SELIGMAN HIGH INCOME FUND SERIES
N-30D, 1999-02-26
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<PAGE>
                             SELIGMAN ADVISORS, INC.
                                 an affiliate of
                                     [LOGO]
                             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.

                                                                    TXUSG2 12/98


                                   
                                   SELIGMAN
                            ---------------------
                               U.S. Government
                              Securities Series


                                Annual Report
                              December 31, 1998


                        Seeking High Current Income by
                    Investing in US Government Securities



<PAGE>
To the Shareholders

Seligman U.S. Government Securities Series had a solid year in 1998, posting a
total return of 8.46% based on the net asset value of Class A shares. This
performance outpaced the 8.08% total return of the Fund's peers, as measured by
the Lipper General US Government Bond Funds Average. The Lehman Brothers
Government Bond Index, which measures the performance of government bonds, had a
total return of 9.85%.

The past year was one of continued growth for the US economy, with real domestic
growth of 3.9%, marking the eighth year of economic expansion in the US.
Throughout the year, unemployment was down and consumer spending up, all in a
low-inflation environment. However, financial uncertainty throughout the world
placed a drag on US economic growth. In response, the Federal Reserve Board cut
the federal-funds rate three times. These actions confirmed the Fed's resolve to
protect the US economy from the global financial crisis and markets responded
favorably throughout November and December.

As investors everywhere became increasingly concerned about a global financial
meltdown, money poured into the world's highest credit quality securities -- US
Treasury bonds. This "flight to quality" helped to push US Treasury yields to
30-year lows. The 30-year US Treasury bond yield began the year at 5.92%, fell
as low as 4.70%, and ended the year at 5.09%. At the same time, the federal
budget surplus caused a decrease in the overall supply of bonds, as the
government needed less paper to finance spending. These factors all proved
positive for Seligman U.S. Government Securities Series.

We believe that many of the factors that benefited the Fund in 1998 should
continue in 1999. In addition, the Fund will continue to seek opportunities in
non-Treasury agency securities, which are backed by the full faith and credit of
the US government, to enhance yield and total return.

Seligman continues to work to ensure that all of its operations are prepared for
the challenges posed by the Year 2000 (Y2K) computer problem. We are confident
that there will be no disruption in the investment and shareholder services
provided by your Fund as a result of Y2K. In addition, your portfolio management
team considers the potential ramifications of Y2K when making decisions on which
securities should be held by the Fund.

Thank you for your continued support of Seligman U.S. Government Securities in
1998. We look forward to serving your investment needs in 1999.

By order of the Trustees,


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

                                                               /s/ Brian T. Zino
                                                                   Brian T. Zino
                                                                       President
January 29, 1999

                                      1

<PAGE>
Interview With Your Portfolio Manager, Gary S. Zeltzer

Q.  How did Seligman U.S. Government Securities Series perform in 1998?

A.  Seligman U.S. Government Securities Series performed well in 1998. The Fund
    posted a total return of 8.46% based on the net asset value of Class A
    shares. At the same time, the Lipper General US Government Bond Funds
    Average, which measures the performance of the Fund's peer group, returned
    8.08%. The Lehman Brothers Government Bond Index, which measures the
    performance of government bonds in the market, returned 9.85%.

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

A.  The US economic expansion has continued for eight consecutive years, and 
    while concerns have surfaced that the pace of growth has been slowing, the 
    economy remains strong. Throughout the past year, unemployment was down 
    and consumer spending was up, all in a low-inflation environment.

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]    
Taxable Fixed Income Team: (standing, from left)
Deborah Joseph (Administrative Assistant), Nicholas Walsh, Brian Turner, 
(seated) Susan Egan, Gary Zeltzer (Portfolio Manager)



    Global events affected the US economy and markets as the year progressed. 
    The Asian economic crisis, which began in a few countries in late 1997, 
    spread throughout the world's emerging markets. Worldwide concern grew in 
    August of 1998 when Russia defaulted on its debt and devalued its 
    currency. Fear then spread to Latin America as Brazil struggled in vain to 
    protect its currency, the real. In the midst of the turmoil, a single US 
    hedge fund, with a number of bad currency investments, almost caused a 
    global financial meltdown.
    
    The global financial uncertainty contributed to a slowing of the pace of 
    US economic growth, while the rate of inflation remained muted. In 
    response, the Federal Reserve Board lowered the federal-funds rate--in
    September, in October, and again in November. The final move was 
    unexpected and underscored the potential threat to the US economy from 
    overseas financial problems. As investors around the world feared 
    

                                      2


<PAGE>
Interview With Your Portfolio Manager, Gary S. Zeltzer

    the worst, they poured money into the largest and most liquid US stocks as 
    well as into US Treasury bonds, which carry the highest credit quality in 
    the world.
    
    The global "flight to quality" helped drive US stock prices to new highs and
    US Treasury yields to 30-year lows. The 30-year US Treasury Bond yield
    closed the year at 5.09%, down from 5.92% at December 31, 1997. In fact, the
    30-year US Treasury Bond yield fell as low as 4.70% before moving up by
    year-end. At the same time, the federal budget surplus caused a decrease in
    the overall supply of bonds, as the government needed less paper to finance
    spending. Falling yields and a supply shortage caused bond prices to rise,
    which was positive for Seligman U.S. Government Securities Series.

Q.  What was your investment strategy?

A.  While we looked to take advantage of attractive fundamentals, we remained 
    more concerned with finding long-term trends than short-term technical 
    situations. As the spreads between Treasury and agency securities widened, 
    we increased our exposure to agencies to add yield to the Portfolio. We 
    made some adjustments to the portfolio's exposure to mortgage-backed 
    securities as the year progressed, selling higher-coupon securities as 
    concerns over prepayments in a falling interest-rate environment made 
    other areas more attractive. Although the Fund had only modest exposure to 
    mortgage-backed securities, the fact that the Fund held any at all was a 
    slight negative on performance in the third quarter as the flight to 
    Treasuries hurt all other types of bonds.

Q.  What is your outlook?

A.  Moderate unemployment, ongoing consumer strength, and weak commodity 
    prices all bode well for the economy. If growth is seen as too strong, the 
    Fed may raise rates. Going forward, we may shorten the Fund's duration as
    the rewards of a longer duration become less compelling. The Fund's 
    duration is currently about 4.9 years, which is slightly shorter than that 
    of our benchmark, the Lehman Brothers Government Bond Index. 

    Ongoing global problems should benefit the US Treasury market, and 
    therefore the Fund. We will continue to seek opportunities in non-Treasury 
    securities to enhance yield and total return. And finally, the continuing
    erosion of the budget deficit should keep supply low and demand high. All 
    these factors are positive for Seligman U.S. Government Securities Series.

                                      3

<PAGE>
Performance Overview

   This chart compares a $10,000 hypothetical investment made in Seligman U.S.
Government Securities Series Class A shares, with and without the initial 4.75%
maximum sales charge, and assumes that all distributions within the period are
invested in additional shares, for the 10-year period ended December 31, 1998,
to a $10,000 investment made in the Lehman Brothers Government Bond Index
(Lehman Bond Index) and the Lipper General US Government Bond Funds Average
(Lipper Average) for the same period. The performances of Seligman U.S.
Government Securities Series Class B and Class D shares are not shown in this
chart, but are included in the table on page 5. It is important to keep in mind
that the Lehman Bond Index and the Lipper Average exclude the effect of fees
and/or sales charges.


Seligman U.S. Government Securities Series Class A

           With       Without     Lehman   Lipper 
           Sales      Sales       Bond     Average
           Charge     Charge      Index

12/31/88   $ 9,528    $10,000    $10,000    $10,000
3/31/89    $ 9,540    $10,013    $10,106    $10,088
6/30/89    $10,046    $10,545    $10,919    $10,779
9/30/89    $10,110    $10,611    $11,009    $10,857
12/31/89   $10,409    $10,925    $11,423    $11,232
3/31/90    $10,154    $10,658    $11,281    $11,112
6/30/90    $10,446    $10,963    $11,676    $11,471
9/30/90    $10,505    $11,026    $11,773    $11,540
12/31/90   $11,073    $11,622    $12,420    $12,157
3/31/91    $11,249    $11,807    $12,689    $12,419
6/30/91    $11,411    $11,977    $12,860    $12,563
9/30/91    $12,036    $12,633    $13,359    $13,275
12/31/91   $12,628    $13,254    $14,322    $13,956
3/31/92    $12,359    $12,972    $14,071    $13,682
6/30/92    $12,838    $13,474    $14,629    $14,198
9/30/92    $13,363    $14,025    $15,351    $14,801
12/31/92   $13,358    $14,021    $15,357    $14,846
3/31/93    $13,743    $14,424    $16,052    $15,439
6/30/93    $14,063    $14,761    $16,515    $15,857
9/30/93    $14,401    $15,115    $17,052    $16,297
12/31/93   $14,354    $15,066    $16,994    $16,236
3/31/94    $14,059    $14,756    $16,483    $15,702
6/30/94    $13,834    $14,519    $16,295    $15,432
9/30/94    $13,870    $14,557    $16,363    $15,443
12/31/94   $13,797    $14,481    $16,420    $15,484
3/31/95    $14,299    $15,008    $17,194    $16,206
6/30/95    $15,208    $15,962    $18,260    $17,163
9/30/95    $15,443    $16,208    $18,583    $17,477
12/31/95   $16,302    $17,110    $19,432    $18,266
3/31/96    $15,734    $16,514    $18,993    $17,771
6/30/96    $15,672    $16,449    $19,084    $17,780
9/30/96    $15,871    $16,658    $19,405    $18,053
12/31/96   $16,254    $17,059    $19,972    $18,574
3/31/97    $16,094    $16,892    $19,810    $18,387
6/30/97    $16,602    $17,425    $20,497    $19,038
9/30/97    $17,017    $17,861    $21,184    $19,658
12/31/97   $17,640    $18,514    $21,887    $20,251
3/31/98    $17,800    $18,682    $22,218    $20,514
6/30/98    $18,276    $19,182    $22,804    $20,994
9/30/98    $19,143    $20,092    $24,065    $21,956
12/31/98   $19,132    $20,081    $24,046    $21,887


   Although the payment of principal and interest with respect to certain
long-term securities held in Seligman U.S. Government Securities Series are
guaranteed by the US government or its agencies, the rate of return will vary
and the principal value of an investment in the Fund will fluctuate. Shares, if
redeemed, may be worth more or less than their original cost. Past performance
is not indicative of future investment results.

                                      4

<PAGE>
Performance Overview

Investment Results Per Share

<TABLE>
<CAPTION>

TOTAL RETURNS
For Periods Ended December 31, 1998                                            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                        (0.34)%        3.35%         4.88%        6.70%        n/a           n/a
Without Sales Charge                      4.68          8.46          5.91         7.22         n/a           n/a
Class B**
With CDSC+                               (0.72)         2.78           n/a          n/a        5.68%          n/a
Without CDSC                              4.28          7.78           n/a          n/a        7.56           n/a
Class D**
With 1% CDSC                              3.28          6.78           n/a          n/a         n/a           n/a
Without CDSC                              4.28          7.78          5.01          n/a         n/a          4.61%
Lehman Brothers Government
   Bond Index++                           5.44          9.85          7.19         9.17        9.72          6.76+++
Lipper General US Government
   Bond Funds Average++                   4.26          8.08          6.16         8.15        8.55          5.77+++

</TABLE>

<TABLE>
<CAPTION>

NET ASSET VALUE                                            DIVIDEND AND YIELD INFORMATION
                                                           For the Year Ended December 31, 1998

          DECEMBER 31,     JUNE 30,    DECEMBER 31,
              1998           1998          1997                       DIVIDENDS0         YIELD00
        ----------------  ---------- ----------------                 -------------     --------
<S>             <C>           <C>           <C>            <C>            <C>              <C>
Class A         $7.09         $6.94         $6.88          Class A        $0.3563          4.40%
Class B          7.11          6.96          6.89          Class B         0.3030          3.70
Class D          7.11          6.96          6.89          Class D         0.3030          3.70

WEIGHTED AVERAGE MATURITY  11.75 years

<FN>
- ------------------
  * 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 charge
    ("CDSC"), 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% CDSC,
    charged on redemptions made within one year of the date of purchase.
  + The CDSC is 5% for periods of one year or less, and 4% since inception.
 ++ The Lehman Brothers Government Bond Index and the Lipper General US
    Government Bond Funds Average are unmanaged benchmarks that assume
    investment of dividends. The Lehman Brothers Government Bond Index and the
    Lipper General US Government Bond Funds Average exclude the effect of fees
    and/or 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 year ended December 31,
    1998.
 00 Current yield, representing the annualized yield for the 30-day period ended
    December 31, 1998, has been computed in accordance with SEC regulations and
    will vary.

</FN>
</TABLE>

                                      5

<PAGE>
Portfolio of Investments
December 31, 1998

<TABLE>
<CAPTION>


                                                                                          PRINCIPAL
                                                                                           AMOUNT              VALUE
                                                                                       --------------     ---------------
<S>                                                                                       <C>              <C>
US TREASURY SECURITIES 44.8% 

US Treasury Bonds:
   8-3/4%, due 5/15/2020..........................................................        $6,000,000       $ 8,538,750
   6-1/4%, due 8/15/2023 .........................................................         3,000,000         3,357,189
   6-5/8%, due 2/15/2027..........................................................         2,500,000         2,957,812
   5-1/4%, due 11/15/2028.........................................................         2,200,000         2,255,689
US Treasury Notes:
   5%, due 2/15/1999..............................................................         4,000,000         4,002,500
   5-3/8%, due 1/31/2000 .........................................................         6,000,000         6,048,750
   6-3/8%, due 9/30/2001 .........................................................         5,000,000         5,218,750
   6-1/4%, due 8/31/2002..........................................................         7,500,000         7,884,375
   6-5/8%, due 5/15/2007..........................................................         8,000,000         9,000,000
                                                                                                           -----------
TOTAL US TREASURY SECURITIES (Cost $47,236,046) ..................................                          49,263,815
                                                                                                           -----------

US GOVERNMENT AGENCY SECURITIES  44.8%
Aid-Israel, 0%, due 11/15/2010....................................................         7,000,000         3,703,910
Federal Farm Credit Bank:
   4.65%, due 8/3/1999............................................................         1,500,000         1,499,409
   5-5/8%, due 9/2/2003...........................................................         2,645,000         2,687,412
Federal Home Loan Bank:
   6%, due 8/27/2002..............................................................         2,000,000         2,000,086
   5.89%, due 6/30/2008 ..........................................................         2,500,000         2,599,945
Federal Home Loan Mortgage ("Freddie Mac"):
   5-3/4%, due 7/15/2003..........................................................         2,500,000         2,572,045
   5-1/8%, due 10/15/2008.........................................................         2,000,000         1,965,076
Federal National Mortgage Association ("Fannie Mae"):
   5-3/4%, due 4/15/2003..........................................................         3,500,000         3,598,427
   5.91%, due 8/25/2003...........................................................           750,000           755,181
Government National Mortgage Association ("Ginnie Mae") Obligations,
   Mortgage-backed Pass-through Certificates:*
   6%, due 5/15/2013..............................................................         4,845,190         4,880,018
   6-1/2%, due 12/15/2028.........................................................         6,400,000         6,470,016
   6%, due 12/20/2028.............................................................         5,400,000         5,352,750
Tennessee Valley Authority, 6-1/8%, due 7/15/2003.................................         2,500,000         2,543,378
US Government Title XI (Rowan Companies),
   6.15%, due 7/1/2010 ...........................................................         2,395,000         2,448,940
US Government Title XI (American Heavy Lift),
   7.18%, due 6/1/2017............................................................         3,000,000         3,128,334

</TABLE>
- ------------------
See footnotes on page 7.

                                        6

<PAGE>
Portfolio of Investments
December 31, 1998

<TABLE>
<CAPTION>
                                                                                       PRINCIPAL
                                                                                        AMOUNT              VALUE
                                                                                    --------------     ---------------
<S>                                                                                    <C>             <C>
US GOVERNMENT AGENCY SECURITIES (continued)

US Government Title XI (Bay Transportation),
   7.30%, due 6/1/2021.........................................................        $2,860,000      $  3,123,921
                                                                                                       ------------
TOTAL US GOVERNMENT AGENCY SECURITIES (Cost $48,974,296) ......................                          49,328,848
                                                                                                       ------------

REPURCHASE AGREEMENT  8.8%  (Cost $9,712,000)
HSBC Securities Inc., 4.45%, maturing 1/4/1999, collateralized by:
   $8,485,000 US Treasury Notes, 11-5/8%, due 8/15/2004, with a fair
   market value of $9,907,621 .................................................         9,712,000         9,712,000
                                                                                                       ------------

TOTAL INVESTMENTS  98.4% (Cost $105,922,342) ..................................                         108,304,663
OTHER ASSETS LESS LIABILITIES  1.6% ...........................................                           1,736,143
                                                                                                       ------------
NET ASSETS  100.0% ............................................................                        $110,040,806
                                                                                                       ============
</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.

                                      7

<PAGE>
Statement of Assets and Liabilities
December 31, 1998

<TABLE>

<S>                                                                       <C>                    <C>
ASSETS:
Investments, at value:
   Long-term holdings (Cost $96,210,342)....................              $98,592,663
   Short-term holdings (Cost $9,712,000)....................                9,712,000            $108,304,663
                                                                         ------------
Cash.................................................................................                 510,567
Interest receivable..................................................................               1,274,034
Receivable for shares of Beneficial Interest sold....................................                 642,077 
Receivable for securities sold.......................................................                 105,000 
Expenses prepaid to shareholder service agent........................................                  12,296
Other................................................................................                  33,670
                                                                                                 ------------
Total Assets.........................................................................             110,882,307
                                                                                                 ------------
LIABILITIES:
Payable for shares of Beneficial Interest repurchased................................                 492,112
Dividends payable....................................................................                 181,563
Accrued expenses, taxes, and other...................................................                 167,826
                                                                                                 ------------
Total Liabilities....................................................................                 841,501
                                                                                                 ------------
Net Assets...........................................................................            $110,040,806
                                                                                                 ============
COMPOSITION OF NET ASSETS:
Shares of Beneficial Interest, at par ($0.001 par value; unlimited shares authorized; 
   15,501,558 shares outstanding):
   Class A...........................................................................            $      7,828
   Class B...........................................................................                   3,929
   Class D...........................................................................                   3,745
Additional paid-in capital...........................................................             117,269,391 
Accumulated net realized loss........................................................              (9,626,408)
Net unrealized appreciation of investments...........................................               2,382,321
                                                                                                 ------------
Net Assets...........................................................................            $110,040,806
                                                                                                 ============
NET ASSET VALUE PER SHARE:
Class A ($55,503,080 / 7,828,006 shares).............................................                   $7.09
                                                                                                        =====
Class B ($27,923,644 / 3,928,932 shares).............................................                   $7.11
                                                                                                        =====
Class D ($26,614,082 / 3,744,620 shares).............................................                   $7.11
                                                                                                        =====

</TABLE>

- ------------------
See notes to financial statements.

                                      8

<PAGE>
Statement of Operations
For the Year Ended December 31, 1998

<TABLE>

<S>                                                                                  <C>                      <C>
INVESTMENT INCOME:
Interest.....................................................................................                 $4,657,795

EXPENSES:
Management fee....................................................                $  382,195
Distribution and service fees.....................................                   375,102
Shareholder account services......................................                   125,133
Registration......................................................                    68,008
Auditing and legal fees...........................................                    15,240
Custody and related services......................................                    11,765
Shareholder reports and communications............................                    11,242
Trustees' fees and expenses.......................................                     5,501
Miscellaneous.....................................................                     7,381
                                                                                  ----------
Total Expenses..............................................................................                   1,001,567
                                                                                                              ----------
Net Investment Income.......................................................................                   3,656,228

NET REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
Net realized gain on investments..................................                 1,895,993
Net change in unrealized appreciation of investments..............                   118,769
                                                                                  ----------
Net Gain on Investments.....................................................................                   2,014,762
                                                                                                              ----------
Increase in Net Assets from Operations......................................................                  $5,670,990
                                                                                                              ==========
</TABLE>

- ------------------
See notes to financial statements.

                                      9

<PAGE>
Statements of Changes in Net Assets

<TABLE>
<CAPTION>

                                                                                                YEAR ENDED DECEMBER 31,
                                                                                   --------------------------------------------
                                                                                               1998               1997
                                                                                          ----------------  ---------------
<S>                                                                                          <C>            <C>
OPERATIONS:
Net investment income..............................................                           $ 3,656,228     $ 3,013,241
Net realized gain (loss) on investments............................                             1,895,993        (611,943)
Net change in unrealized appreciation of investments...............                               118,769       1,949,757
                                                                                              -----------       ---------
Increase in Net Assets from Operations.............................                            5,670,990        4,351,055
                                                                                              -----------      ----------
DISTRIBUTIONS TO SHAREHOLDERS:
Net investment income:
   Class A.........................................................                            (2,495,781)     (2,522,929)
   Class B.........................................................                              (431,493)        (45,289)
   Class D.........................................................                              (728,954)       (445,023)
                                                                                               -----------    -----------
Decrease in Net Assets from Distributions..........................                            (3,656,228)     (3,013,241)
                                                                                               -----------    -----------
</TABLE>

<TABLE>
<CAPTION>
                                                                SHARES
                                                 ----------------------------------------
                                                          YEAR ENDED DECEMBER 31,
TRANSACTIONS IN SHARES                           ----------------------------------------
  OF BENEFICIAL INTEREST:                             1998                      1997
                                                 --------------            --------------
<S>                                                <C>                         <C>             <C>               <C>
Net proceeds from sale of shares:
   Class A................................           2,363,194                  829,234         16,457,004        5,624,748
   Class B................................             562,070                  182,897          3,968,163        1,228,800
   Class D................................             499,654                  198,244          3,525,890        1,326,662
Investment of dividends:
   Class A................................             202,386                  202,913          1,412,846        1,359,967
   Class B................................              39,408                    5,291            278,047           35,836
   Class D................................              71,043                   42,659            500,118          286,730
Exchanged from associated Funds:
   Class A................................           5,226,303                1,572,537         36,731,913       10,660,240
   Class B................................           4,842,484                  574,598         34,312,850        3,899,673
   Class D................................           6,629,069                1,591,469         46,721,951       10,742,800
                                                   -----------               ----------         ----------      -----------
Total.....................................          20,435,611                5,199,842         43,908,782       35,165,456
                                                   -----------               ----------         ----------      -----------
Cost of shares repurchased:
   Class A................................          (1,430,402)              (1,364,274)        10,025,783)      (9,183,343)
   Class B................................            (326,753)                 (14,942)        (2,312,760)        (101,411)
   Class D................................            (849,272)                (369,696)        (5,973,934)      (2,477,886)
Exchanged into associated Funds:
   Class A................................          (5,139,464)              (1,618,861)       (35,957,745)     (10,932,716)
   Class B................................          (1,655,633)                (280,488)       (11,698,641)      (1,910,778)
   Class D................................          (4,398,523)              (1,050,159)       (30,908,764)      (7,074,255)
                                                   -----------               ----------        ------------      -----------
Total.....................................         (13,800,047)              (4,698,420)       (96,877,627)     (31,680,389)
                                                   -----------               ----------        ------------      -----------
Increase in Net Assets from
   Transactions in Shares of
   Beneficial Interest....................           6,635,564                  501,422         47,031,155        3,485,067
                                                   ===========               ==========        -----------      -----------
Increase in Net Assets.................................................................         49,045,917        4,822,881
NET ASSETS:
Beginning of year......................................................................         60,994,889       56,172,008
                                                                                               -----------      -----------
End of Year............................................................................       $110,040,806      $60,994,889
                                                                                              ============      ===========
</TABLE>

- ------------------
See notes to financial statements.

                                      10

<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 charge ("CDSC") 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 CDSC, 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 CDSC, 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 dis
   tribute 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 agreements, 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 

                                      11

<PAGE>
Notes to Financial Statements

   year ended December 31, 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 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 year ended December 31,
1998, amounted to $110,032,619 and $70,894,043, respectively.

    At December 31, 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 $2,605,345 and $223,024, 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 Advisors, Inc. (the "Distributor") (formerly Seligman Financial
Services, Inc.), agent for the distribution of the Fund's shares, and an
affiliate of the Manager, received concessions of $6,123 from sales of Class A
shares after commissions of $55,467 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 year ended December 31,
1998, fees incurred under the Plan aggregated $107,529 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 share
holder 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.

                                      12

<PAGE>
Notes to Financial Statements

    For the year ended December 31, 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 $99,487 and $168,086, respectively.

    The Distributor is entitled to retain any CDSC 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 year ended
December 31, 1998, such charges amounted to $11,570.

    The Distributor has sold its rights to collect any CDSC imposed on
redemptions of Class B shares to the Purchaser. In connection with the sale of
its rights to collect any CDSC 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 year ended December 31, 1998, amounted to
$5,872.

    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 year ended
December 31, 1998, Seligman Services, Inc. received commissions of $888 from the
sale of Fund shares. Seligman Services, Inc. also received distribution and
service fees of $16,822, pursuant to the Plan.

    Seligman Data Corp., which is owned by certain associated investment
companies, charged the Fund at cost $125,133 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 December 31, 1998, of $39,337
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, 1998, the Fund had a net loss
carryforward for federal income tax purposes of $9,485,627, 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%. 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.

                                      13


<PAGE>
Financial Highlights

     The tables below are intended to help you understand each Class's financial
performance for the past five years or from its inception, if less than five
years. Certain information reflects financial results for a single share of
Beneficial Interest of a Class that was held throughout the periods shown. Per
share amounts are calculated using average shares outstanding. "Total return"
shows the rate that you would have earned (or lost) on an investment in each
Class, assuming you reinvested all your dividends. Total returns do not reflect
any sales charges and are not annualized for periods of less than one year.

<TABLE>
<CAPTION>

                                                                                       CLASS A
                                                               --------------------------------------------------------
                                                                               YEAR ENDED DECEMBER 31,
                                                               --------------------------------------------------------
                                                                  1998       1997        1996       1995        1994
                                                               ----------   -------     -------    -------    ---------
<S>                                                              <C>         <C>         <C>        <C>        <C>
PER SHARE DATA:
Net Asset Value, Beginning of Year ....................          $6.88       $6.71       $7.15      $6.47      $7.18
                                                                 -----       -----       -----      -----      -----
Income from Investment Operations:
Net investment income .................................           0.36        0.38        0.41       0.46       0.44
Net realized and unrealized gain (loss)
  on investments ......................................           0.21        0.17       (0.44)      0.68      (0.71)
                                                                 -----       -----       -----      -----      -----
Total from Investment Operations ......................           0.57        0.55       (0.03)      1.14      (0.27)
Less Distributions:
Dividends from net investment income ..................          (0.36)      (0.38)      (0.41)     (0.46)     (0.44)
                                                                 -----       -----       -----      -----      -----
Total Distributions....................................          (0.36)      (0.38)      (0.41)     (0.46)     (0.44)
                                                                 -----       -----       -----      -----      -----
Net Asset Value, End of Year ..........................          $7.09       $6.88       $6.71      $7.15      $6.47
                                                                 =====       =====       =====      =====      =====
TOTAL RETURN:                                                     8.46%       8.53%      (0.29)%    18.15%     (3.88)%

RATIOS/SUPPLEMENTAL DATA:
Net assets, end of year (000s omitted).................         $55,503     $45,426     $46,889    $55,061    $54,714
Ratio of expenses to average net assets................           1.05%       1.23%       1.14%      1.14%      1.10%
Ratio of net income to average net assets .............           5.11%       5.68%       6.05%      6.71%      6.49%
Portfolio turnover rate ...............................          99.43%     193.90%     175.25%    213.06%    445.18%

</TABLE>
- ------------------
See footnotes on page 15.

                                      14

<PAGE>
Financial Highlights

<TABLE>
<CAPTION>

                                                        CLASS B                             CLASS D
                                         -----------------------------------------------------------------------------------
                                                     YEAR    1/1/97*               YEAR ENDED DECEMBER 31,
                                                     ENDED     TO       ----------------------------------------------------
                                                   12/31/98 12/31/97      1998       1997       1996       1995       1994
                                                   -----------------    ---------   ------     ------     ------     -------
<S>                                                   <C>      <C>        <C>       <C>        <C>        <C>         <C>
PER SHARE DATA:
Net Asset Value, Beginning of Year.................   $6.89    $6.73      $6.89     $6.73      $7.16      $6.48       $7.20
                                                      -----    -----      -----     -----      -----      -----       -----
Income from Investment Operations:
Net investment income .............................    0.30     0.33       0.30      0.33       0.36       0.40        0.37
Net realized and unrealized gain
  (loss) on investments ...........................    0.22     0.16       0.22      0.16      (0.43)      0.68       (0.72)
                                                      -----    -----      -----     -----      -----      -----       -----
Total from Investment Operations ..................    0.52     0.49       0.52      0.49      (0.07)      1.08       (0.35)
Less Distributions:
Dividends from net investment income ..............   (0.30)   (0.33)     (0.30)    (0.33)     (0.36)     (0.40)      (0.37)
                                                      -----    -----      -----     -----      -----      -----       -----
Total Distributions................................   (0.30)   (0.33)     (0.30)    (0.33)     (0.36)     (0.40)      (0.37)
                                                      -----    -----      -----     -----      -----      -----       -----
Net Asset Value, End of Year.......................   $7.11    $6.89      $7.11     $6.89      $6.73      $7.16       $6.48
                                                      =====    =====      =====     =====      =====      =====       =====
TOTAL RETURN:                                          7.78%    7.32%      7.78%     7.53%     (0.92)%    17.10%      (5.05)%

RATIOS/SUPPLEMENTAL DATA:
Net assets, end of year (000s omitted) ............  $27,924   $3,219    $26,614   $12,350     $9,283     $8,181      $6,062
Ratio of expenses to average net assets ...........    1.83%    2.01%      1.83%     2.01%      1.92%      2.01%       2.22%
Ratio of net income to average net assets .........    4.33%    4.90%      4.33%     4.90%      5.27%      5.84%       5.40%
Portfolio turnover rate ...........................   99.43%  193.90%     99.43%   193.90%    175.25%    213.06%     445.18%

</TABLE>
- ------------------
* Commencement of offering of shares.

See notes to financial statements.

                                      15

<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 December 31, 1998, the related statements of operations for the year then
ended and of changes in net assets for each of the years in the two-year period
then ended, 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
December 31, 1998, by correspondence with the Fund's custodian. An audit also
includes assessing the accounting principles used and significant estimates 
made by management, as well as evaluating the overall financial statement 
presentation. We believe that our audits provide a reasonable basis for our 
opinion.

In our opinion, such financial statements and financial highlights present
fairly, in all material respects, the financial position of Seligman U.S.
Government Securities Series as of December 31, 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.


DELOITTE & TOUCHE LLP
New York, New York
January 29, 1999

                                     16

<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.
Director, New York 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, KeySpan Energy Corporation
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.
Director, ICI Mutual Insurance Company

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

                                      17

<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 Advisors, 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

                                      18

<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. 

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 Charge (CDSC) -- Depending on the class of shares
owned, a fee charged by a mutual fund when shares are sold back to the fund
(the CDSC 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, how shares are bought and sold, fund fees and other
charges, and the fund's financial highlights. 

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 an investment company 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 1998 Mutual Fund Fact Book.

                                      19


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