SELIGMAN HENDERSON GLOBAL FUND SERIES INC
24F-2NT, 1998-12-31
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                  U.S. SECURITIES AND EXCHANGE COMMISSION
                           Washington, D.C. 20549


                                 Form 24F-2
                     Annual Notice of Securities Sold
                           Pursuant to Rule 24f-2

Read instructions at end of Form before preparing Form.  Please print or type.

1.       Name and address of issuer:Seligman Henderson Global Fund Series, Inc.
                                    100 Park Avenue
                                    New York, NY 10017

2.       The name of each series or class of securities for which this Form is
         filed (If the Form is being filed for all series and classes of
         securities of the issuer, check the box but do not list series or
         classes):       [     X      ]


3.       Investment Company Act File Number:         811-6485

         Securities Act File Number:                 33-44186

4(a).    Last day of fiscal year for which this notice is filed:       10/31/98

4(b).    Check box if this Form is being filed late (i.e. more than 90 calendar
         days after the end of the issuer's fiscal year). (See Instruction A.2)
         [              ]
         Note: If the Form is being filed late, interest must be paid on the 
               registration fee due.

4(c).    Check box if this is the last time the issuer will be filing this Form.
         [              ]
<TABLE>
<CAPTION>
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5.       Calculation of registration fee:
 
         (i)      Aggregate sale price of securities sold during
                  the fiscal year pursuant  to section 24 (f):                          $ 1,345,410,882

         (ii)     Aggregate price of securities redeemed or
                  repurchased during the fiscal year:                                   $ 1,345,410,882

         (iii)    Aggregate price of securities redeemed or
                  repurchased during any PRIOR fiscal year
                  ending no earlier than October 11, 1995
                  that were not previously used to reduce
                  registration fees payable to the Commission:                          $ -0-

         (iv)     Total available redemption credits (add
                  Items 5(ii) and 5(iii):                                               $ 1,345,410,882

         (v)      Net Sales - if Item 5(i) is greater than                              $  -0-
                  Item 5(iv), subtract Item 5(iv) from
                  Item 5(i):

 
(vi)     Redemption credits available for use in
         future years (If Item 5(i) is less than
         Item 5(iv), subtract Item 5(iv) from
         Item 5(i):                                                                     $ -0-

(vii)    Multiplier for determining registration
         fee (See Instruction C.9):                                                     x  .000278

(viii)   Registration fee due (multiply Item 5(v)
         by Item 5(vii) (enter "0" if no fee is due):                                   $ -0-

</TABLE>

6.       If the response to item 5(i) was determined by deducting an amount of
         securities that were registered under the Securities Act of 1933
         pursuant to rule 24e-2 in effect before October 11, 1997, then report
         the amount of securities (number of shares or other units) deducted  
         here:    [  - 0 -  ]
                                                                                
         If there is a number of shares or other units that were registered
         pursuant to rule 24e-2 remaining unsold at the end of the fiscal year 
         for which this form is filed that are available for use by the issuer 
         in future fiscal years, then state that number here:  [  - 0 -  ]

7.       Interest due -- if this form is being filed more than 90 days after
         the end of the issuer's fiscal year (see Instruction D): $ -0-

8.       Total of the amount of the registration fee due plus any interest
         due (line 5(viii) plus line 7):    $ -0-

9.       Date the registration fee and interest payment was sent to the
         Commission's lockbox depository:     12/31/98

         Method of delivery         [  X  ]Wire Transfer
                                    [       ]Mail or other means

                                 SIGNATURES

This report has been signed below by the following person on behalf of
the issuer and in the capacity and on the date indicated.

By (Signature and Title)

                                /S/
                           Thomas G. Rose
                             Treasurer
Date: December 31, 1998













               SELIGMAN HENDERSON GLOBAL FUND SERIES, INC.

         The undersigned, Treasurer of Seligman Henderson Global Fund Series,
         Inc., a Maryland corporation (the "Company"), does hereby certify as 
         follows:

    1.    From November 1, 1997 through October 31, 1998, the Company issued
          an aggregate of 98,591,759 shares of its Capital Stock, $0.001 par
          value as follows:

          Seligman Henderson Emerging Markets Growth Fund            6,002,810
          Seligman Henderson Global Growth Opportunities Fund        7,283,475
          Seligman Henderson Global Smaller Companies Fund          35,738,787
          Seligman Henderson Global Technology                      42,596,066
          Seligman Henderson International Fund                      6,970,621

    2.    In respect of the issuance of such 98,591,759 shares, the
          Company received aggregate cash consideration (net of any
          sales commissions) of $1,343,067,676 as follows:

          Seligman Henderson Emerging Markets Growth Fund           39,388,856
          Seligman Henderson Global Growth Opportunities Fund       72,100,602
          Seligman Henderson Global Smaller Companies Fund         553,977,607
          Seligman Henderson Global Technology                     551,731,697
          Seligman Henderson International Fund                    125,868,914

    3.    With respect to each share issued, the Company received cash
          consideration not less than the net asset value per
          share on the date issued and not less than $0.001.

    4.    At no time during the period from November 1, 1997 through October
          31, 1998, were any shares of the Company's Capital Stock issued and
          outstanding in excess of the following numbers of authorized shares:

         Seligman Henderson Emerging Markets Growth Fund           400,000,000
         Seligman Henderson Global Growth Opportunities Fund       400,000,000
         Seligman Henderson Global Smaller Companies Fund          400,000,000
         Seligman Henderson Global Technology                      400,000,000
         Seligman Henderson International Fund                     400,000,000

         In Witness Whereof, I have hereunto signed my name as Treasurer of the
         Company.

Date:    December 31, 1998

                                              ___________/S/_____________
                                                   Thomas G. Rose
                                                     Treasurer




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