DREYFUS PREMIER STATE MUNICIPAL BOND FUND
N-30D, 1997-07-08
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DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to report the performance of the Dreyfus Premier State
Municipal Bond Fund _ Georgia Series for its fiscal year ended April 30, 1997
as shown in the following table:
                              TOTAL RETURN*             DISTRIBUTION RATE**
                              ______________            ___________________
  Class A..................       6.16%                        4.50%
  Class B..................       5.55%                        4.21%
  Class C..................       5.30%                        3.89%
ECONOMIC REVIEW
    The U.S. economy just kept rolling ahead over the reporting period.
Inflation remained subdued. The unemployment rate fell to
its lowest level in 24 years, and a surge in tax revenues meant good news for
the Administration's budget reduction program. Overall, the economic news has
been stellar.
    The economy grew at a robust 5.6% annual rate during the first quarter,
the best quarter in nine years. Aided by falling energy prices, and with no
sign of shortages of raw materials, inflation remained in check. On the
consumer level, the Consumer Price Index (CPI) remained below 3%. Excluding
volatile food and energy prices, the CPI is actually trending downward so far
this year, running at an annual rate of 2.5%. Inflation has been further
restrained by the strong dollar which has moderated the price of imports and
eased potential strains on domestic production capacity.
    The strong economy has put increasing numbers of people to work. This
tightening of the labor market has been a key factor in the implementation of
monetary policy by the Federal Reserve Board's Open Market Committee (FOMC).
The unemployment rate has been less than 5.5% since June 1996, the lowest
sustained rate since the late 1980s. The rate fell to 4.9% in April of this
year, its lowest level in 24 years. So far, neither strong economic growth
nor wage increases have resulted in any price pressure at the consumer level.
Through the first quarter (the latest available data), total employment costs
(including wages and benefits) rose about the same as inflation.
    Renewed confidence, spurred by increasing job security and low inflation,
has resulted in a surge in consumer spending. In the first quarter of the
year, spending rose 6.4%, almost double the rate of the previous year's
fourth quarter. The combined six-month performance was the largest increase
in consumer spending over the past ten years. Retail sales have spurted in
the early part of this year as well; first quarter results were sharply
higher than in the last quarter of 1996. Not surprisingly, industrial
production has been building momentum over the reporting period. The latest
report on capacity utilization indicated the highest level in two years. So
far, while the potential exists for production bottlenecks, prices for raw
materials and worker wage demands have remained modest.
    Continued economic growth and the resulting rise in tax revenues have
slashed further the Federal budget deficit. Recent estimates by
Administration officials suggest that the deficit for fiscal 1997 is now
about $75 billion, its lowest level in 23 years. Such good news on the
deficit could make it easier to negotiate the Administration's bipartisan
plan to balance the budget by 2002.
    While we seem to be enjoying the best of all possible economic worlds,
the potential for future inflation is what concerns the Fed. Such concern
resulted in the March decision by the FOMC, the policy-making arm of the
Federal Reserve, to raise the Federal Funds rate one quarter of a percentage
point to 5.50%. (The Federal Funds rate is the rate of interest banks charge
each other for overnight loans.) The traditional assumption that strong
economic growth and low unemployment will eventually result in rising inflation
still drives the Fed's monetary policy initiatives. Although there was little
reported evidence of incipient inflation, the Fed executed a preemptive move
of moderate monetary restraint in March, perhaps to avoid being forced to act
more harshly later. There is little reason to suspect that the Fed will soon
change this policy, although with the economy seeming to enjoy strong growth
without surging inflation, the FOMC may be reluctant to raise rates again in
the immediate future.
MARKET ENVIRONMENT
    Supply of new issue Georgia paper has been somewhat minimal for the last
year, and will most likely remain so over the next few months. On the other
hand, demand has been rather strong, hence the Fund has been able to slowly
sell overvalued bonds which had achieved our price goals. Even though the new
issue supply was fairly weak, the Fund has been able to occasionally purchase
undervalued issues in the secondary market which was more active. These types
of opportunities tend to occur when the market is fairly weak. The Fund
intends to continue to purchase both primary and secondary issues at value
levels when they become available.
    Municipals have gone from being cheap to currently being fairly valued
when compared to the U.S. Government bond markets, because demand improved
when the markets declined. This trend was especially true of the long
maturities, where the bulk of new supply has traditionally been issued.
During normal market conditions, as interest rates drop, municipal supply
will increase as demand subsides. Municipals may then begin to lag the
Treasury market.
PORTFOLIO OVERVIEW
    As interest rates have increased, the Fund has been able to sell premium
bonds with short calls and high yields. In the current market environment,
the sale of these types of issues represents an opportunity to take profits
and reinvest the proceeds in discount bonds to instill more performance into
the Fund and balance the income/performance equation. The Fund has been
maintaining a modest cash position as well, in order to lower duration and to
have the reserves on hand necessary to capitalize on market opportunities.
    Since interest rates have been rising, the Fund has become more
aggressive and is slowly increasing its maturity and duration. By purchasing
discounts, the Fund is now positioned to capitalize in the event of an
improving market. Since the Fund was positioned defensively going into a
rising interest rate environment, it can take advantage of the current market
conditions while minimizing the risk that is associated with longer maturing
bonds. This risk is minimized because the Fund was selling moderate discounts
and longer maturities when interest rates were substantially lower.
    Lower rated issues remain very expensive when compared to higher rated
securities. The Fund continues to take advantage of this tight spread
relationship by favoring higher rated securities which are traditionally more
liquid. This strategy will give the Fund more flexibility to react to a weak
market which can experience liquidity constraints.
    Because the Fund positioned itself defensively in late 1996 when interest
rates were low, it was able to take advantage of the declining market that
occurred in 1997 by purchasing issues which were undervalued. The Fund also
implemented this strategy earlier in 1996 when interest rates were
fluctuating.

    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 the Fund
and in The Dreyfus Corporation.
                              Very truly yours,

                          [Richard J. Moynihan signature logo]

                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
May 16, 1997
New York, N.Y.

* Total return includes reinvestment of dividends and any capital gains paid,
and does not take into consideration the maximum initial sales charge in the
case of Class A shares or the contingent deferred sales charge imposed on
redemptions in the case of Class B and Class C shares.
**     Distribution rate per share is based upon dividends per share paid
from net investment income during the period, divided by the maximum offering
price at the end of the period in the case of Class A shares, or the net
asset value per share in the case of Class B and Class C shares, adjusted for
capital gain distributions. Some income may be subject to the Federal
Alternative Minimum Tax (AMT) for certain shareholders.

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES    APRIL 30, 1997
[Exhibit A]
COMPARISON OF CHANGE IN VALUE OF $10,000 INVESTMENT IN DREYFUS PREMIER STATE
MUNICIPAL BOND FUND,
GEORGIA SERIES CLASS A SHARES AND THE LEHMAN BROTHERS MUNICIPAL BOND INDEX

$13,465
Lehman Brothers
Municipal Bond Index*
Dollars
$12,946
Dreyfus Premier State Municipal
Bond Fund, Georgia Series
(Class A Shares)
*Source: Lehman Brothers
[Exhibit A]
<TABLE>
<CAPTION>

Average Annual Total Returns
                                CLASS A SHARES                                              CLASS B SHARES
__________________________________________________________________     __________________________________________________________
                                                                                                             % Return Reflecting
                                                   % Return                                                 Applicable Contingent
                                                  Reflecting                                     % Return      Deferred Sales
                          % Return Without      Maximum Initial                                 Assuming No     Charge Upon
PERIOD ENDED 4/30/97        Sales Charge       Sales Charge (4.5%)     PERIOD ENDED 4/30/97     Redemption      Redemption*
__________               ________________     ____________________     _____________________   ____________   __________________
<S>                            <C>                    <C>              <C>                         <C>               <C>
1 Year                         6.16%                  1.43%            1 Year                      5.55%             1.55%
From Inception (9/3/92)        6.75                   5.70             From Inception (1/15/93)    5.83              5.44
                        CLASS C SHARES
__________________________________________________________________
                                             % Return Reflecting
                                            Applicable Contingent
                              % Return         Deferred Sales
                              Assuming         Charge Upon
PERIOD ENDED 4/30/97      No Redemption        Redemption**
_________                _______________    ____________________
1 Year                         5.30%              4.30%
From Inception (8/15/95)       5.74               5.74

Past performance is not predictive of future performance.
The above graph compares a $10,000 investment made in Class A shares of
Dreyfus Premier State Municipal Bond Fund, Georgia Series on 9/3/92
(Inception Date) to a $10,000 investment made in the Lehman Brothers
Municipal Bond Index on that date. For comparative purposes, the value of the
Index on 8/31/92 is used as the beginning value on 9/3/92. All dividends and
capital gain distributions are reinvested. Performance for Class B and Class
C shares will vary from the performance of Class A shares shown above due to
differences in charges and expenses.
The Series invests primarily in Georgia municipal securities and its
performance shown in the line graph takes into account the maximum initial
sales charge on Class A shares and all other applicable fees and expenses.
Unlike the Series, the Lehman Brothers Municipal Bond Index is an unmanaged
total return performance benchmark for the long-term, investment-grade,
geographically unrestricted tax exempt bond market, calculated by using
municipal bonds selected to be representative of the municipal market
overall. The Index does not take into account charges, fees and other
expenses and is not limited to investments principally in Georgia municipal
obligations. These factors can contribute to the Index potentially
outperforming the Series. Further information relating to Series performance,
including expense reimbursements, if applicable, is contained in the
Financial Highlights section of the Prospectus and elsewhere in this report.
*  The maximum contingent deferred sales charge for Class B shares is 4% and
is reduced to 0% after six years.
**The maximum contingent deferred sales charge for Class C shares is 1% for
shares redeemed within one year of the date of purchase.
DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
STATEMENT OF INVESTMENTS                                  APRIL 30, 1997
                                                                                                      Principal
Long-Term Municipal Investments_86.2%                                                                   Amount          Value
                                                                                                        _______       _______
Albany, Sewer System Revenue 6.50%, 7/1/2009 (Insured; MBIA)
  (Prerefunded 7/1/2002 ) (a)...............................................                     $     100,000     $   109,090
Atlanta:
  Airport Facilities Revenue:
    5.25%, 1/1/2010 (Insured; AMBAC)........................................                         1,000,000        984,940
    6%, 1/1/2014 (Insured; AMBAC)...........................................                         1,000,000      1,016,100
  GO 6.10%, 12/1/2019.......................................................                         1,000,000      1,028,050
Barrow County School District 5.60%, 2/1/2015 (Insured; MBIA)...............                         1,000,000      1,001,750
Clayton County and Clayton County Water Authority, Water and Sewer Revenue, Refunding
  5.60%, 5/1/2013 (Insured; AMBAC)..........................................                         1,200,000      1,197,864
Columbia, Water and Sewer Revenue, Refunding 5.40%, 6/1/2011 (Insured; AMBAC)                          750,000        744,630
Colquitt County Hospital Authority, Refunding 5.50%, 3/1/2016...............                         1,000,000        973,060
Columbus Hospital Authority, Revenue Certificates (Saint Francis Hospital)
  6.20%, 1/1/2010 (Insured; MBIA)...........................................                           200,000        207,558
Dekalb County Development Authority, Revenue
  (Wesley Homes, Inc.-Budd Terrace Project)
  6.75%, 10/1/2013 (LOC; Wachovia Bank of Georgia, N.A.) (b)................                           200,000        208,986
Fayette County School District 6.125%, 3/1/2015.............................                           500,000        518,230
Fulton County, Water and Sewer Revenue, Refunding 6.375%, 1/1/2014 (Insured; FGIC)                     290,000        317,266
Fulton County Building Authority, Revenue, Refunding
  (County Government and Health Facilities Project) 6.125%, 1/1/2011........                           300,000        312,624
Fulton County Development Authority, Special Facilities Revenue, Refunding
  (Delta Air Lines Inc. Project) 6.95%, 11/1/2012...........................                           245,000        260,690
Gainesville, Water and Sewer Revenue, Refunding 6%, 11/15/2012 (Insured; FGIC)                         300,000        318,600
Georgia, GO:
  6.65%, 3/1/2009...........................................................                         1,000,000      1,132,090
  5.65%, 3/1/2012...........................................................                         1,000,000      1,024,700
Georgia Housing and Finance Authority, SFMR :
  7%, 12/1/2015 (Insured; FSA)..............................................                         1,500,000      1,574,580
  6.50%, 12/1/2017 (Insured; FSA)...........................................                         1,000,000      1,026,120
Georgia Municipal Gas Authority, Gas Revenue (Warner Robins Project)
  5.80%, 1/1/2015 (Insured; MBIA)...........................................                         1,000,000      1,008,060
Glynn-Brunswick Memorial Hospital Authority (Southeast Georgia Health)
  5.25%, 8/1/2013 (Insured; MBIA)...........................................                         2,000,000      1,918,560
Hancock County, Various Purpose Asset Guaranty 6.70%, 4/1/2015..............                         1,000,000      1,090,740
Marietta Development Authority, Revenue (First Mortgage-Life College)
  5.75%, 9/1/2014 (Insured; CGIC)...........................................                           850,000        850,255
Meriwether County School District 5.50%, 2/1/2016...........................                         1,000,000        978,740
Metropolitan Atlanta Rapid Transportation Authority, Sales Tax Revenue, Refunding
  6.25%, 7/1/2020 (Insured; AMBAC)..........................................                           300,000        324,495

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
STATEMENT OF INVESTMENTS (CONTINUED)                         APRIL 30, 1997
                                                                                                    Principal
Long-Term Municipal Investments (continued)                                                          Amount          Value
                                                                                                   __________      __________
Private Colleges and Universities Authority, Revenue, Refunding
  (Spellman College Project) 6.20%, 6/1/2014 (Insured; FGIC)................                      $  1,000,000   $  1,046,930
                                                                                                                _____________
TOTAL LONG-TERM MUNICIPAL INVESTMENTS (cost $20,548,098)....................                                      $21,174,708
                                                                                                                =============
Short-Term Municipal Investments_13.8%
U.S. Related;
Commonwealth of Puerto Rico, Development Bank, Refunding, VRDN
  4.30% (LOC; Credit Suisse) (b,c) (cost $3,400,000)........................                      $  3,400,000   $  3,400,000
                                                                                                                =============
TOTAL INVESTMENTS_100.0% (cost $23,948,098).................................                                      $24,574,708
                                                                                                                =============

Summary of Abbreviations
AMBAC         American Municipal Bond Assurance Corporation      LOC     Letter of Credit
CGIC          Capital Guaranty Insurance Company                 MBIA    Municipal Bond Investors Assurance
FGIC          Financial Guaranty Insurance Company                            Insurance Corporation
GO            General Obligation                                 SFMR    Single Family Mortgage Revenue
FSA           Financial Security Assurance                       VRDN    Variable Rate Demand Notes
Summary of Combined Ratings (Unaudited)
Fitch (d)              or          Moody's             or         Standard & Poor's          Percentage of Value
____                               ______                         _________________          ____________________
AAA                                Aaa                            AAA                               61.7%
AA                                 Aa                             AA                                23.4
BBB                                Baa                            BBB                                1.1
F-1,F-1+                           VMIG1,MIG1,P1                  SP1,A1                            13.8
                                                                                                   ________
                                                                                                   100.0%
                                                                                                  =========
Notes to Statement of Investments:
    (a)  Bonds which are prerefunded are collateralized by U.S. Government
    securities which are held in escrow and are used to pay principal and
    interest on the municipal issue and to retire the bonds in full at the
    earliest refunding date.
    (b)  Secured by letters of credit.
    (c)  Securities payable on demand. The interest rate, which is subject to
    change, is based upon bank prime rates or an index of market interest
    rates.
    (d)  Fitch currently provides creditworthiness information for a limited
    number of investments.
SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
STATEMENT OF ASSETS AND LIABILITIES                         APRIL 30, 1997
                                                                                               Cost                Value
                                                                                           _____________       _____________
ASSETS:                          Investments in securities_See Statement of Investments     $23,948,098          $24,574,708
                                 Cash.......................................                                         45,734
                                 Interest receivable........................                                         385,542
                                 Receivable for shares of Beneficial Interest subscribed                               3,313
                                 Prepaid expenses...........................                                           1,391
                                                                                                                _____________
                                                                                                                   25,010,688
                                                                                                                _____________
LIABILITIES:                     Due to The Dreyfus Corporation and affiliates                                        11,303
                                 Due to Distributor.........................                                          12,737
                                 Payable for shares of Beneficial Interest redeemed                                   51,989
                                 Accrued expenses...........................                                          21,090
                                                                                                                _____________
                                                                                                                      97,119
                                                                                                                _____________
NET ASSETS..................................................................                                     $24,913,569
                                                                                                              ==============
REPRESENTED BY:                  Paid-in capital............................                                     $24,951,417
                                 Accumulated net realized gain (loss) on investments                                (664,458)
                                 Accumulated net unrealized appreciation (depreciation)
                                 on investments_Note 4......................                                         626,610
                                                                                                               _____________
NET ASSETS..................................................................                                     $24,913,569
                                                                                                              ==============

                                                    NET ASSET VALUE PER SHARE
                                                _________________________________
                                                                      Class A                 Class B                Class C
                                                                  _______________         _______________      _______________

Net Assets............................................               $6,597,741             $18,211,184             $104,644
Shares Outstanding..........................................            499,155               1,377,147                7,916
NET ASSET VALUE PER SHARE...................................             $13.22                  $13.22               $13.22
                                                                         ======                 =======              =======




SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
STATEMENT OF OPERATIONS                                                 YEAR ENDED APRIL 30, 1997
INVESTMENT INCOME
INCOME                           Interest Income............................                                      $1,523,447
EXPENSES:                        Management fee_Note 3(a)...................                   $147,484
                                 Distribution fees_Note 3(b)................                     96,512
                                 Shareholder servicing costs_Note 3(c)......                     84,983
                                 Professional fees..........................                      7,574
                                 Prospectus and shareholders' reports.......                      5,210
                                 Custodian fees.............................                      3,409
                                 Registration fees..........................                      2,545
                                 Trustees' fees and expenses_Note 3(d)......                        367
                                 Loan commitment fees_Note 2................                        147
                                 Miscellaneous..............................                      9,567
                                                                                            ___________
                                     Total Expenses.........................                                         357,798
                                                                                                                 ____________
INVESTMENT INCOME_NET.......................................................                                       1,165,649
REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS_Note 4:
                                 Net realized gain (loss) on investments....                  $  69,477
                                 Net unrealized appreciation (depreciation)
                                     on investments.........................                    293,070
                                                                                            ___________
NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS......................                                         362,547
                                                                                                                 ____________
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                      $1,528,196
                                                                                                                 ============
SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
STATEMENT OF CHANGES IN NET ASSETS
                                                                                          Year Ended             Year Ended
                                                                                        April 30, 1997         April 30, 1996
                                                                                     ____________________     ________________
OPERATIONS:
    Investment income_net..................................................              $  1,165,649          $  1,353,288
    Net realized gain (loss) on investments................................                    69,477              (205,254)
    Net unrealized appreciation (depreciation) on investments..............                   293,070               774,119
                                                                                     ____________________     ________________
          Net Increase (Decrease) in Net Assets Resulting from Operations..                 1,528,196             1,922,153
                                                                                     ____________________     ________________
DIVIDENDS TO SHAREHOLDERS FROM:
    Investment income_net:
      Class A shares.......................................................                  (356,396)             (443,972)
      Class B shares.......................................................                  (805,477)             (908,818)
      Class C shares.......................................................                    (3,776)                 (498)
                                                                                     ____________________     ________________
          Total Dividends..................................................                (1,165,649)           (1,353,288)
                                                                                     ____________________     ________________
BENEFICIAL INTEREST TRANSACTIONS:
    Net proceeds from shares sold:
      Class A shares.......................................................                   212,279               326,483
      Class B shares.......................................................                   709,076             2,305,085
      Class C shares.......................................................                    12,238                88,634
    Dividends reinvested:
      Class A shares.......................................................                   260,106               316,447
      Class B shares.......................................................                   396,438               438,970
      Class C shares.......................................................                     3,525                   498
    Cost of shares redeemed:
      Class A shares.......................................................                (2,334,070)           (1,482,789)
      Class B shares.......................................................                (3,248,467)           (2,436,019)
                                                                                     ____________________     ________________
          Increase (Decrease) in Net Assets from Beneficial Interest Transactions          (3,988,875)             (442,691)
                                                                                     ____________________     ________________
            Total Increase (Decrease) in Net Assets........................                (3,626,328)              126,174
NET ASSETS:
    Beginning of Period....................................................                28,539,897            28,413,723
                                                                                     ____________________     ________________
    End of Period..........................................................               $24,913,569           $28,539,897
                                                                                     ===================     ================






SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
STATEMENT OF CHANGES IN NET ASSETS (CONTINUED)
                                                                                                     Shares
                                                                                      _________________________________________
                                                                                          Year Ended             Year Ended
                                                                                        April 30, 1997         April 30, 1996
                                                                                      __________________     __________________
CAPITAL SHARE TRANSACTIONS:
    Class A
    _____
    Shares sold..........................................................                      16,032                24,765
    Shares issued for dividends reinvested...............................                      19,634                23,848
    Shares redeemed......................................................                    (175,973)             (111,113)
                                                                                      __________________     __________________
                                 Net Increase (Decrease) in Shares Outstanding               (140,307)              (62,500)
                                                                                     ==================     ==================
    Class B
    _______
    Shares sold..........................................................                      53,684               173,357
    Shares issued for dividends reinvested...............................                      29,914                33,082
    Shares redeemed......................................................                    (246,421)             (183,789)
                                                                                      __________________     __________________
                                 Net Increase (Decrease) in Shares Outstanding               (162,823)               22,650
                                                                                     ==================     ==================
    Class C*
    _______
    Shares sold..........................................................                         927                 6,685
    Shares issued for dividends reinvested...............................                         266                    38
                                                                                      __________________     __________________
                                 Net Increase (Decrease) in Shares Outstanding                  1,193                 6,723
                                                                                     ==================     ==================
__________________________
    *From August 15, 1995 (commencement of initial offering) to April 30,
    1996.



SEE NOTES TO FINANCIAL STATEMENTS.

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

                                                                                    Class A Shares
                                                               _______________________________________________________
                                                                                 Year Ended April 30,
                                                               _______________________________________________________
PER SHARE DATA:                                                  1997        1996        1995        1994        1993(1)
                                                               _______     _______     _______     _______     _______
    Net asset value, beginning of period.........              $13.05      $12.80      $12.69      $13.27       $12.50
                                                               _______     _______     _______     _______     _______
    Investment Operations:
    Investment income_net........................                 .62         .66         .73         .73          .51
    Net realized and unrealized gain (loss)
      on investments.............................                 .17         .25         .11         (.58)        .77
                                                               _______     _______     _______     _______     _______
    Total from Investment Operations.............                 .79         .91         .84         .15         1.28
                                                               _______     _______     _______     _______     _______
    Distributions:
    Dividends from investment income_net.........                (.62)       (.66)       (.73)       (.73)        (.51)
                                                               _______     _______     _______     _______     _______
    Net asset value, end of period...............              $13.22      $13.05      $12.80      $12.69      $13.27
                                                              ========     =======     =======    ========    ========
TOTAL INVESTMENT RETURN(2).......................               6.16%       7.14%       6.87%        .97%       15.91%(3)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets......                .98%        .74%        .25%        .07%          __
    Ratio of net investment income
      to average net assets......................               4.71%       5.00%       5.80%       5.41%      5.55%(3)
    Decrease reflected in above expense ratios
      due to undertakings by the Manager.........                 __         .21%        .78%       1.02%        1.46%(3)
    Portfolio Turnover Rate......................              50.96%      33.09%      34.04%       6.76%       37.79%(4)
    Net Assets, end of period (000's Omitted)....              $6,598      $8,346      $8,985     $10,058       $7,304
____________________________
    (1)  From September 3, 1992 (commencement of operations) to April 30, 1993.
    (2)  Exclusive of sales load.
    (3)  Annualized.
    (4)  Not annualized.







SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
FINANCIAL HIGHLIGHTS (CONTINUED)
    Contained below is per share operating performance data for a share of
Beneficial Interest outstanding, total investment return, ratios to average
net assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.

                                                                                    Class B Shares
                                                               _______________________________________________________
                                                                                 Year Ended April 30,
                                                               _______________________________________________________
PER SHARE DATA:                                                  1997        1996        1995        1994        1993(1)
                                                               _______     _______     _______     _______     _______
    Net asset value, beginning of period.........              $13.06      $12.80      $12.69      $13.27       $12.71
                                                               _______     _______     _______     _______     _______
    Investment Operations:
    Investment income_net........................                 .56         .59         .66         .67          .20
    Net realized and unrealized gain (loss)
      on investments.............................                 .16         .26         .11        (.58)         .56
                                                               _______     _______     _______     _______     _______
    Total from Investment Operations.............                 .72         .85         .77         .09          .76
                                                               _______     _______     _______     _______     _______
    Distributions:
    Dividends from investment income_net.........                (.56)       (.59)       (.66)       (.67)        (.20)
                                                               _______     _______     _______     _______     _______
    Net asset value, end of period...............              $13.22      $13.06      $12.80      $12.69      $13.27
                                                              ========     =======     =======    ========    ========
TOTAL INVESTMENT RETURN(2).......................               5.55%       6.69%       6.33%        .46%        20.66%(3)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets......               1.47%       1.24%        .75%        .58%      .50%(3)
    Ratio of net investment income
      to average net assets......................               4.20%       4.46%       5.27%       4.85%      4.60%(3)
    Decrease reflected in above expense ratios
      due to undertakings by the Manager.........                 __         .20%        .80%       1.02%      1.37%(3)
    Portfolio Turnover Rate......................              50.96%      33.09%      34.04%       6.76%    37.79%(4)
    Net Assets, end of period (000's Omitted)....             $18,211     $20,106     $19,429     $16,243        $6,319
______________________
    (1)  From January 15, 1993 (commencement of operations) to April 30, 1993.
    (2)  Exclusive of sales load.
    (3)  Annualized.
    (4)  Not annualized.







SEE NOTES TO FINANCIAL STATEMENTS.

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
FINANCIAL HIGHLIGHTS (CONTINUED)
    Contained below is per share operating performance data for a share of
Beneficial Interest outstanding, total investment return, ratios to average
net assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.

                                                                                                   CLASS C SHARES
                                                                                           ______________________________
                                                                                                YEAR ENDED APRIL 30,
                                                                                           ______________________________
PER SHARE DATA:                                                                              1997                1996(1)
                                                                                           ________             ________
    Net asset value, beginning of period....................................               $13.05                $12.85
                                                                                           ________             ________
    Investment Operations:
    Investment income_net...................................................                  .51                   .38
    Net realized and unrealized gain (loss)
      on investments........................................................                  .17                   .20
                                                                                           ________             ________
    Total from Investment Operations........................................                  .68                   .58
                                                                                           ________             ________
    Distributions:
    Dividends from investment income_net....................................                 (.51)                 (.38)
                                                                                           ________             ________
    Net asset value, end of period..........................................               $13.22                $13.05
                                                                                          ========            ===========
TOTAL INVESTMENT RETURN(2)..................................................                5.30%                 6.28%(3)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets.................................                1.80%                 1.98%(3)
    Ratio of net investment income
      to average net assets.................................................                3.87%                 3.73%(3)
    Portfolio Turnover Rate.................................................               50.96%                33.09%
    Net Assets, end of period (000's Omitted)..............................                  $105                   $88
________________________
    (1)  From August 15, 1995 (commencement of initial offering) to April 30, 1996.
    (2)  Exclusive of sales load.
    (3)  Annualized.
SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
NOTES TO FINANCIAL STATEMENTS
NOTE 1_SIGNIFICANT ACCOUNTING POLICIES:
    Dreyfus Premier State Municipal Bond Fund (the "Trust") is registered
under the Investment Company Act of 1940 ("Act") as a non-diversified
open-end management investment company, and operates as a series company
currently offering thirteen series including the Georgia Series (the "Fund").
The Fund's investment objective is to maximize current income exempt from
Federal and, where applicable, from State income taxes, without undue risk.
The Dreyfus Corporation (the "Manager") serves as the Fund's investment
adviser. The Manager is a direct subsidiary of Mellon Bank, N.A.
    On January 8, 1997, the Trust's Trustees approved a change to the Trust's
name from "Premier State Municipal Bond Fund" to "Dreyfus Premier State
Municipal Bond Fund" which change became effective March 31, 1997.
    Premier Mutual Fund Services, Inc. (the "Distributor") is the distributor
of the Fund's shares. The Fund is authorized to issue an unlimited number of
$.001 par value shares in the following classes of shares: Class A, Class B
and Class C shares. Class A shares are subject to a sales charge imposed at
the time of purchase, Class B shares are subject to a contingent deferred
sales charge ("CDSC") imposed on Class B share redemptions made within six
years of purchase (five years for shareholders beneficially owning Class B
shares on November 30, 1996) and Class C shares are subject to a CDSC imposed
on Class C shares redeemed within one year of purchase. Other differences
between the classes include the services offered to and the expenses borne by
each class and certain voting rights.
    The Trust 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.
    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 options and
financial futures on municipal and U.S. treasury securities) 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
municipal securities of comparable quality, coupon, maturity and type;
indications as to values from dealers; and general market conditions. Options
and financial futures on municipal and U.S. treasury securities 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. Investments not listed on an exchange or the national
securities market, or securities for which there were no transactions, are
valued at the average of the most recent bid and asked prices. Bid price is
used when no asked price is available.
    (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, adjusted for amortization of premiums and original issue discounts on
investments, is earned from settlement date and recognized on the accrual
basis. Securities purchased or sold on a when-issued or delayed-delivery
basis may be settled a month or more after the trade date.

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
    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 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. 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 Internal
Revenue Code, and to make distributions of income and net realized capital
gain sufficient to relieve it from substantially all Federal income and
excise taxes.
    The Fund has an unused capital loss carryover of approximately $665,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to April 30, 1997. If not
applied, $15,000 of the carryover expires in fiscal 2002, $367,000 expires in
fiscal 2003, $267,000 expires in fiscal 2004 and $16,000 expires in fiscal
2005.
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. For the period ended April
30, 1997, 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 .55 of 1% of the value of the Fund's
average daily net assets and is payable monthly.
    Dreyfus Service Corporation, a wholly-owned subsidiary of the Manager,
retained $208 during the period ended April 30, 1997, from commissions earned
on sales of the Fund's shares.
    (B) Under the Distribution Plan adopted pursuant to Rule 12b-1 under the
Act, the Fund pays the Distributor for distributing the Fund's Class B and
Class C shares at an annual rate of .50 of 1% of the value of the average
daily net assets of Class B shares and .75 of 1% of the value of the average
daily net assets of Class C shares. During the period ended April 30, 1997,
$95,780 was charged to the Fund for the Class B shares and $732 was charged
to the Fund for the Class C shares.
    (C) Under the Shareholder Services Plan, the Fund pays the Distributor at
an annual rate of .25 of 1% of the value of the average daily net assets of
Class A, Class B and Class C shares for the provision of certain services.
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. The Distributor may make payments to
Service Agents (a securities dealer, financial institution or other industry
professional) in respect of these services. The Distributor determines the
amounts to be paid to Service Agents. During the
DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
period ended April 30, 1997, $18,904, $47,890 and $244 were charged to Class
A, Class B and Class C shares, respectively, by the Distributor 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. Such
compensation amounted to $12,217 during the period ended April 30, 1997.
    (D) Each trustee who is not an "affiliated person" as defined in the Act
receives from the Trust 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.
NOTE 4_SECURITIES TRANSACTIONS:
    The aggregate amount of purchases and sales of investment securities,
excluding short-term securities, during the period ended April 30, 1997
amounted to $13,295,255 and $20,504,290, respectively.
    At April 30, 1997, accumulated net unrealized appreciation on investments
was $626,610, consisting of $649,761 gross unrealized appreciation and
$23,151 gross unrealized depreciation.
    At April 30, 1997, 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).

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
SHAREHOLDERS AND BOARD OF TRUSTEES
DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
    We have audited the accompanying statement of assets and liabilities,
including the statement of investments, of Dreyfus Premier State Municipal
Bond Fund, Georgia Series (one of the Funds constituting the Dreyfus Premier
State Municipal Bond Fund) as of April 30, 1997, 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 April 30, 1997 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 Premier State Municipal Bond Fund, Georgia Series at
April 30, 1997, 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.

                              [Ernst & Young LLP signature logo]
New York, New York
June 5, 1997

DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA SERIES
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 April
30, 1997 as "exempt-interest dividends" (not generally subject to regular
Federal and, for individuals who are Georgia residents, Georgia personal
income taxes).
    As required by Federal tax law rules, shareholders will receive
notification of their portion of the Fund's taxable ordinary dividends (if
any) and capital gain distributions (if any) paid for the 1997 calendar year
on Form 1099-DIV which will be mailed by January 31, 1998.
Dreyfus Premier State Municipal
Bond Fund, Georgia Series
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.                        068/627AR974
Annual Report
Dreyfus Premier State
Municipal Bond Fund
Georgia Series
April 30, 1997
[lion2hres logo]
Registration Mark


COMPARISON OF CHANGE IN VALUE OF $10,000 INVESTMENT
IN DREYFUS PREMIER STATE MUNICIPAL BOND FUND, GEORGIA
SERIES CLASS A SHARES AND THE LEHMAN BROTHERS MUNICIPAL
BOND INDEX

EXHIBIT A:

                                            DREYFUS
                                            PREMIER STATE
 PERIOD         LEHMAN BROTHERS             MUNICIPAL BOND FUND,
                MUNICIPAL                   GEORGIA SERIES
                BOND INDEX *                (CLASS A SHARES)

 9/3/92          10,000                       9,549
4/30/93          10,736                      10,548
4/30/94          10,968                      10,650
4/30/95          11,698                      11,382
4/30/96          12,627                      12,195
4/30/97          13,465                      12,946

*Source: Lehman Brothers



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