . . . . . . . . . . . . . . .     $  1.00       $  1.00      $  1.00

                                                                                              ______        ______       ______
   Investment Operations:

   Investment income--net  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        .030          .031         .025

                                                                                              ______        ______       ______

   Distributions:

   Dividends from investment income--net . . . . . . . . . . . . . . . . . . . . . . . .      (.030)        (.031)       (.025)

                                                                                              ______        ______       ______

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

                                                                                              ======        ======       ======


TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        3.01%         3.17%        3.38%(2)

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . . . . . . . . . . . . . . . . . . . . . .         .45%          .36%         .06%(2)

   Ratio of net investment income

       to average net assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        2.97%         3.12%        3.25%(2)

   Decrease reflected in above expense ratios

       due to undertakings by the Manager  . . . . . . . . . . . . . . . . . . . . . . .         .19%          .27%         .68%(2)

   Net Assets, end of period (000's Omitted) . . . . . . . . . . . . . . . . . . . . . .    $118,622     $136,553      $100,248
- -----------------------------

(1)  From December 1, 1995 (commencement of operations) to August 31, 1996.
(2)  Annualized.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS

NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:

  Dreyfus  BASIC  New  Jersey Municipal Money Market Portfolio (the "Fund") is a
separate  non-diversified  series  of  Dreyfus  BASIC  Municipal Fund, Inc. (the
" Company" ) which  is  registered  under the Investment Company Act of 1940, as
amended (the "Act") as an open-end management investment company and operates as
a  series  company currently offering four series including the Fund. The Fund's
investment  objective  is  to  provide investors with as high a level of current
income  exempt  from Federal and New Jersey income tax as is consistent with the
preservation  of  capital  and 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.

  The  Company accounts separately for the assets, liabilities and operations of
each  fund.  Expenses  directly  attributable  to  each fund are charged to that
fund' s  operations;  expenses  which  are applicable to all funds are allocated
among them on a pro rata basis.

  It  is the Fund's policy to maintain a continuous net asset value per share of
$1.00; 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.

  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 are valued at amortized
cost, which has been determined by the Company's Board of Directors 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. Interest income, adjusted for amortization of
premiums  and original issue discounts on investments, is earned from settlement
date and recognized on the accrual basis. Realized gain and loss from securities
transactions  are  recorded  on  the  identified cost basis. Cost of investments
represents  amortized cost. Under the terms of the custodian agreement, the Fund
received  net earnings credits of $3,512 during the period ended August 31, 1998
based  on  available  cash  balances  left  on deposit. Income earned under this
arrangement is included in interest income.

  The  Fund  follows  an  investment  policy of investing primarily in municipal
obligations  of  one  state. Economic changes affecting the state and certain of
its  public  bodies  and municipalities may affect the ability of issuers within
the  state to pay interest on, or repay principal of, municipal obligations held
by the Fund.

  (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, if any, 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, it is the policy of the Fund not to distribute such
gain.

  (D)  FEDERAL INCOME TAXES: It is the policy of the Fund to continue to qualify
as a regulated investment company, which can distribute tax exempt dividends, by
complying  with the applicable provisions of the Code, and to make distributions
of  income  and  net  realized  capital  gain  sufficient  to  relieve  it  from
substantially all Federal income and excise taxes.

DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

  The  Fund  has  an unused capital loss carryover of $352 available for Federal
income  tax purposes to be applied against future net securities profits, if any
realized  subsequent  to  August  31,  1998.  The carryover does not include net
realized  securities  losses from November 1, 1997 through August 31, 1998 which
are  treated, for Federal income tax purposes, as arising in fiscal 1999. If not
applied, the carryover expires in fiscal 2006.

  At  August  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 2--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 .50 of 1% of the value of the Fund's average
daily  net  assets  and  is  payable  monthly.  The  Manager has undertaken from
September  1,  1997 through June 30, 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 .45 of 1% of the value of
the  Fund' s average daily net assets. The reduction in management fee, pursuant
to  the  undertakings,  amounted  to $247,828 during the period ended August 31,
1998.

  (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
August  31,  1998,  the  Fund  was  charged $113,163 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  August  31,  1998,  the  Fund was charged $9,816 pursuant to the transfer
agency agreement.

  (C)  Each  director  who  is  not an "affiliated person" as defined in the Act
receives  from the Company an annual fee of $1,000 and an attendance fee of $250
per  meeting.  The  Chairman  of  the  Board  receives an additional 25% of such
compensation.


DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO
- -----------------------------------------------------------------------------

REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF DIRECTORS

DREYFUS BASIC NEW JERSEY MUNICIPAL MONEY MARKET PORTFOLIO

  We  have  audited  the  accompanying  statement  of  assets  and  liabilities,
including  the  statement  of investments, of Dreyfus BASIC New Jersey Municipal
Money  Market  Portfolio (one of the Series constituting Dreyfus BASIC Municipal
Fund,  Inc.)  as of August 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 August 31, 1998 by correspondence with the custodian. 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  New  Jersey Municipal Money Market Portfolio at August 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

October 2, 1998

IMPORTANT TAX INFORMATION (UNAUDITED)

  In  accordance  with  Federal  tax  law,  the  Fund  hereby designates all the
dividends  paid  from  investment income-net during the fiscal year ended August
31, 1998 as "exempt-interest dividends" (not subject to regular Federal and, for
individuals who are New Jersey residents, New Jersey personal income taxes).



Dreyfus lion "d" logo                                   (reg.tm)

Dreyfus logo                                   (reg.tm)


DREYFUS BASIC NEW JERSEY MUNICIPAL

MONEY MARKET PORTFOLIO

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.                                              127AR988

BASIC New Jersey

Municipal Money

Market Portfolio

Annual Report

August 31, 1998



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