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                                  SCHEDULE 14A

                                 (RULE 14A-101)

                    INFORMATION REQUIRED IN PROXY STATEMENT

                            SCHEDULE 14A INFORMATION

          PROXY STATEMENT PURSUANT TO SECTION 14(A) OF THE SECURITIES

                     EXCHANGE ACT OF 1934 (AMENDMENT NO.  )
 
Filed by the registrant /X/
 
Filed by a party other than the registrant / /
 
Check the appropriate box:
 
/ / Preliminary proxy statement             / / Confidential, for Use of the
                                                Commission Only (as permitted by
                                                Rule 14a-6(e)(2))
 
/ / Definitive proxy statement
 
/X/ Definitive additional materials
 
/ / Soliciting material pursuant to Rule 14a-11(c) or Rule 14a-12

                        KEMPER MULTI-MARKET INCOME TRUST
- --------------------------------------------------------------------------------
                (Name of Registrant as Specified in Its Charter)

                        KEMPER MULTI-MARKET INCOME TRUST
- --------------------------------------------------------------------------------
    (Name of Person(s) Filing Proxy Statement, if other than the Registrant)
 
Payment of filing fee (Check the appropriate box):
 
/ / $125 per Exchange Act Rule 0-11(c)(1)(ii), 14a-6(i)(1), or 14a-6(i)(2) or
Item 22(a)(2) of Schedule 14A.
 
/ / $500 per each party to the controversy pursuant to Exchange Act Rule
14a-6(i)(3).
 
/ / Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.
 
(1) Title of each class of securities to which transaction applies:
 
- --------------------------------------------------------------------------------
 
(2) Aggregate number of securities to which transaction applies:
 
- --------------------------------------------------------------------------------
 
(3) Per unit price or other underlying value of transaction computed pursuant to
Exchange Act Rule 0-11 (Set forth the amount on which the filing fee is
calculated and state how it was determined):
 
- --------------------------------------------------------------------------------
 
(4) Proposed maximum aggregate value of transaction:
 
- --------------------------------------------------------------------------------
 
(5) Total fee paid:
 
- --------------------------------------------------------------------------------
 
/X/ Fee paid previously with preliminary materials.
 
- --------------------------------------------------------------------------------
 
/ / Check box if any part of the fee is offset as provided by Exchange Act Rule
0-11(a)(2) and identify the filing for which the offsetting fee was paid
previously. Identify the previous filing by registration statement number, or
the form or schedule and the date of its filing.
 
(1) Amount previously paid:
 
- --------------------------------------------------------------------------------
 
(2) Form, schedule or registration statement no.:
 
- --------------------------------------------------------------------------------
 
(3) Filing party:
 
- --------------------------------------------------------------------------------
 
(4) Date filed:
 
- --------------------------------------------------------------------------------
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                        KEMPER EXECUTIVE COUNCIL LOGO

                Attention Kemper Executive Council Members!!!

                             Zurich Proxy Mailing

As you were previously informed, proxy materials regarding the pending
Zurich/Kemper merger mailed to shareholders between July 7 and July 13.  That
means you may be getting questions from your clients soon, if you haven't
already.

The following is a sample letter that you may wish to use to contact your
Kemper fund shareholders with regard to the proxy, and encourage their vote on
these important matters.  Please note that due to filing requirements, this
letter may not be changed.

Samples of the proxy statement are now available for your review.  Just call
your Kemper Executive Council Sales Support Representatives at 1-800-474-5320.

Thanks for your continued support.

   3
July 1995

Shareholder Name
Address
City, State Zip

Dear         :

As you may already know, Kemper Corporation, the parent company of Kemper
Financial Services, Inc., has entered into an agreement to be acquired by an
investor group comprised of Zurich Insurance Group and Insurance Partners.      
Your Kemper fund and investment will not change as a result of this merger. 
You will still own the same shares in the same fund.

The merger of Kemper Corp. and Zurich Insurance is contingent upon several
customary conditions, including the approval of the Kemper mutual fund boards
of trustees and shareholders.  Consequently, you were recently sent a
shareholder proxy statement that requires your vote on several important
issues.

The first item addressed in the proxy is the election of the funds' board of
trustees.  The second item asks you to ratify the selection of Ernst & Young
LLP as the funds independent auditors.  You are then asked to approve an
investment management agreement with Kemper Financial Services, Inc. or its
successor.  The terms of the agreement are the same as the current agreement. 
However, federal law requires that shareholders approve a new agreement in
cases where control of the investment manager changes.

Finally, shareholders with Class B or Class C Shares will be asked to approve a
new Rule 12b-1 distribution plan with Kemper Distributors, Inc. or its
successor.  Although the advisory fees charged to your fund will not change and
the fee rate payable under your fund's 12b-1 plan will not change, federal law
requires shareholder approval with regard to this matter as well.

I encourage you to take a few moments to review your proxy statement and
exercise your right as a shareholder to vote on these issues.  If you have any
questions concerning the proxy, please feel free to call me directly at (phone
#) or contact Kemper Shareholder Services toll-free at 1-800-621-1048.

Very truly yours,