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                                                                  EXHIBIT (a)(4)

Dear Shareholder:

     As you requested, we are enclosing a copy of the Van Kampen Senior Floating
Rate Fund ("Trust") Offer to Purchase 23,135,904 of its issued and outstanding
common shares of beneficial interest ("Common Shares") and the related Letter of
Transmittal (which together constitute the "Offer"). The Offer is at the net
asset value per Common Share ("NAV") determined as of 5:00 P.M. Eastern Standard
time on the Expiration Date of the Offer. An "Early Withdrawal Charge" will be
imposed on most Common Shares accepted for payment that have been held for less
than one year. Please read carefully the enclosed documents.

     If, after reviewing the information set forth in the Offer, you wish to
tender Common Shares for purchase by the Trust, please either follow the
instructions contained in the Offer to Purchase and Letter of Transmittal or, if
your Common Shares are held of record in the name of a broker, dealer or other
nominee, contact such broker, dealer or nominee to effect the tender for you.

     Neither the Trust nor its Board of Trustees is making any recommendation to
any holder of Common Shares as to whether to tender Common Shares. Each
shareholder is urged to consult his or her broker or tax adviser before deciding
whether to tender any Common Shares.

     The Trust's NAV per Common Share from April 13, 1998 through April 13, 2000
ranged from a high of $10.12 to a low of $9.76. On April 13, 2000 the NAV was
$9.77 per Common Share. You can obtain current NAV quotations from Van Kampen
Funds Inc. by calling (800) 341-2911 between the hours of 7:00 A.M. and 7:00
P.M. Central Standard time, Monday through Friday, except holidays. NAV quotes
also may be obtained through the ICI Pricing Service which will be released each
Friday evening and published by the Dow Jones Capital Markets Wire Service on
each Friday; published in the New York Times on each Saturday; published in the
Chicago Tribune on each Sunday; and published weekly in Barron's magazine. The
Trust offers and sells its Common Shares to the public on a continuous basis.
The Trust is not aware of any secondary market trading for the Common Shares.

     Should you have any questions on the enclosed material, please call Van
Kampen Funds Inc. at (800) 341-2911 during ordinary business hours. We
appreciate your continued interest in Van Kampen Senior Floating Rate Fund.

                                        Sincerely,

                                        VAN KAMPEN SENIOR FLOATING RATE FUND

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TO ENSURE PROCESSING OF YOUR REQUEST, A LETTER OF TRANSMITTAL OR A MANUALLY
SIGNED FACSIMILE OF IT (TOGETHER WITH ANY CERTIFICATES FOR COMMON SHARES AND ALL
OTHER REQUIRED DOCUMENTS) MUST BE RECEIVED BY THE DEPOSITARY ON OR BEFORE THE
EXPIRATION DATE (MAY 19, 2000).

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