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

The three months ended September 30, 1999, were a difficult period for
fixed-income securities, in general, and for municipal bonds, in particular.

   During calendar year 1999, taxable interest rates rose steadily, causing
taxable bond prices to fall. Municipal bonds, however, remained relatively
stable, due primarily to a lack of new-issue supply during the first six months
of the year. During the past fiscal quarter, however, municipal bonds then began
to react to the broader environment -- of robust growth, a tighter Federal
Reserve Board policy, and inflation worries -- which was generally unfavorable
to fixed-income securities. By the end of the quarter, municipal bond yields had
risen to their highest levels of the year.

   Looking ahead, we believe that the US economy will slow, as was intended by
the Fed's recent restrictive actions, and that inflation fears will thus subside
and reduce bond market volatility. We anticipate that the municipal market will
outperform the Treasury market for the balance of the Fund's fiscal year, as a
result of the positive and continually improving municipal market fundamentals,
the most significant of which is the expected slowdown in municipal issuance
which should continue into the new year.

   J. & W. Seligman & Co. Incorporated, your Fund's manager, and Seligman Data
Corp., your Corporation's stockholder service agent, have completed preparations
for potential computer problems related to the Year 2000 (Y2K). As of June 30,
1999, all internal mission-critical systems, software, and interfaces had been
tested for Y2K compliance with successful results. This is an issue to which we
have devoted considerable time and resources for the past several years. We
believe that the Corporation's stockholders will not be inconvenienced or
experience disruptions as a result of Y2K-related issues at Seligman.

   Thank you for your continued support of Seligman Select Municipal Fund. We
look forward to serving your investment needs for many years to come. A
discussion with your Portfolio Manager, as well as the Fund's portfolio of
investments and performance history, follows this letter.

By order of the Board of Directors,



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



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

November 5, 1999

                                                                               1

<PAGE>

================================================================================
INTERVIEW WITH YOUR PORTFOLIO MANAGER, THOMAS G. MOLES

[PHOTO OMITTED]

SELIGMAN MUNICIPALS TEAM: (STANDING FROM LEFT) AUDREY KUCHTYAK, THERESA BARION,
DEBRA MCGUINNESS, (SEATED) EILEEN COMERFORD, THOMAS G. MOLES (PORTFOLIO MANAGER)

WHAT ECONOMIC AND MARKET FACTORS INFLUENCED SELIGMAN SELECT MUNICIPAL FUND OVER
THE PAST THREE MONTHS?

   For most of calendar year 1999, the bond markets were pulled down by tighter
monetary policy, uncertainty regarding the future direction of interest rates,
and inflation fears. Up until this past fiscal quarter, however, municipal bonds
remained relatively stable and outperformed US Treasury bonds due to a lack of
new municipal issues on the market.

   During the past three months, however, this trend began to reverse as mutual
fund redemptions intensified, causing institutional demand for municipal bonds
to decline. By the end of the quarter, long-term municipal bond yields had moved
to their highest levels of the year. In contrast, the yield on the 30-year
Treasury bond spiked sharply in mid-August, but abruptly retreated to end the
quarter almost unchanged from the start of the quarter. The rising interest rate
environment in the municipal bond market caused Seligman Select Municipal Fund's
net asset value to decline during the period.

WHAT WAS YOUR INVESTMENT STRATEGY?

   Over the past three months, long-term municipal yields rose to levels not
seen in several years. This pre-sented an opportunity to intensify our ongoing
effort to maintain Seligman Select Municipal Fund's monthly dividend level. Over
the past few years of generally falling rates, municipal bond funds, including
Seligman Select Municipal Fund, have had their investment income negatively
impacted by the loss of older, higher-coupon bonds through bond calls and
redemptions. In an effort to offset the effects of these calls and redemptions,
we took advantage of higher current interest rates by purchasing
higher-yielding, longer-term bonds.

   As a result of this strategy, however, Seligman Select Municipal Fund's net
asset value declined more than it would have had we purchased shorter-term,
lower-yielding bonds. In general, the longer the maturity of a bond, the more
sensitive it is to changes in interest rates. During periods of declining
interest rates, longer-term bonds outperform shorter-term bonds. However, during
periods of rising interest rates, such as we have been experiencing recently,
longer-term bonds decline more in price than shorter-term bonds.

WHAT IS YOUR OUTLOOK?

   The long-awaited economic slowdown has yet to materialize, increasing the
risk that the rate of inflation will accelerate. In response, bond yields have
been rising steadily year to date. For the remainder of calendar year 1999, the
bond markets will likely experience continued volatility until solid signs that
the economy is moderating emerge. Many market participants expect the Fed to
raise rates once more before year-end. This, together with higher market rates,
may ease inflationary pressures and spark a bond-market rally.

   As we head toward the new millennium, we believe that there is much to be
optimistic about. In the year 2000, the US economy will likely enter its tenth
year of expansion, an extraordinary achievement. The financial well being of the
nation's states, cities, and municipalities continues to improve, with many
reporting record budget surpluses. The jobless rate remains below 5% nationally,
and consumer confidence remains high. Finally, as one of the few remaining
possible ways to shelter income, municipal bond funds currently offer attractive
yields compared to the after-tax yields of many taxable bond investments.

2

<PAGE>

================================================================================
INVESTMENT RESULTS PER COMMON SHARE

--------------------------------------------------------------------------------
TOTAL RETURNS*
FOR PERIODS ENDED SEPTEMBER 30, 1999

                                                           Average Annual
                                                    ----------------------------
                                                                          Since
                                Three     Nine       One      Five     Inception
                               Months    Months     Year      Years     2/15/90
                               ------    ------     ----      -----     -------
        Market Price**         (8.91)%  (18.87)%   (15.67)%    4.14%     5.26%
        Net Asset Value**      (2.31)%   (4.58)%    (4.31)%    6.18%     7.61%


PRICE PER SHARE
                           September 30,  June 30,    March 31,  December 31,
                               1999         1999        1999         1998
                            -----------  ----------- ----------- -----------
        Market Price          $ 9.75       $10.875     $12.00      $12.5625
        Net Asset Value        11.22        11.67       12.20       12.29

DIVIDEND AND CAPITAL GAIN INFORMATION
FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1999

                                                    Capital Gain
                                                --------------------
                              Dividends Paid+   Realized  Unrealized
                              ---------------   --------  ----------
                                 $0.486         $0.055      $0.126++

ANNUAL DISTRIBUTION RATE

The annual distribution rate based on current market price at September 30,
1999, was 6.65%, which is equivalent to a taxable yield of 11.00% based on the
maximum federal tax rate of 39.6%.
       ------------------------------------------------------------------

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.

  * Returns for periods of less than one year are not annualized.

 ** 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.

  + Preferred Stockholders were paid dividends at annual rates ranging from
    2.995% to 3.75%. 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, 1999.
--------------------------------------------------------------------------------

                                                                               3
<PAGE>

PORTFOLIO OF INVESTMENTS (unaudited)
<TABLE>
<CAPTION>
---------------------------------------------------------------------------------------------------------------
                         FACE                                                         RATINGS
STATE                   AMOUNT              MUNICIPAL BONDS                          MOODY'S/S&P   MARKET VALUE
---------------------------------------------------------------------------------------------------------------
<S>                  <C>          <C>                                                   <C>        <C>
ALABAMA--5.9%        $10,000,000  Jefferson County Sewer Rev.
                                    (Capital Improvement Warrants),
                                    5.125% due 2/1/2039 ..............................  Aaa/AAA    $ 8,684,700

                       5,000,000  McIntosh Industrial Development Board,
                                    Environmental Facilities Rev. (CIBASpecialty
                                    Chemicals), 5.375% due 6/1/2028 ..................  A2/AA-       4,580,750

ALASKA--2.4%           5,215,000  Alaska Housing Finance Corp. (Collateralized
                                   Home Mortgage Rev.), 7.65% due 6/1/2024 ...........  Aaa/AAA      5,442,948

CALIFORNIA--17.2%      9,130,000  California Pollution Control Financing Authority
                                    Sewage and Solid Waste Disposal Facilities
                                    Rev. (Anheuser-Busch Project),
                                    5.75% due 12/1/2030* .............................  A1/A+        9,037,696

                       4,100,000  Foothill/Eastern Transportation
                                    Corridor Agency Toll Road Rev.,
                                    5.75% due 1/15/2040 ..............................  Baa3/BBB-    3,896,968

                       4,000,000  San DiegoPublic Facilities Financing Authority
                                    Sewer Rev. Series 1999-A,
                                    5% due 5/15/2029 .................................  Aaa/AAA      3,559,720

                      5,700,000   San Diego Public Facilities Financing Authority
                                    Sewer Rev. Series 1999-B,
                                    5% due 5/15/2029 .................................  Aaa/AAA      5,072,601

                      10,000,000  San Francisco City and County Airports
                                    Commission Rev. (International Airport),
                                    6.30% due 5/1/2025* ..............................  Aaa/AAA     10,428,500

                       6,000,000  San Joaquin Hills Transportation Corridor Agency
                                    Rev. (Orange County Senior Lien Toll Road),
                                    6.75% due 1/1/2032o ..............................  Aaa/AAA      6,588,120

DELAWARE--2.3%         5,000,000  Delaware Economic Development Authority
                                    Exempt Facilities Rev. (Delmarva Power and
                                    Light Co. Project), 7.60% due 3/1/2020* ..........  Aaa/AAA      5,164,400

FLORIDA--1.9%          1,405,000  Florida Housing Finance Agency (Home Ownership
                                    Rev.), 7.90% due 3/1/2022* .......................  Aaa/NR       1,455,931

                       2,680,000  Orange County Housing Finance Authority
                                    (Mortgage Rev.), 7.80% due 10/1/2022* ............  Aaa/NR       2,762,329

ILLINOIS--3.0%         7,500,000  Chicago GOs, 5.25% due 1/1/2028 ....................  Aaa/AAA      6,766,425

INDIANA--2.3%          5,000,000  Indiana Employment Development Commission
                                    Environmental Rev. (Public Service Company of
                                    Indiana Inc.), 7.50% due 3/15/2015* ..............  Aaa/AAA      5,167,800

LOUISIANA--4.7%        8,940,000  Louisiana Public Facilities Authority Hospital Rev.
                                    (Southern Baptist Hospitals, Inc. Project), 8%
                                    due 5/15/2012+ ...................................  NR/AAA      10,464,449

MASSACHUSETTS--2.6%    5,500,000  Massachusetts Bay Transportation Authority General
                                    Transportation System Rev., 5.625% due 3/1/2026o..  Aaa/AAA      5,800,960
</TABLE>

------------------------
See footnotes on page 6.

4


<PAGE>

<TABLE>
<CAPTION>
===============================================================================================================
                                                                                             SEPTEMBER 30, 1999

---------------------------------------------------------------------------------------------------------------
                         FACE                                                         RATINGS
STATE                   AMOUNT              MUNICIPAL BONDS                          MOODY'S/S&P   MARKET VALUE
---------------------------------------------------------------------------------------------------------------
<S>                  <C>          <C>                                                   <C>        <C>
MICHIGAN--0.9%       $ 2,000,000  Kalamazoo Hospital Finance Authority Rev.
                                    (Bronson Methodist Hospital),
                                    5.50% due 5/15/2028 ..............................  Aaa/NR     $ 1,892,560

NEVADA--3.3%           7,000,000  Clark County Industrial Development Rev. (Nevada
                                    Power Company Project), 7.80% due 6/1/2020* ......  Aaa/AAA      7,290,220

NEW JERSEY--4.6%     7,000,000    New Jersey Economic Development Authority
                                    Water Facilities Rev. (American Water Co. Inc.),
                                    5.375% due 5/1/2032* .............................  Aaa/AAA      6,615,070

                      2,000,000   New Jersey Educational Facilities Authority Rev.
                                    (Princeton University), 6% due 7/1/2024o .........  Aaa/AAA      2,129,560

                      1,435,000   New Jersey Housing & Mortgage Finance Agency
                                    (Home Buyer Rev.), 7.70% due 10/1/2029*o .........  Aaa/AAA      1,464,762

NEW YORk--9.4%        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     10,246,800

                      10,000,000  New York State Thruway Authority General Rev.,
                                    6% due 1/1/20250 .................................  Aaa/AAA     10,798,500

NEW YORK AND           6,500,000  Port Authority of New York and New Jersey
  NEW JERSEY--2.9%                  (JFK International Air Terminal LLC Project
                                    Rev.), 5.75% due 12/1/2022* ......................  Aaa/AAA      6,544,200

OHIO--1.4%             2,895,000  Cleveland Waterworks Improvement First
                                    Mortgage Rev., 5.75% due 1/1/2021o ...............  Aaa/AAA      3,097,853

                         105,000  Cleveland Waterworks Improvement First
                                    Mortgage Rev., 5.75% due 1/1/2021 ................  Aaa/AAA        105,262

PENNSYLVANIA--7.1%     2,500,000  Allegheny County Airport Rev. (Greater Pittsburgh
                                    International Airport), 6.80% due 1/1/2010* ......  Aaa/AAA      2,644,725

                       3,000,000  Lehigh County Industrial Development Authority
                                    Pollution Control Rev. (Pennsylvania Power &
                                    Light Company Project), 6.15% due 8/1/2029 .......  Aaa/AAA      3,055,650

                      10,000,000  Philadelphia Airport Rev., 6.10% due 6/15/2025* ....  Aaa/AAA     10,066,000

SOUTH CAROLINA--2.0%   5,000,000  South Carolina Ports Authority Rev.,
                                    5.30% due 7/1/2026* ..............................  Aaa/AAA      4,538,600

TENNESSEE--3.8%        8,000,000  Humphreys County Industrial Development Board
                                    Solid Waste Disposal Rev. (E.I. duPont de
                                    Nemours & Co. Project), 6.70% due 5/1/2024* ......  Aa3/AA-      8,528,880

TEXAS--6.9%            3,000,000  Houston Higher Education Finance Corporation Rev.
                                    (Rice University Project), 5.375% due 11/15/2029..  Aaa/AAA      2,787,090

                       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       5,151,200
</TABLE>

---------------------
See footnotes on page 6.
                                                                               5
<PAGE>

<TABLE>
<CAPTION>
===============================================================================================================
PORTFOLIO OF INVESTMENTS (unaudited) (continued)                                             SEPTEMBER 30, 1999

---------------------------------------------------------------------------------------------------------------
                         FACE                                                         RATINGS
STATE                   AMOUNT              MUNICIPAL BONDS                          MOODY'S/S&P   MARKET VALUE
---------------------------------------------------------------------------------------------------------------
<S>                  <C>          <C>                                                   <C>        <C>
TEXAS (continued)    $ 7,500,000  Matagorda County Navigation District No. 1
                                    Pollution Control Rev. (Central Power and Light
                                    Co. Project), 6.125% due 5/1/2030* ...............  Aaa/AAA   $  7,581,750

VIRGINIA--2.0%         5,000,000  Pocahontas Parkway Association Toll Road Rev.
                                    (Route 895 Connector), 5.50% due 8/15/2028 .......  Baa3/BBB-    4,488,850

WASHINGTON--9.1%       4,795,000  Chelan County Public Utility District No. 001
                                    (Chelan Hydro Consolidated System Rev.),
                                    6.25% due 7/1/2017* ..............................  Aaa/AAA      4,953,475

                       5,000,000  Chelan County Public Utility District No. 001
                                    (Chelan Hydro Consolidated System Rev.),
                                    6.35% due 7/1/2028* ..............................  Aaa/AAA      5,205,850

                      10,000,000  King County Sewer GOs, 6.125% due 1/1/2033 .........  Aaa/AAA     10,313,600
                                                                                                  ------------
TOTAL MUNICIPAL BONDS (Cost $212,697,347)--95.7% ..............................................    214,374,754
VARIABLE RATE DEMAND NOTES (Cost $5,300,000)--2.4% ............................................      5,300,000
OTHER ASSETS LESS LIABILITIES--1.9% ...........................................................      4,355,120
                                                                                                  ------------
NET INVESTMENT ASSETS-- 100.0% ................................................................   $224,029,874
                                                                                                  ============
</TABLE>

-------------------
* Interest income earned from this security is subject to the federal
  alternative minimum tax.
+ Escrowed-to-maturity security.
o Pre-refunded security.

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.

--------------------------------------------------------------------------------
FOR MORE INFORMATION

MANAGER                                     IMPORTANT TELEPHONE NUMBERS
J. & W. Seligman & Co. Incorporated         (800) 874-1092  Stockholder Services
100 Park Avenue                             (212) 682-7600  Outside the United
New York, NY 10017                                          States
                                            (800) 622-4597  24-Hour Automated
                                                            Telephone Access
STOCKHOLDER SERVICE AGENT                                   Service
Seligman Data Corp.
100 Park Avenue
New York, NY 10017


6

<PAGE>


                                                  SELIGMAN
                                               ===============
                                                   SELECT
                                               ===============
                                                  MUNICIPAL
                                                 FUND, INC.

                                               [PHOTO OMITTED]



 Seligman Select Municipal Fund, Inc.

             MANAGED BY

           [LOGO OMITTED]                      [LOGO OMITTED]

       J. & W. SELIGMAN & CO.               THIRD QUARTER REPORT
            INCORPORATED                     SEPTEMBER 30, 1999

  Investment Managers and Advisors
          ESTABLISHED 1864
 100 PARK AVENUE, NEW YORK, NY 10017

PHOTO: COURTESY MICHIGAN TRAVEL BUREAU

                            CESEL3c 9/99