SELIGMAN SELECT MUNICIPAL FUND INC
N-30B-2, 1997-12-15
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                                    SELIGMAN
================================================================================
                                     SELECT
================================================================================
                                    MUNICIPAL
                                   FUND, INC.

                                     [LOGO]

                              Third Quarter Report
                               September 30, 1997





                      Seligman Select Municipal Fund, Inc.
                                   Managed by

                                     [LOGO]

                             J. & W. SELIGMAN & CO.
                                  INCORPORATED
                        Investment Managers and Advisors
                                ESTABLISHED 1864
                       100 Park Avenue, New York, NY 10017


                     Photo: Courtesy Michigan Travel Bureau

                                                                   CESEL3c 9/97

<PAGE>

================================================================================
TO THE STOCKHOLDERS

Seligman Select Municipal Fund posted strong results in the third quarter of
1997. The steady growth of the economy, combined with benign levels of
inflation, led to a continuation of the second-quarter municipal bond market
rally. Yields fell and bond prices rose, improving your Fund's total return
while it provided consistent monthly income free from regular income tax. The
Fund's investment results appear on page 5.

     As economic growth continued without prompting a noticeable increase in
inflation, the municipal bond market rallied through July. Thereafter, yields
traded within a narrow range through the end of September. The yield on the Bond
Buyer 20-Bond General Obligation Index, a benchmark for the municipal market,
ended the quarter at 5.36% on September 30, down from 5.53% at June 30.

     There were few signs of accelerating inflation despite increased consumer
spending and high employment levels. As a result, market participants remained
fairly confident that the Federal Reserve Board would not need to increase
short-term interest rates in the near term to slow the economy and reduce the
risk of inflation.

     The next few months could be more challenging, given the recent volatility
in the global equity markets and the business slowdown in Southeast Asia.
Nevertheless, US economic reports remain positive overall. There are still a few
areas where potential inflationary problems persist, particularly in the labor
market. A significant increase in labor costs could prompt the Fed to become
more restrictive and move interest rates up another notch, though this is a
fading risk given recent international events. Nonetheless, the future prospects
of both the municipal bond market and your Fund remain positive, as supply and
demand levels in the municipal market should remain favorable regardless of the
short-term impact of any Fed move.

     We thank you for your continued interest in Seligman Select Municipal Fund,
and look forward to serving your investment needs in the many years to come.

     A discussion with your Portfolio Manager, and the Fund's portfolio of
investments, follow this letter.

By order of the Board of Directors,



/s/ William Morris
- ------------------
William C. Morris
Chairman

                                                        /s/ Thomas G. Moles
                                                        --------------------
                                                        Thomas G. Moles
                                                        President


October 31, 1997


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INTERVIEW WITH YOUR PORTFOLIO MANAGER, THOMAS G. MOLES

- ---------------------   Seligman Municipals Team: (from left) Audrey Kuchtyak,
     [PHOTO]            Theresa Barion, Debra McGuinness, (seated) Eileen
- ---------------------   Comerford, Thomas G. Moles (Portfolio Manager)


WHAT ECONOMIC AND MARKET FACTORS AFFECTED SELIGMAN SELECT MUNICIPAL FUND IN THE
LAST THREE MONTHS?

    Long-term municipal yields continued their downward trend in the third
quarter, prompted by signs of stable economic growth and low inflation. By the
end of July, municipal yields had fallen to the lowest levels of the year to
date. However, they reversed direction in response to a pickup in economic
activity. After rising modestly in early August, yields stabilized and remained
essentially unchanged through mid-September. At that point, the municipal market
began to rally again. As a result, prices rose and long-term yields ended the
quarter slightly below their June 30 levels. Overall, Seligman Select Municipal
Fund benefited from the generally stable interest rate environment, posting
solid returns for the quarter.


WHAT WAS YOUR INVESTMENT STRATEGY?

    Our investment strategy has remained essentially unchanged throughout the
year. Consistent with our positive long-term interest rate outlook, we continue
to focus on the longer end of the municipal yield curve, purchasing bonds with
maturities of 25 years and beyond. Generally, for a parallel decline in yields,
long-term bonds appreciate more in price than shorter-term bonds. Long-term
bonds also offer significantly higher yields than shorter-term bonds, allowing
us to maximize the Fund's yield.

    As has been the case for most of the year, long-term municipal yields
fluctuated within a narrow range in the third quarter, limiting opportunities
for capital gains. In this type of environment, we have focused on improving
coupon returns by concentrating investments in higher-yielding sectors such as
airport and pollution control bonds. Further, to extend the duration of Seligman
Select Municipal Fund's attractive income distributions, we have been working to
improve call protection. Therefore, we have been selling shorter-call bonds and
replacing them with longer-call bonds. (Callable bonds are bonds that are
redeemable on specified dates and at specified prices -- prior to maturity -- at
the option of the issuer.)


WHAT IS THE OUTLOOK?

    Although fixed-income market participants are likely to remain cautious,
economic fundamentals seem to indicate continued steady, moderate growth with
low inflation. Stable long-term interest rates, improving credit trends, and
attractive real rates of return bode well for the continued performance of the
municipal bond market and the Fund. We will pursue our long-term investment
strategy, building a diversified portfolio of quality bonds while working to
provide our Stockholders with competitive investment results.



                                       2

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PORTFOLIO OF INVESTMENTS (unaudited)    
                                                                     
- ------------------------------------------------------------------------------------------------------------------------------------
                           Face                                                                Ratings
State                     Amount                    Municipal Bonds                          Moody's/S&P              Market Value
- ------------------------------------------------------------------------------------------------------------------------------------
<S>                    <C>            <C>                                                      <C>                   <C>
Alaska--7.6%           $ 9,860,000    Alaska Housing Finance Corp. (Collateralized
                                        Home Mortgage Rev.), 7.65% due 6/1/2024 .............  Aaa/AAA               $ 10,451,403
                         7,500,000    Valdez Marine Terminal Rev. (BP Pipelines Inc.
                                        Project), 5.65% due 12/1/2028 .......................  Aa2/AA                   7,488,375
California--11.2%        9,130,000    California Pollution Control Financing Authority
                                        Sewage and Solid Waste Disposal Facilities
                                        Rev. (Anheuser-Busch Project), 5 3/4% due
                                        12/1/2030* ..........................................  A1/A+                    9,244,855
                        10,000,000    San Francisco City and County Airports Commission
                                        (San Francisco International Airport Rev.), 6.30%
                                        due 5/1/2025* .......................................  Aaa/AAA                 10,559,900
                         6,000,000    San Joaquin Hills Transportation Corridor Agency
                                        Senior Lien Toll Road Rev. (Orange County),
                                        6 3/4% due 1/1/2032 .................................  NR/NR                    6,801,300
Delaware--3.0%           6,500,000    Delaware Economic Development Authority
                                        Exempt Facilities Rev. (Delmarva Power and
                                        Light Co. Project), 7.60% due 3/1/2020* .............  Aaa/AAA                  7,055,750
District of  
  Columbia--3.4%         7,500,000    District of Columbia GOs, 7 1/2% due 6/1/2009 .........  Aaa/AAA                  8,059,650
Florida--5.7%            5,700,000    Brevard County Utility Rev., 7 3/8% due 3/1/2014 ......  Aaa/AAA                  5,898,474
                           775,000    Brevard County Utility Rev., 7 3/8% due 3/1/2014 ......  Aaa/AAA                    801,272
                         2,320,000    Florida Housing Finance Agency (Home Ownership
                                        Rev.), 7.90% due 3/1/2022* ..........................  Aaa/NR                   2,462,495
                         4,085,000    Orange County Housing Finance Authority
                                        (Mortgage Rev.), 7.80% due 10/1/2022* ...............  Aaa/NR                   4,303,670
Illinois--2.3%           5,000,000    Chicago O'Hare International Airport International
                                        Terminal Special Rev., 7 5/8% due 1/1/2010* .........  Aaa/AAA                  5,408,800
Indiana--2.3%            5,000,000    Indiana Employment Development Commission
                                        Environmental Rev. (Public Service Company of
                                        Indiana Inc.), 7 1/2% due 3/15/2015* ................  Aaa/AAA                  5,421,000
Louisiana--4.9%          9,675,000    Louisiana Public Facilities Authority Hospital Rev.
                                        (Southern Baptist Hospitals, Inc. Project), 8%
                                        due 5/15/2012 .......................................  NR/AAA                  11,735,098
Massachusetts--4.7%      5,370,000    Massachusetts Housing Finance Agency (Multi-
                                        Family Residential Development Rev.), 7.65%
                                        due 2/1/2028* .......................................  Aaa/AAA                  5,607,086
                         5,500,000    Massachusetts Bay Transportation Authority General
                                        Transportation System Rev., 5 5/8% due 3/1/2026 .....  Aaa/AAA                  5,584,205
Nebraska--1.2%           2,700,000    Nebraska Investment Finance Authority (Single
                                        Family Mortgage Rev.), 8 1/8% due 8/15/2038* ........  Aaa/AAA                  2,798,253
Nevada--3.2%             7,000,000    Clark County Industrial Development Rev. (Nevada
                                        Power Company Project), 7.80% due 6/1/2020* .........  Aaa/AAA                  7,676,690
New Hampshire--3.2%      6,950,000    New Hampshire State Industrial Development
                                        Authority Pollution Control Rev. (The
                                        Connecticut Light and Power Company
                                        Project), 7 3/8% due 12/1/2019* .....................  Aaa/AAA                  7,484,177
New Jersey--2.0%         2,000,000    New Jersey Educational Facilities Authority Rev.
                                        (Princeton University), 6% due 7/1/2024 .............  Aaa/AAA                  2,095,740
                         2,510,000    New Jersey Housing & Mortgage Finance Agency
                                        (Home Buyer Rev.), 7.70% due 10/1/2029* .............  Aaa/AAA                  2,631,082

                                       
</TABLE>

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<TABLE>
<CAPTION>
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                                                                                                                  SEPTEMBER 30, 1997
                                                                     
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                           Face                                                                Ratings
State                     Amount                    Municipal Bonds                          Moody's/S&P              Market Value
- ------------------------------------------------------------------------------------------------------------------------------------
<S>                    <C>            <C>                                                      <C>                   <C>
New York--8.9%         $10,000,000    New York State Energy Research & Development
                                        Authority Electric Facilities Rev. (Consolidated
                                        Edison Co. NY Inc. Project), 6.10% due 8/15/2020 ....  Aaa/AAA               $ 10,617,800
                        10,000,000    New York State Thruway Authority General Rev.,
                                        6% due 1/1/2025 .....................................  Aaa/AAA                 10,513,300
New York and             6,500,000    Port Authority of New York and New Jersey
  New Jersey--2.8%                      (JFK International Air Terminal LLC Project Rev.),
                                        5-3/4% due 12/1/2022* ...............................  Aaa/AAA                  6,671,275
Ohio--4.9%               6,000,000    Cleveland Waterworks Improvement First Mortgage
                                        Rev., 5-3/4% due 1/1/2021 ...........................  Aaa/AAA                  6,220,500
                         5,205,000    Ohio Housing Finance Agency (Single Family
                                        Mortgage Rev.), 7.65% due 3/1/2029* .................  NR/AAA                   5,465,614
Pennsylvania--6.9%       2,500,000    Allegheny County Airport Rev. (Greater Pittsburgh
                                        International Airport), 6.80% due 1/1/2010* .........  Aaa/AAA                  2,726,850
                         3,000,000    Lehigh County Industrial Development Authority
                                        Pollution Control Rev. (Pennsylvania Power &
                                        Light Company Project), 6.15% due 8/1/2029 ..........  Aaa/AAA                  3,193,260
                        10,000,000    Philadelphia Airport Rev., 6.10% due 6/15/2025* .......  Aaa/AAA                 10,445,700
Tennessee--3.7%          8,000,000    Humphreys County Industrial Development Board
                                        Solid Waste Disposal Rev. (E.I. du Pont de
                                        Nemours & Co. Project), 6.70% due 5/1/2024* .........  Aa3/AA-                  8,784,080
Texas--5.6%              5,000,000    Lower Neches Valley Authority Industrial
                                        Development Corp. Sewer Facilities Rev. (Mobil
                                        Oil Refining Corp. Project), 6.40% due 3/1/2030* ....  Aa2/AA                   5,334,700
                         7,500,000    Matagorda County Navigation District No. 1
                                        Pollution Control Rev. (Central Power and Light
                                        Co. Project), 6-1/8% due 5/1/2030* ..................  Aaa/AAA                  7,871,925
Washington--9.3%         4,795,000    Chelan County Public Utility District No. 001
                                        (Chelan Hydro Consolidated System Rev.), 6-1/4%
                                        due 7/1/2017* .......................................  Aaa/AAA                  5,171,791
                         5,000,000    Chelan County Public Utility District No. 001
                                        (Chelan Hydro Consolidated System Rev.), 6.35%
                                        due 7/1/2028* .......................................  Aaa/AAA                  5,417,900
                        10,000,000    King County Sewer GOs, 6-1/8% due 1/1/2033 ............  Aaa/AAA                 10,520,900
                         1,000,000    Spokane Regional Solid Waste Management System
                                        Rev., 7-3/4% due 1/1/2011* ..........................  Aaa/AAA                  1,057,970
                                                                                                                     ------------
Total Municipal Bonds (Cost $216,032,618)-- 96.8%.................................................................    229,582,840
Short-Term Holdings (Cost $3,500,000)-- 1.5%......................................................................      3,500,000
Other Assets Less Liabilities-- 1.7%..............................................................................      4,000,731
                                                                                                                     ------------
NET INVESTMENT ASSETS -- 100.0% ..................................................................................   $237,083,571
                                                                                                                     ============
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- ------------------
* Interest income earned from this security is subject to the federal
  alternative minimum tax.

Note: Investments in municipal securities and other short-term holdings maturing
in more than 60 days are valued based upon quotations provided by an independent
pricing service or, in their absence, at fair value determined in accordance
with procedures approved by the Board of Directors. Short-term holdings maturing
in 60 days or less are generally valued at amortized cost.

                                       4

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INVESTMENT RESULTS PER COMMON SHARE

- --------------------------------------------------------------------------------
TOTAL RETURNS*
For Periods Ended September 30, 1997

                                        Average Annual
                       -------------------------------------------------
                                                                 Since
                       Three       Nine       One      Five    Inception
                       Months     Months      Year     Years    2/15/90
                       ------     ------      ----     -----    -------

     Market Price       6.08%     13.69%     17.21%    9.43%     9.23%

     Net Asset Value    3.60       6.57       9.04     7.58      8.95


PRICE PER SHARE
                        September 30,     June 30,     March 31,    December 31,
                            1997            1997         1997          1996
                        -------------     --------     ---------    ------------

     Market Price          $13.50         $12.9375      $12.625       $12.50

     Net Asset Value        12.31          12.08         11.85         12.16



DIVIDEND AND CAPITAL GAIN INFORMATION
For the Nine Months Ended September 30, 1997

                                                        Capital Gain
                                                  --------------------------
             Dividends Paid**                     Realized        Unrealized
             --------------                       --------        ----------
                 $0.63                             $0.155           $1.029+


ANNUAL DISTRIBUTION RATE

The annual distribution rate based on current market price at September 30,
1997, is 6.22%, which is equivalent to a taxable yield of 10.30% based on the
maximum federal tax rate of 39.6%.


     ---------------------------------------------------------------------

    *These rates of return reflect changes in the market price or net asset
     value, as applicable, and assume that all distributions within the period
     are invested in additional shares. The rates of return will vary and the
     principal value of an investment will fluctuate. Shares, if sold, may be
     worth more or less than their original cost. Past performance is not
     indicative of future investment results.

   **Preferred Stockholders were paid dividends at annual rates ranging from
     3.40% to 3.83%. Earnings on the Fund's assets in excess of the Preferred
     dividend requirements constituted dividend income for Common Stockholders.

    +Represents  the per share amount of  unrealized  appreciation  of portfolio
     securities as of September 30, 1997.

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