SELIGMAN HIGH INCOME FUND SERIES
N-30D, 1998-08-24
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<PAGE>

                                                                 S E L I G M A N
                                                      --------------------------

                                                                 U.S. GOVERNMENT

                                                               SECURITIES SERIES

                                 Mid-Year Report

                                  June 30, 1998

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

                         Seeking High Current Income by 
                      Investing in US Government Securities


<PAGE>

TO THE SHAREHOLDERS

In the first six months of 1998, Seligman U.S. Government Securities Series
posted a total return of 3.61% based on the net asset value of Class A shares,
compared to the 3.62% return of the Lipper General US Government Bond Funds
Average. The Lehman Brothers Government Bond Index, which measures the
performance of government bonds in the market, had a total return of 4.18% for
the first six months of the year. 

The US economy continued to grow throughout the first half of the year, bringing
the expansion into an unprecedented eighth year. The fundamentals underpinning
the economy also boosted the fixed-income market. Inflation remained low, and
the federal budget surplus caused a decrease in the overall supply of bonds.
Further, the supply of consumer goods kept pace with demand, which helped the
economic expansion remain balanced.

The Asian financial crisis had a positive impact on the bond market, as both
foreign and domestic investors sought the safety and quality of US Treasury
securities, sending yields down and prices up. However, some economic indicators
foreshadowed a deceleration in the pace of economic growth. The potential for
slower growth, coupled with the Asian crisis, effectively caused the Fed to
leave short-term interest rates unchanged in the first half of the year. This
further benefited the bond market. The 30-year US Treasury bond yield finished
the period at 5.63% on June 30, down from 5.92% on December 31, 1997.

Looking forward, we are optimistic about the fixed-income markets. Weakness in
the Asian currencies and economies is beginning to negatively impact some US
corporations, and recent earnings pre-announcements indicate that the profits of
some companies are coming under pressure in many industries. These factors could
make US fixed-income securities an even more attractive investment. Moreover, as
the federal budget surplus grows, the US Treasury will probably issue fewer
bonds in the coming months. This would further reduce supply, and could increase
the value of the Fund's holdings.

As of July 1, the portfolio management responsibilities of Seligman U.S.
Government Securities Series were fully assumed by Mr. Gary S. Zeltzer, a
Managing Director of J. & W. Seligman & Co. Incorporated, and head of the
Seligman Taxable Fixed Income Team. Mr. Zeltzer is supported by a group of
investment professionals dedicated to the objectives of Seligman U.S. Government
Securities Series.

As you may know, companies are modifying their computer systems to recognize
dates of January 1, 2000, and beyond. This is often referred to as the "Y2K"
problem. Unless systems are updated, many applications may interpret the last
two digits of the year to mean 1900 instead of 2000. J. & W. Seligman & Co.
Incorporated, the Seligman Investment Companies, and Seligman Data Corp., your
shareholder service agent, have jointly established a team to ensure that your
investment and shareholder services are not disrupted. This team is supported by
consulting firms specializing in Y2K solutions. Substantial work has been
performed to date, and we are confident that there will be no disruption in the
services provided by your Fund.

Thank you for your continued interest in Seligman U.S. Government Securities
Series. We look forward to serving your investment needs in the many years to
come. The Fund's portfolio of investments and financial statements follow this
letter. Information on the Fund's investment results appears on page 4.

By order of the Trustees,

/s/William C. Morrris
- ----------------------
William C. Morris
Chairman
                                                            
                                                            /s/ Brian T. Zino 
                                                            -----------------
                                                             Brian T. Zino
                                                             President

July 31, 1998
                                       1


<PAGE>

INTERVIEW WITH THE SELIGMAN TAXABLE FIXED INCOME TEAM

Q.  How did Seligman U.S. Government Securities Series perform in the first six
    months of 1998?

A.  Seligman U.S. Government Securities Series had solid performance in the
    first half of the year. The Fund posted a total return of 3.61% based on the
    net asset value of Class A shares. The total return of the Lipper General US
    Government Bond Funds Average was 3.62%. The Lehman Brothers Government Bond
    Index, which measures the performance of government bonds in the market, had
    a total return of 4.18% for the first six months of the year.

Q.  How did economic and market factors influence the Fund's results in the 
    first half of 1998?

A.  The economic fundamentals underpinning the US bond market were strong in the
    first half of the year. Inflation remained low, economic indicators
    bolstered widespread sentiment that growth appeared to be slowing, and the
    federal budget surplus caused a decrease in the overall supply of bonds, as
    fewer were issued.

    Additionally, commodity prices fell, including gold, while concerns about
    the Asian financial crisis caused the Federal Reserve Board to leave
    interest rates unchanged in the period. Despite a robust US economy and a
    tight labor market, US Treasury bond yields continued their decline. The
    30-year US Treasury bond yield closed at 5.63% at June 30, down from 5.92%
    at December 31, 1997.

    Within the US bond market, investors continued to seek the safety and
    quality of US Treasury securities. In particular, many overseas investors



A TEAM APPROACH

Seligman U.S. Government Securities Series is managed by the Seligman Taxable
Fixed Income Team. Gary S. Zeltzer, Portfolio Manager, is assisted by seasoned
research professionals who identify securities that are backed by the full faith
and credit of the US government. The Team seeks to position the Fund so as to
minimize the negative effects of any sharp rise in interest rates while
maximizing current income.

                                    [PHOTO]

Seligman Taxable Fixed Income Team: (from left) Susan Egan, Nicholas Walsh, Gary
S. Zeltzer (Portfolio Manager)

                                       2


<PAGE>

INTERVIEW WITH THE SELIGMAN TAXABLE FIXED INCOME TEAM

    pulled assets out of foreign stock and bond markets in favor of US
    Treasuries. In fact, foreign investors doubled purchases of US bonds over
    the past three years, according to the Fed, and foreign investors now own
    about $1.5 trillion of US Treasuries, or about one-third of all those
    outstanding.

Q. What was your investment strategy?

A.  We took advantage of the positive economic fundamentals. During the latter
    part of 1997, we lengthened the maturities of the portfolio holdings. Most
    of these positions were maintained during the first six months of 1998.

    In the period, we sold high-coupon (premium) mortgage-backed securities
    (Ginnie Maes), and used the proceeds to purchase low-coupon (discount)
    mortgage-backed securities. We pursued this strategy because in a declining
    interest rate environment, low-coupon securities that trade at a discount to
    their par value generally outperform high-coupon securities that trade at a
    premium to their par value. This occurs when holders of high rate mortgages
    refinance into lower rates, causing high-coupon securities to pre-pay their
    principal faster.

    More recently, as the 30-year US Treasury bond yield has reached record
    lows, we trimmed some of the longer-term holdings, and increased holdings in
    higher-yielding US Government Agency securities. By doing so, we shortened
    the portfolio's average weighted maturity compared to what it was at the
    beginning of the year.

Q.  What is the outlook?

A.  Although we remain positive on the prospects for the bond market, the
    30-year Treasury bond yield is already trading at a record low. For another
    significant drop in Treasury yields to occur, the US economy needs to slow
    significantly. Many believe a slowdown is already under way, but to what
    extent is unclear. At the same time, it is unlikely that a significant rise
    in bond yields will occur in the near term. Continued global economic
    instability, leading to falling commodity prices and intense global
    competition, should keep a lid on inflation. Finally, the disappearing
    budget deficit has allowed the US Treasury to reduce the amount of debt it
    issues. These events could lead to further declines in US Treasury yields
    and a rise in bond prices, which would enhance returns for Seligman U.S.
    Government Securities Series.

                                       3


<PAGE>

PERFORMANCE OVERVIEW

Investment Results Per Share

TOTAL RETURNS
For Periods Ended June 30, 1998
<TABLE>
<CAPTION>
                                                                              AVERAGE ANNUAL
                                                        -------------------------------------------------------------
                                                                                               CLASS B       CLASS D
                                                                                                SINCE         SINCE
                                                         ONE          FIVE          10        INCEPTION     INCEPTION
                                       SIX MONTHS*       YEAR         YEARS        YEARS       1/1/97        9/21/93
                                       -----------      ------        -----        ------     ---------     ---------
<S>                                    <C>              <C>           <C>          <C>        <C>           <C>
Class A**
With Sales Charge...................    (1.27)%          4.89%         4.37%        6.47%         n/a          n/a
Without Sales Charge................     3.61           10.08          5.38         6.99          n/a          n/a

Class B**
With CDSL+..........................    (1.65)           4.38           n/a          n/a         4.58%         n/a
Without CDSL........................     3.35            9.38           n/a          n/a         7.19          n/a

Class D**
With 1% CDSL........................     2.35            8.38           n/a          n/a          n/a          n/a
Without CDSL........................     3.35            9.38           n/a          n/a          n/a         4.19%
Lipper General US Government
Bond Funds Average++................     3.62           10.17          5.72         7.88         8.35         5.44+++
Lehman Brothers Government
Bond Index++........................     4.18           11.25          6.66         8.87         9.27         8.47+++
</TABLE>

<TABLE>
<CAPTION>
NET ASSET VALUE                                            DIVIDEND AND YIELD INFORMATION
                                                           For the Six Months Ended June 30, 1998

              JUNE 30,     DECEMBER 31,    JUNE 30,
                1998           1997          1997                       DIVIDENDS 0       YIELD 00
              --------     ------------    -------                      -----------       --------
<S>             <C>           <C>           <C>            <C>            <C>              <C>  
Class A         $6.94         $6.88         $6.66          Class A        $0.1836          4.62%
Class B          6.96          6.89          6.67          Class B         0.1569          4.06
Class D          6.96          6.89          6.67          Class D         0.1569          4.06

WEIGHTED AVERAGE MATURITY  17.42 years
</TABLE>
- ------------------
  * Returns for periods of less than one year are not annualized.

 ** Return figures reflect any change in price per share and assume the
    investment of dividends and capital gain distributions. Returns for Class A
    shares are calculated with and without the effect of the initial 4.75%
    maximum sales charge. Returns for Class B shares are calculated with and
    without the effect of the maximum 5% contingent deferred sales load
    ("CDSL"), charged on redemptions made within one year of the date of
    purchase, declining to 1% in the sixth year and 0% thereafter. Returns for
    Class D shares are calculated with and without the effect of the 1% CDSL,
    charged on redemptions made within one year of the date of purchase.

  + The CDSL is 5% for periods of one year or less, and 4% since inception.

 ++ The Lipper General US Government Bond Funds Average and the Lehman Brothers
    Government Bond Index are unmanaged benchmarks that assume investment of
    dividends. The Lipper General US Government Bond Funds Average excludes the
    effect of sales charges. The Lehman Brothers Government Bond Index excludes
    the effect of fees and sales charges. The monthly performances of the Lipper
    General US Government Bond Funds Average are used for the Performance
    Overview. Investors cannot invest directly in an average or an index.

+++ From September 30, 1993.

  0 Represents per share amount paid or declared for the six months ended June
    30, 1998.

 00 Current yield, representing the annualized yield for the 30-day period ended
    June 30, 1998, has been computed in accordance with SEC regulations and will
    vary.

                                       4


<PAGE>

PERFORMANCE OVERVIEW

Growth of an Assumed $10,000 Investment in Class A Shares

June 30, 1988, to June 30, 1998

   6/30/88   $9,524
             $9,669
             $9,757
             $9,769
   6/30/89  $10,288
            $10,353
            $10,660
            $10,398
   6/30/90  $10,697
            $10,758
            $11,339
            $11,520
   6/30/91  $11,686
            $12,326
            $12,932
            $12,656
   6/30/92  $13,147
            $13,684
            $13,680
            $14,074
   6/30/93  $14,402
            $14,748
            $14,700
            $14,397
   6/30/94  $14,166
            $14,203
            $14,129
            $14,643
   6/30/95  $15,574
            $15,814
            $16,694
            $16,112
   6/30/96  $16,049
            $16,253
            $16,645
            $16,481
   6/30/97  $17,001
            $17,427
            $18,064
            $18,228
   6/30/98  $18,716


Growth of an Assumed $10,000 Investment in Class B Shares

January 1, 1997,+ to June 30, 1998

    1/1/97     $10,000
   1/31/97      $9,981
   2/28/97      $9,976
   3/31/97      $9,850
   4/30/97      $9,982
   5/31/97     $10,039
   6/30/97     $10,140
   7/31/97     $10,425
   8/31/97     $10,256
   9/30/97     $10,374
  10/31/97     $10,543
  11/30/97     $10,583
  12/31/97     $10,732
   1/31/98     $10,901
   2/28/98     $10,833
   3/31/98     $10,808
   4/30/98     $10,840
   5/31/98     $10,957
   6/30/98     $11,092


Growth of an Assumed $10,000 Investment in Class D Shares

September 21, 1993,+ to June 30, 1998

   9/21/93  $10,000
   9/30/93  $10,000
  12/31/93   $9,935
   3/31/94   $9,694
   6/30/94   $9,513
   9/30/94   $9,526
  12/31/94   $9,434
   3/31/95   $9,765
   6/30/95  $10,349
   9/30/95  $10,502
  12/31/95  $11,047
   3/31/96  $10,642
   6/30/96  $10,580
   9/30/96  $10,693
  12/31/96  $10,945
   3/31/97  $10,802
   6/30/97  $11,121
   9/30/97  $11,376
  12/31/97  $11,769
   3/31/98  $11,853
   6/30/98  $12,164


These charts reflect the growth of a $10,000 investment for a 10-year period for
Class A shares and since inception for Class B and Class D shares, assuming that
all distributions within the periods are invested in additional shares. Since
the measured periods vary, the charts are plotted using different scales and are
not comparable.

- ------------------
  * Net of the 4.75% maximum initial sales charge.
 ** Excludes the effect of the 4% CDSL.
  + Inception date.
                                       5


<PAGE>

PORTFOLIO OF INVESTMENTS
June 30, 1998
<TABLE>
<CAPTION>
                                                                                       PRINCIPAL
                                                                                        AMOUNT              VALUE
                                                                                      -----------       -----------
<S>                                                                                   <C>               <C>
US GOVERNMENT SECURITIES  46.4%

US Treasury Bonds:
   8 3/4%, due 5/15/2020..........................................................    $ 6,000,000       $ 8,242,506
   6 5/8%, due 2/15/2027..........................................................      3,000,000         3,390,003

US Treasury Notes:
   6 1/4%, due 8/31/2002..........................................................      7,500,000         7,696,883
   6 5/8%, due 5/15/2007..........................................................      8,000,000         8,600,008
                                                                                                        -----------
TOTAL US GOVERNMENT SECURITIES (Cost $26,806,446).................................                       27,929,400
                                                                                                        -----------
US GOVERNMENT AGENCY SECURITIES  51.9%

Federal Home Loan Mortgage Association, 5 3/4%, due 7/15/2003.....................      2,500,000         2,502,075
Federal National Mortgage Association, 5 3/4%, due 4/15/2003......................      2,500,000         2,509,295
Government National Mortgage Association Obligations, Mortgage-backed
   Pass-through Certificates:
   6 1/2%, due 4/15/2028*.........................................................     21,240,491        21,213,941
Tennessee Valley Authority, 6 1/8%, due 7/15/2003.................................      2,500,000         2,510,540
US Government Title XI (Rowan Companies), 6.15%, due 7/1/2010.....................      2,500,000         2,501,425
                                                                                                        -----------
TOTAL US GOVERNMENT AGENCY SECURITIES (Cost $31,182,403)..........................                       31,237,276
                                                                                                        -----------

REPURCHASE AGREEMENTS (Cost $3,138,000) 5.2% 

HSBC Securities Inc., 5%, maturing 7/1/1998 collateralized by:
   $2,878,000 US Treasury Notes 7 1/4%, due 8/15/2004, with a fair
   market value of $3,205,840.....................................................      3,138,000         3,138,000
                                                                                                        -----------

TOTAL INVESTMENTS (Cost $61,126,849)  103.5%......................................                       62,304,676

OTHER ASSETS LESS LIABILITIES  (3.5)%.............................................                       (2,125,997)
                                                                                                        -----------
NET ASSETS   100.0% ..............................................................                      $60,178,679
                                                                                                        ===========
</TABLE>
- ------------------
* Investments in mortgage-backed securities are subject to principal paydowns.
  As a result of prepayments from refinancing or satisfaction of the underlying
  mortgage instruments, the average life may be less than the original maturity.
  This in turn may impact the ultimate yield realized from these securities.

See Notes to Financial Statements.
                                       6


<PAGE>

STATEMENT OF ASSETS AND LIABILITIES
June 30, 1998
<TABLE>

<S>                                                                       <C>                                  <C>
ASSETS:
Investments, at value:
   Long-term holdings (Cost $57,988,849)..............................    $59,166,676
   Short-term holdings (Cost $3,138,000)..............................      3,138,000                          $62,304,676
                                                                          -----------
Cash.................................................................................                               70,769
Interest receivable..................................................................                              586,376
Receivable for shares of Beneficial Interest sold....................................                               98,264
Expenses prepaid to shareholder service agent........................................                               12,250
Other................................................................................                               43,537
                                                                                                               -----------
Total Assets.........................................................................                           63,115,872
                                                                                                               -----------
LIABILITIES:

Payable for securities purchased.....................................................                            2,500,000
Payable for shares of Beneficial Interest repurchased................................                              203,766
Dividends payable....................................................................                              105,600
Accrued expenses, taxes, and other...................................................                              127,827
                                                                                                               -----------
Total Liabilities....................................................................                            2,937,193
                                                                                                               -----------
Net Assets...........................................................................                          $60,178,679
                                                                                                               ===========
COMPOSITION OF NET ASSETS:

Shares of Beneficial Interest, at par ($0.001 par value; unlimited shares
   authorized; 8,661,287 shares outstanding):
   Class A...........................................................................                          $     6,610
   Class B...........................................................................                                  620
   Class D...........................................................................                                1,431
Additional paid-in capital...........................................................                           71,586,729
Accumulated net realized loss........................................................                          (12,594,538)
Net unrealized appreciation of investments...........................................                            1,177,827
                                                                                                               -----------
Net Assets...........................................................................                          $60,178,679
                                                                                                               ===========
NET ASSET VALUE PER SHARE:

Class A ($45,903,761 / 6,610,043 shares).............................................                                $6.94
                                                                                                                     =====
Class B ($4,316,429 / 620,361 shares)................................................                                $6.96
                                                                                                                     =====
Class D ($9,958,489 / 1,430,883 shares)..............................................                                $6.96
                                                                                                                     =====
</TABLE>
- ------------------
See Notes to Financial Statements.

                                       7

<PAGE>

STATEMENT OF OPERATIONS
For the Six Months Ended June 30, 1998
<TABLE>
<S>                                                                                  <C>                             <C>
INVESTMENT INCOME:
Interest.....................................................................................                        $1,931,693

EXPENSES:
Management fee..............................................................       $  148,744
Distribution and service fees...............................................          120,533
Shareholder account services................................................           53,028
Registration................................................................           33,832
Shareholder reports and communications......................................           13,266
Auditing and legal fees.....................................................           10,114
Custody and related services................................................            7,000
Trustees' fees and expenses.................................................            2,579
Miscellaneous...............................................................            4,572
                                                                                   ----------
Total Expenses...............................................................................                           393,668
                                                                                                                     ----------
Net Investment Income........................................................................                         1,538,025

NET REALIZED AND UNREALIZED
GAIN (LOSS) ON INVESTMENTS:

Net realized gain on investments............................................        1,664,787
Net change in unrealized appreciation of investments........................       (1,085,725)
                                                                                   ----------
Net Gain on Investments......................................................................                           579,062
                                                                                                                     ----------
Increase in Net Assets from Operations.......................................................                        $2,117,087
                                                                                                                     ==========
</TABLE>
- ------------------
See Notes to Financial Statements.
                                       8


<PAGE>

STATEMENTS OF CHANGES IN NET ASSETS
<TABLE>
<CAPTION>
                                                                                                 SIX MONTHS               YEAR
                                                                                                    ENDED                 ENDED
OPERATIONS:                                                                                        6/30/98              12/31/97
                                                                                                 -----------           -----------
<S>                                                                                              <C>                   <C>       
Net investment income.................................................................           $ 1,538,025           $ 3,013,241
Net realized gain (loss) on investments...............................................             1,664,787              (611,943)
Net change in unrealized appreciation of investments..................................            (1,085,725)            1,949,757
                                                                                                 -----------           -----------
Increase in Net Assets from Operations................................................             2,117,087             4,351,055
                                                                                                 -----------           -----------
DISTRIBUTIONS TO SHAREHOLDERS:
Net investment income:
   Class A............................................................................            (1,211,944)           (2,522,929)
   Class B............................................................................               (85,502)              (45,289)
   Class D............................................................................              (240,579)             (445,023)
                                                                                                 -----------           -----------
Decrease in Net Assets from Distributions.............................................            (1,538,025)           (3,013,241)
                                                                                                 -----------           -----------
</TABLE>

<TABLE>
<CAPTION>
                                                                     SHARES
                                                          -----------------------------
                                                          SIX MONTHS            YEAR
TRANSACTIONS IN SHARES                                       ENDED              ENDED
OF BENEFICIAL INTEREST:*                                    6/30/98            12/31/97
                                                          ----------         ----------
<S>                                                       <C>                <C>                 <C>                   <C>
Net proceeds from sale of shares:
   Class A...........................................      1,187,641            829,234            8,177,943             5,624,748
   Class B...........................................        158,319            182,897            1,094,260             1,228,800
   Class D...........................................        115,345            198,244              796,494             1,326,662

Investment of dividends:
   Class A...........................................         99,817            202,913              689,072             1,359,967
   Class B...........................................          9,838              5,291               68,047                35,836
   Class D...........................................         22,813             42,659              157,854               286,730

Exchanged from associated Funds:
   Class A...........................................        950,654          1,572,537            6,553,453            10,660,240
   Class B...........................................        286,149            574,598            1,977,302             3,899,673
   Class D...........................................      1,252,255          1,591,469            8,645,605            10,742,800
                                                          ----------         ----------          -----------           -----------
Total................................................      4,082,831          5,199,842           28,160,030            35,165,456
                                                          ----------         ----------          -----------           -----------
Cost of shares repurchased:
   Class A...........................................       (585,254)        (1,364,274)          (4,042,090)           (9,183,343)
   Class B...........................................        (49,735)           (14,942)            (341,991)             (101,411)
   Class D...........................................       (140,001)          (369,696)            (967,418)           (2,477,886)

Exchanged into associated Funds:
   Class A...........................................     (1,648,804)        (1,618,861)         (11,347,763)          (10,932,716)
   Class B...........................................       (251,566)          (280,488)          (1,736,800)           (1,910,778)
   Class D...........................................     (1,612,178)        (1,050,159)         (11,119,240)           (7,074,255)
                                                          ----------         ----------          -----------           -----------
Total................................................     (4,287,538)        (4,698,420)         (29,555,302)          (31,680,389)
                                                          ----------         ----------          -----------           -----------
Increase (Decrease) in Net Assets from
Transactions in Shares of
Beneficial Interest..................................       (204,707)           501,422           (1,395,272)            3,485,067
                                                          ==========         ==========          -----------           -----------
Increase (Decrease) in Net Assets......................................................             (816,210)            4,822,881

NET ASSETS:
Beginning of period....................................................................           60,994,889            56,172,008
                                                                                                 -----------           -----------
End of Period..........................................................................          $60,178,679           $60,994,889
                                                                                                 ===========           ===========
</TABLE>
- ------------------
* The Fund began offering Class B shares on January 1, 1997.
See Notes to Financial Statements.



                                       9

<PAGE>

NOTES TO FINANCIAL STATEMENTS

1. Multiple Classes of Shares -- Seligman U.S. Government Securities Series (the
"Fund"), a series of Seligman High Income Fund Series, offers three classes of
shares. Class A shares are sold with an initial sales charge of up to 4.75% and
a continuing service fee of up to 0.25% on an annual basis. Class A shares
purchased in an amount of $1,000,000 or more are sold without an initial sales
charge but are subject to a contingent deferred sales load ("CDSL") of 1% on
redemptions within 18 months of purchase. The Fund began offering Class B shares
on January 1, 1997. Class B shares are sold without an initial sales charge but
are subject to a distribution fee of 0.75%, a service fee of up to 0.25% on an
annual basis, and a CDSL, if applicable, of 5% on redemptions in the first year
of purchase, declining to 1% in the sixth year and 0% thereafter. Class B shares
will automatically convert to Class A shares on the last day of the month that
precedes the eighth anniversary of their date of purchase. Class D shares are
sold without an initial sales charge but are subject to a distribution fee of up
to 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSL, if
applicable, of 1% imposed on certain redemptions made within one year of
purchase. The three classes of shares represent interests in the same portfolio
of investments, have the same rights and are generally identical in all respects
except that each class bears its separate distribution and certain other class
expenses, and has exclusive voting rights with respect to any matter on which a
separate vote of any class is required.

2. Significant Accounting Policies -- The financial statements have been
prepared in conformity with generally accepted accounting principles which
require management to make certain estimates and assumptions at the date of the
financial statements. The following summarizes the significant accounting
policies of the Fund:

a.  Security Valuation -- Investments in US Government and Government agency
    securities are valued at current market values or, in their absence, at fair
    values determined in accordance with procedures approved by the Trustees.
    Securities traded on national exchanges are valued at last sales prices or,
    in their absence and in the case of over-the-counter securities, at the mean
    of bid and asked prices. Short-term holdings maturing in 60 days or less are
    valued at amortized cost.

b.  Federal Taxes -- There is no provision for federal income tax. The Fund has
    elected to be taxed as a regulated investment company and intends to 
    distribute substantially all taxable net income and net gain realized.

c.  Security Transactions and Related Investment Income -- Investment
    transactions are recorded on trade dates. Identified cost of investments
    sold is used for both financial statement and federal income tax purposes.
    Dividends receivable and payable are recorded on ex-dividend dates. Interest
    income is recorded on an accrual basis. The Fund accretes original issue
    discounts and market discounts on purchases of portfolio securities.

d.  Repurchase Agreements -- The Fund may enter into repurchase agreements with
    commercial banks and with broker/dealers deemed to be creditworthy by J. &
    W. Seligman & Co. Incorporated (the "Manager"). Securities received as
    collateral subject to repurchase agreements are deposited with the Fund's
    custodian and, pursuant to the terms of the repurchase agreement must have
    an aggregate market value greater than or equal to the repurchase price plus
    accrued interest, at all times. Procedures have been established to monitor,
    on a daily basis, the market value of repurchase agreements' underlying
    securities to ensure the existence of the proper level of collateral.

e.  Multiple Class Allocations -- All income, expenses (other than
    class-specific expenses), and realized and unrealized gains or losses are
    allocated daily to each class of shares based upon the relative value of
    shares of each class. Class-specific expenses, which include distribution
    and service fees and any other items that are specifically attributable to a
    particular class, are charged directly to such class. For the six months
    ended June 30, 1998, distribution and service fees were the only
    class-specific expenses.

f.  Distributions to Shareholders -- Dividends are declared daily and paid
    monthly. Other distributions paid by the Fund are recorded on the
    ex-dividend date. The treatment for financial statement purposes of
    distributions made to shareholders during the year from net investment
    income or net realized gains may differ from their ultimate treatment for
    federal income 
                                       10


<PAGE>

NOTES TO FINANCIAL STATEMENTS

    tax purposes. These differences are caused primarily by differences in the
    timing of the recognition of certain components of income, expense, or
    realized capital gain for federal income tax purposes. Where such
    differences are permanent in nature, they are reclassified in the components
    of net assets based on their ultimate characterization for federal income
    tax purposes. Any such reclassification will have no effect on net assets,
    results of operations, or net asset value per share of the Fund.

3. Purchases and Sales of Securities -- Purchases and sales of US Government
obligations, excluding short-term investments, for the six months ended June 30,
1998, amounted to $47,961,693 and $48,258,421, respectively.

At June 30, 1998, the cost of investments for federal income tax purposes was
substantially the same as the cost for financial reporting purposes, and the tax
basis gross unrealized appreciation and depreciation of portfolio securities
amounted to $1,178,112 and $285, respectively.

4. Management Fee, Distribution Services, and Other Transactions -- The Manager
manages the affairs of the Fund and provides the necessary personnel and
facilities. Compensation of all officers of the Fund, all trustees of the
Fund who are employees or consultants of the Manager, and all personnel of the
Fund and the Manager is paid by the Manager. The Manager receives a fee,
calculated daily and payable monthly, equal to 0.50% per annum of the Fund's
average daily net assets.

    Seligman Financial Services, Inc. (the "Distributor"), agent for the
distribution of the Fund's shares, and an affiliate of the Manager, received
concessions of $2,147 from sales of Class A shares after commissions of $25,947
were paid to dealers.

    The Fund has an Administration, Shareholder Services and Distribution
Plan (the "Plan") with respect to distribution of its shares. Under the Plan,
with respect to Class A shares, service organizations can enter into agreements
with the Distributor and receive a continuing fee of up to 0.25% on an annual
basis, payable quarterly, of the average daily net assets of the Class A shares
attributable to the particular service organizations for providing personal
services and/or the maintenance of shareholder accounts. The Distributor charges
such fees to the Fund pursuant to the Plan. For the six months ended June 30,
1998, fees incurred under the Plan aggregated $49,443 or 0.22% per annum of the
average daily net assets of Class A shares.

    Under the Plan, with respect to Class B and Class D shares, service
organizations can enter into agreements with the Distributor and receive a
continuing fee for providing personal services and/or the maintenance of 
shareholder accounts of up to 0.25% on an annual basis of the average daily net
assets of the Class B and Class D shares for which the organizations are
responsible; and, for Class D shares only, fees for providing other distribution
assistance of up to 0.75% on an annual basis of such average daily net assets.
Such fees are paid monthly by the Fund to the Distributor pursuant to the Plan.

    With respect to Class B shares, a distribution fee of 0.75% on an annual
basis of average daily net assets is payable monthly by the Fund to the
Distributor; however, the Distributor has sold its rights to this fee to a third
party (the "Purchaser"), which provides funding to the Distributor to enable it
to pay commissions to dealers at the time of the sale of the related Class B
shares.

    For the six months ended June 30, 1998, fees incurred under the Plan,
equivalent to 1% per annum of the average daily net assets of Class B and Class
D shares, amounted to $18,722 and $52,368, respectively.

    The Distributor is entitled to retain any CDSL imposed on redemptions of
Class D shares occurring within one year of purchase and on certain redemptions
of Class A shares occurring within 18 months of purchase. For the six months
ended June 30, 1998, such charges amounted to $2,424.

    The Distributor has sold its rights to collect any CDSL imposed on
redemptions of Class B shares to the Purchaser. In connection with the sale of
its rights to collect any CDSL and the distribution fees with respect to Class B
shares described above, the Distributor receives payments from the Purchaser
based on the value of Class B shares sold. The aggregate amount of such payments
retained by the Distributor for the six months ended June 30, 1998, amounted to
$1,639.

                                       11


<PAGE>

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

    Seligman Services, Inc., an affiliate of the Manager, is eligible to receive
commissions from certain sales of shares of Beneficial Interest of the Fund, as
well as distribution and service fees pursuant to the Plan. For the six months
ended June 30, 1998, Seligman Services, Inc. received commissions of $501 from
the sale of Fund shares. Seligman Services, Inc. also received distribution and
service fees of $7,561, pursuant to the Plan.

    Seligman Data Corp., which is owned by certain associated investment
companies, charged the Fund at cost $53,028 for shareholder account services.

    Certain officers and trustees of the Fund are officers or directors of the
Manager, the Distributor, Seligman Services, Inc., and/or Seligman Data Corp.

    The Fund has a compensation arrangement under which trustees who receive
fees may elect to defer receiving such fees. Trustees may elect to have their
deferred fees accrue interest or earn a return based on the performance of the
Fund or other funds in the Seligman Group of Investment Companies. The cost of
such fees and earnings accrued thereon is included in trustees' fees and
expenses, and the accumulated balance thereof at June 30, 1998, of $39,087 is
included in other liabilities. Deferred fees and related accrued earnings are
not deductible for federal income tax purposes until such amounts are paid.

5. Loss Carryforward -- At December 31, 1997, the Fund had a net loss
carryforward for federal income tax purposes of $14,118,544, which is available
for offset against future taxable net gains, expiring in various amounts through
2005. Accordingly, no capital gain distributions are expected to be paid to
shareholders until net capital gains have been realized in excess of the
available capital loss carryforwards.

6. Committed Line of Credit -- Effective July 1, 1998, the Fund entered into a
joint $800 million committed line of credit that is shared by substantially all
funds in the Seligman Group of Investment Companies. The Fund's borrowings are
limited to 10% of its net assets. Borrowings pursuant to the credit facility are
subject to interest at a rate equal to the overnight federal funds rate plus
0.50% on an overnight basis. The Fund incurs a commitment fee of 0.08% per annum
on its share of the unused portion of the credit facility. The credit facility
may be drawn upon only for temporary purposes and is subject to certain other
customary restrictions. The credit facility commitment expires one year from the
date of the agreement but is renewable with the consent of the participating
banks. To date, the Fund has not borrowed from the credit facility. 

                                       12


<PAGE>

FINANCIAL HIGHLIGHTS

   The Fund's financial highlights are presented below. "Per share operating
performance" data is designed to allow investors to trace the operating
performance of each Class, on a per share basis, from the beginning net asset
value to the ending net asset value, so that investors can understand what
effect the individual items have on their investment, assuming it was held
throughout the period. Generally, per share amounts are derived by converting
the actual dollar amounts incurred for each item, as disclosed in the financial
statements, to their equivalent per share amounts, using average shares
outstanding.

   "Total return based on net asset value" measures each Class's performance
assuming that investors purchased Fund shares at net asset value as of the
beginning of the period, invested dividends and capital gains paid at net asset
value, and then sold their shares at the net asset value on the last day of the
period. The total return computations do not reflect any sales charges investors
may incur in purchasing or selling shares of the Fund. Total returns for periods
of less than one year are not annualized.
<TABLE>
<CAPTION>
                                                                                       CLASS A
                                                             ------------------------------------------------------------
                                                               SIX
                                                              MONTHS                  YEAR ENDED DECEMBER 31,
                                                              ENDED      ------------------------------------------------
                                                             6/30/98     1997       1996       1995       1994      1993
                                                             -------     -----      -----      -----      -----     -----
<S>                                                           <C>        <C>        <C>        <C>        <C>       <C>
PER SHARE OPERATING PERFORMANCE:

Net Asset Value, Beginning of Period.....................     $6.88      $6.71      $7.15      $6.47      $7.18     $7.19
                                                              -----      -----      -----      -----      -----     -----
Net investment income....................................      0.18       0.38       0.41       0.46       0.44      0.53
Net realized and unrealized investment gain (loss).......      0.06       0.17      (0.44)      0.68      (0.71)    (0.01)
                                                              -----      -----      -----      -----      -----     -----
Increase (Decrease) from Investment Operations...........      0.24       0.55      (0.03)      1.14      (0.27)     0.52
Dividends paid or declared...............................     (0.18)     (0.38)     (0.41)     (0.46)     (0.44)    (0.53)
                                                              -----      -----      -----      -----      -----     -----
Net Increase (Decrease) in Net Asset Value...............      0.06       0.17      (0.44)      0.68      (0.71)    (0.01)
                                                              -----      -----      -----      -----      -----     -----
Net Asset Value, End of Period...........................     $6.94      $6.88      $6.71      $7.15      $6.47     $7.18
                                                              =====      =====      =====      =====      =====     =====

TOTAL RETURN BASED ON NET ASSET VALUE:                         3.61%      8.53%     (0.29)%    18.15%     (3.88)%    7.46%

RATIOS/SUPPLEMENTAL DATA:

Expenses to average net assets...........................      1.14%+     1.23%      1.14%      1.14%      1.10%     1.11%
Net investment income to average net assets..............      5.37%+     5.68%      6.05%      6.71%      6.49%     7.22%
Portfolio turnover.......................................     83.13%    193.90%    175.25%    213.06%    445.18%   170.35%
Net Assets, End of Period (000s omitted).................    $45,904    $45,426    $46,889    $55,061    $54,714   $69,805

</TABLE>
- ------------------
See footnotes on page 14.
                                       13


<PAGE>

FINANCIAL HIGHLIGHTS (CONTINUED)
<TABLE>
<CAPTION>
                                                                CLASS B                            CLASS D
                                                           ----------------  ------------------------------------------------------
                                                             SIX              SIX
                                                           MONTHS   1/1/97*  MONTHS      YEAR ENDED DECEMBER 31,           9/21/93*
                                                            ENDED     TO      ENDED     --------------------------------      TO 
                                                           6/30/98 12/31/97  6/30/98    1997     1996     1995     1994    12/31/93 
                                                           ------- --------  -------    -----    -----    -----    -----   --------
<S>                                                        <C>      <C>      <C>        <C>      <C>      <C>      <C>     <C>
PER SHARE OPERATING PERFORMANCE:
Net Asset Value, Beginning of Period................        $6.89    $6.73    $6.89     $6.73    $7.16    $6.48    $7.20    $7.33
                                                            -----    -----    -----     -----    -----    -----    -----    -----
Net investment income...............................         0.16     0.33     0.16      0.33     0.36     0.40     0.37     0.09
Net realized and unrealized investment gain (loss)..         0.07     0.16     0.07      0.16    (0.43)    0.68    (0.72)   (0.13)
                                                            -----    -----    -----     -----    -----    -----    -----    -----
Increase (Decrease) from Investment Operations......         0.23     0.49     0.23      0.49    (0.07)    1.08    (0.35)   (0.04)
Dividends paid or declared..........................        (0.16)   (0.33)   (0.16)    (0.33)   (0.36)   (0.40)   (0.37)   (0.09)
                                                            -----    -----    -----     -----    -----    -----    -----    -----
Net Increase (Decrease) in Net Asset Value..........         0.07     0.16     0.07      0.16    (0.43)    0.68    (0.72)   (0.13)
                                                            -----    -----    -----     -----    -----    -----    -----    -----
Net Asset Value, End of Period......................        $6.96    $6.89    $6.96     $6.89    $6.73    $7.16    $6.48    $7.20
                                                            =====    =====    =====     =====    =====   ======    =====    =====
TOTAL RETURN BASED ON NET ASSET VALUE:                       3.35%    7.32%    3.35%     7.53%   (0.92)%  17.10%   (5.05)%  (0.65)%

RATIOS/SUPPLEMENTAL DATA:
Expenses to average net assets .....................         1.92%+   2.01%    1.92%+    2.01%    1.92%    2.01%    2.22%    2.09%+
Net investment income to average net assets ........         4.59%+   4.90%    4.59%+    4.90%    5.27%    5.84%    5.40%    5.28%+
Portfolio turnover .................................        83.13%  193.90%   83.13%    93.90%  175.25%  213.06%  445.18%  170.35%++
Net Assets, End of Period (000s omitted)............        $4,316   $3,219   $9,959   $12,350   $9,283   $8,181   $6,062   $2,317

</TABLE>
- ------------------
 * Commencement of offering of shares.
 + Annualized.
++ For the year ended December 31, 1993.
See Notes to Financial Statements.

                                       14


<PAGE>

REPORT OF INDEPENDENT AUDITORS

The Trustees and Shareholders,
Seligman U.S. Government Securities Series:

We have audited the accompanying statement of assets and liabilities, including
the portfolio of investments, of Seligman U.S. Government Securities Series as
of June 30, 1998, the related statements of operations for the six months then
ended and of changes in net assets for the six months then ended and for the
year ended December 31, 1997, and the financial highlights for each of the
periods presented. 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. Our procedures included confirmation of securities owned as of June
30, 1998, by correspondence with the Fund's custodian and brokers; where replies
were not received from brokers we performed other auditing procedures. 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, such financial statements and financial highlights present
fairly, in all material respects, the financial position of Seligman U.S.
Government Securities Series as of June 30, 1998, the results of its operations,
the changes in its net assets, and the financial highlights for the respective
stated periods in conformity with generally accepted accounting principles.

/s/DELOITTE & TOUCHE LLP

DELOITTE & TOUCHE LLP

New York, New York
July 31, 1998

                                       15


<PAGE>

TRUSTEES

John R. Galvin 2, 4
Dean, Fletcher School of Law and Diplomacy
   at Tufts University
Director, Raytheon Company

Alice S. Ilchman 3, 4
Trustee, Committee for Economic Development
Chairman, The Rockefeller Foundation

Frank A. McPherson 2, 4
Director, Kimberly-Clark Corporation
Director, Baptist Medical Center

John E. Merow 2, 4
Retired Chairman and Senior Partner,
   Sullivan & Cromwell, Law Firm
Director, Commonwealth Industries, Inc.
Trustee, The New York and Presbyterian Hospital

Betsy S. Michel 2, 4
Trustee, The Geraldine R. Dodge Foundation
Chairman of the Board of Trustees, St. George's School

William C. Morris 1
Chairman
Chairman of the Board, J. & W. Seligman & Co.
   Incorporated
Chairman, Carbo Ceramics Inc.
Director, Kerr-McGee Corporation

James C. Pitney 3, 4
Retired Partner, Pitney, Hardin, Kipp & Szuch,
   Law Firm

James Q. Riordan 3, 4
Director, The Brooklyn Union Gas Company
Trustee, Committee for Economic Development
Director, Public Broadcasting Service

Richard R. Schmaltz 1
Managing Director, Director of Investments,
   J. & W. Seligman & Co. Incorporated
Trustee Emeritus, Colby College

Robert L. Shafer 3, 4
Retired Vice President, Pfizer Inc.

James N. Whitson 2, 4
Director and Consultant, Sammons Enterprises, Inc.
Director, C-SPAN
Director, CommScope, Inc.

Brian T. Zino 1
President
President, J. & W. Seligman & Co.  Incorporated
Chairman, Seligman Data Corp.

Trustee Emeritus
Fred E. Brown
Director and Consultant, J. & W. Seligman & Co. Incorporated

- ----------------
Member:    1 Executive Committee
           2 Audit Committee
           3 Trustee Nominating Committee
           4 Board Operations Committee

                                       16


<PAGE>

EXECUTIVE OFFICERS

William C. Morris
Chairman

Brian T. Zino
President

Lawrence P. Vogel
Vice President

Gary S. Zeltzer
Vice President

Thomas G. Rose
Treasurer

Frank J. Nasta
Secretary



FOR MORE INFORMATION

Manager
J. & W. Seligman & Co. Incorporated
100 Park Avenue
New York, NY 10017

General Counsel
Sullivan & Cromwell

Independent Auditors
Deloitte & Touche LLP

General Distributor
Seligman Financial Services, Inc.
100 Park Avenue
New York, NY 10017

Shareholder Service Agent
Seligman Data Corp.
100 Park Avenue
New York, NY 10017

Important Telephone Numbers

(800) 221-2450     Shareholder Services

(800) 445-1777     Retirement Plan
                   Services

(212) 682-7600     Outside the United States

(800) 622-4597     24-Hour
                   Automated
                   Telephone Access Service

                                       17


<PAGE>

GLOSSARY OF FINANCIAL TERMS

Capital Gain Distribution -- A payment to mutual fund shareholders of profits
realized on the sale of securities in the fund's portfolio. For tax purposes,
these profits may be taxed at different rates, primarily depending upon the
length of time the securities were owned by the fund.

Capital Appreciation/Depreciation -- An increase or decrease in the market value
of a mutual fund's portfolio securities, which is reflected in the net asset
value of the fund's shares. Capital appreciation/depreciation of an individual
security is in relation to the original purchase price.

Compounding -- The change in the value of an investment as shareholders receive
earnings on their investment's earnings. For example, if $1,000 is invested at a
fixed rate of 7% a year, the initial investment is worth $1,070 after one year.
If the return is compounded, second year earnings will not be based on the
original $1,000, but on the $1,070, which includes the first year's earnings.

Contingent Deferred Sales Load (CDSL) -- Depending on the class of shares owned,
a fee charged by a mutual fund when shares are sold back to the fund (the CDSL
expires after a fixed time period).

Dividend -- A payment by a mutual fund, usually derived from the fund's net
investment income (dividends and interest less expenses).

Dividend Yield -- A measurement of a fund's dividend as a percentage of the
maximum offering price.

Expense Ratio -- The cost of doing business for a mutual fund, expressed as a
percent of the fund's net assets.

Investment Objective -- The shared investment goal of a fund and its
shareholders.

Management Fee -- The amount paid by a mutual fund to its investment advisor(s).

Multiple Classes of Shares -- Although an individual mutual fund invests in only
one portfolio of securities, it may offer investors several purchase options
which are "classes" of shares. Multiple classes permit shareholders to choose
the fee structure that best meets their needs and goals. Generally, each class
will differ in terms of how and when sales charges and certain fees are
assessed.

National Association of Securities Dealers, Inc. (NASD) -- A self-regulatory
body with authority over firms that distribute mutual funds.

Net Asset Value (NAV) Per Share -- The market worth of one fund share, obtained
by adding a mutual fund's total assets (securities, cash, and any accrued
earnings), subtracting liabilities, and dividing the resulting net assets by the
number of shares outstanding.

Offering Price (OP) -- The price at which a mutual fund's share can be
purchased. The offering price is the current net asset value per share plus any
sales charge.

Portfolio Turnover -- A measure of the trading activity in a mutual fund's
investment portfolio that reflects how often securities are bought and sold.

Prospectus -- The legal document describing a mutual fund to all prospective
shareholders. It contains information required by the Securities and Exchange
Commission, such as the fund's investment objective and policies, services,
investment restrictions, officers and directors, how shares are bought and
redeemed, fund fees and other charges, and the fund's financial statements. 

SEC Yield -- SEC Yield refers to the net income earned by a fund during a recent
30-day period. This income is annualized and then divided by the maximum
offering price per share on the last day of the 30-day period. The SEC Yield
formula reflects semiannual compounding.

Securities and Exchange Commission -- The primary US federal agency that
regulates the registration and distribution of mutual fund shares.

Statement of Additional Information -- A document that contains updated or more
detailed information about a mutual fund and that supplements the prospectus. It
is available at no charge upon request.

Total Return -- A measure of fund performance encompassing all elements of
return. Reflects the change in share price over a given period and assumes all
distributions are taken in additional fund shares. The Average Annual Total
Return represents the average annual compounded rate of return for the periods
presented.

Yield on Securities -- For bonds, the current yield is the coupon rate of
interest, divided by the purchase price. For stocks, the yield is measured by
dividing dividends paid by the maximum offering price of the stock.

- ----------------
Adapted from the Investment Company Institute's 1997 Mutual Fund Fact Book.

                                       18

<PAGE>
                        SELIGMAN FINANCIAL SERVICES, INC.

                                 an affiliate of

                             J. & W. SELIGMAN & CO.
                                  INCORPORATED

                                ESTABLISHED 1864

This report is intended only for the information of shareholders or those who
have received the offering prospectus covering shares of Beneficial Interest of
Seligman U.S. Government Securities Series, which contains information about the
sales charges, management fee, and other costs. Please read the prospectus
carefully before investing or sending money.

                                                                    TXUSG3 6/98


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