KEMPER U S GOVERNMENT SECURITIES FUND
497, 1999-01-12
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                               KEMPER INCOME FUNDS
                            SUPPLEMENT TO PROSPECTUS
                              DATED JANUARY 1, 1999
                               ------------------
                                 CLASS I SHARES
                               ------------------
                   Kemper Adjustable Rate U.S. Government Fund
                    Kemper Short-Intermediate Government Fund
                         Kemper Diversified Income Fund
                     Kemper U.S. Government Securities Fund
                             Kemper High Yield Fund
                       Kemper High Yield Opportunity Fund
                   Kemper Income and Capital Preservation Fund
                            Kemper U.S. Mortgage Fund
                               ------------------

The above funds currently offer four classes of shares to provide investors with
different  purchasing  options.  These are Class A,  Class B and Class C shares,
which are  described  in the funds'  prospectus,  and Class I shares,  which are
described in the  prospectus  as  supplemented  hereby.  When  placing  purchase
orders,  investors must specify whether the order is for Class A, Class B, Class
C or Class I shares.

Class  I  shares  are  available  for  purchase  exclusively  by  the  following
categories of institutional  investors:  (1) tax-exempt retirement plans (Profit
Sharing,  401(k),  Money Purchase  Pension and Defined Benefit Plans) of Scudder
Kemper  Investments,  Inc.  ("Scudder  Kemper") and its  affiliates and rollover
accounts from those plans;  (2) the  following  investment  advisory  clients of
Scudder Kemper and its investment  advisory  affiliates  that invest at least $1
million in a Fund:  unaffiliated  benefit  plans,  such as qualified  retirement
plans (other than individual  retirement  accounts and self-directed  retirement
plans);  unaffiliated  banks and insurance  companies  purchasing  for their own
accounts;  and endowment funds of  unaffiliated  non-profit  organizations;  (3)
investment-only accounts for large qualified plans, with at least $50 million in
total  plan  assets or at least  1000  participants;  (4)  trust  and  fiduciary
accounts  of trust  companies  and bank trust  departments  providing  fee-based
advisory  services  that  invest at least $1 million in a Fund on behalf of each
trust; (5) policy holders under  Zurich-American  Insurance  Group's  collateral
investment  program  investing at least  $200,000 in a Fund;  and (6) investment
companies  managed by Scudder Kemper that invest  primarily in other  investment
companies.

January 1, 1999

<PAGE>


Class  I  shares   currently   are  available  for  purchase  only  from  Kemper
Distributors,  Inc.  ("KDI"),  principal  underwriter for the Funds, and, in the
case of category 4 above, selected dealers authorized by KDI. Share certificates
are not available for Class I shares.

The primary  distinctions  among the classes of each Fund's  shares lie in their
initial and  contingent  deferred  sales charge  schedules  and in their ongoing
expenses,  including  asset-based  sales  charges  in the  form  of  Rule  12b-1
distribution  fees.  Class I shares are  offered at net asset  value  without an
initial sales charge and are not subject to a contingent  deferred  sales charge
or a Rule 12b-1 distribution fee. Also, there is no administrative  services fee
charged to Class I shares.  As a result of the  relatively  lower  expenses  for
Class I shares,  the level of income dividends per share (as a percentage of net
asset value) and,  therefore,  the overall investment return,  typically will be
higher for Class I shares than for Class A, Class B and Class C shares.

The following information supplements the indicated sections of the prospectus.

Past Performance

The charts and tables  contained  in the  accompanying  prospectus  provide some
indication of the risks of investing in the funds by illustrating  how the funds
have  performed  from year to year,  and comparing  this  information to a broad
measure of market performance. Of course, past performance is not necessarily an
indication of future  performance.  Additional  financial  information for those
funds  which  currently  have  Class I shares  outstanding  is set forth  below.

Average Annual Total Returns -- Class I shares

 For periods ended
 December 31, 1997         One Year      Life of Class       Inception of Class
 -----------------         --------      -------------       ------------------
 Kemper U.S. Government      9.35%            7.42%               7/3/95
 Securities Fund
 Kemper High Yield Fund     11.91%           14.45%              10/1/97
 Kemper Income and Capital   9.02%            7.66%               7/3/95
 Preservation Fund

Expense information

This  information  is designed to help you understand the fees and expenses that
you may pay if you buy and hold shares of the funds.

<PAGE>


Shareholder fees: Fees paid directly from your investment.
<TABLE>
<CAPTION>

                    Maximum      Maximum                           Maximum Deferred
                 Sales Charge     Sales                               Sales Charge
                 on Purchases   Charge on                             (as a % of
                  (as a % of    Reinvested  Redemption  Exchange      redemption
               offering price)   Dividends     Fee        Fee          proceeds)
               ---------------   ---------     ---        ---          ---------

<S>                  <C>           <C>         <C>        <C>            <C>
Kemper               None         None         None       None           None
Adjustable Rate
U.S. Government
Fund

Kemper               None         None         None       None           None
Short-Intermediate
Government Fund

Kemper               None         None         None       None           None
Diversified
Income Fund

Kemper U.S.          None         None         None       None           None
Government
Securities Fund

Kemper High Yield    None         None         None       None           None
Fund

Kemper High Yield    None         None         None       None           None
Opportunity Fund

Kemper Income and    None         None         None       None           None
Capital
Preservation Fund

Kemper U.S.            None         None         None       None         None
Mortgage Fund
</TABLE>


Annual fund operating expenses: Expenses that are deducted from fund assets.

                                                                    Total fund
                         Investment        Rule       Other          operating
                       management fee   12b-1 fees   expenses*       expenses*
                       --------------   ----------   ---------       ---------

Kemper Adjustable        0.55%           None          0.29%           0.84%
Rate U.S.
Government Fund

Kemper                   0.55%           None          0.19%           0.74%
Short-Intermediate
Government Fund

Kemper Diversified       0.56%           None          0.12%           0.68%
Income Fund

Kemper U.S.              0.41%           None          0.16%           0.57%
Government
Securities Fund

Kemper High Yield        0.52%           None          0.08%           0.60%
Fund

<PAGE>
                                                                    Total fund
                         Investment        Rule       Other          operating
                       management fee   12b-1 fees   expenses*       expenses*
                       --------------   ----------   ---------       ---------

Kemper High Yield        0.65%           None          0.36%           1.01%
Opportunity Fund

Kemper Income and        0.53%           None          0.13%           0.66%
Capital
Preservation Fund

Kemper U.S.              0.51%           None          0.13%           0.64%
Mortgage Fund

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

*    Estimated  for  Kemper   Adjustable  Rate  U.S.   Government  Fund,  Kemper
     Short-Intermediate  Government Fund, Kemper Diversified Income Fund, Kemper
     High Yield  Opportunity Fund and Kemper U.S. Mortgage Fund since no Class I
     shares were issued as of the respective fiscal year ends.

Example

This  example is to help you  compare the cost of  investing  in a fund with the
cost of investing in other mutual funds.

This example illustrates the impact of the above fees and expenses on an account
with an initial  investment of $10,000,  based on the expenses  shown above.  It
assumes a 5% annual return,  the reinvestment of all dividends and distributions
and "annual fund operating  expenses"  remaining the same each year. The example
is hypothetical: actual fund expenses and return vary from year to year, and may
be higher or lower than those shown.

Fees and expenses if you sold shares after:

                                   1 Year      3 Years      5 Years    10 Years
                                   ------      -------      -------    --------
 Kemper Adjustable Rate U.S.
 Government Fund                      $86        $268         $466      $1,037

 Kemper Short-Intermediate
 Government Fund                      $76        $237         $411        $918

 Kemper Diversified Income Fund
                                      $69        $218         $379        $847
 Kemper U.S. Government
 Securities Fund                      $58        $183         $318        $714

 Kemper High Yield Fund
                                      $61        $192         $335        $750
 Kemper High Yield Opportunity
 Fund                                $103        $322         $558      $1,236

 Kemper Income and Capital
 Preservation Fund                    $67        $211         $368        $822

 Kemper U.S. Mortgage Fund            $65        $205         $357        $798


<PAGE>


FINANCIAL HIGHLIGHTS

No financial  information  is presented for Class I shares of Kemper  Adjustable
Rate U.S.  Government Fund,  Kemper  Short-Intermediate  Government Fund, Kemper
Diversified  Income  Fund,  Kemper High Yield  Opportunity  Fund and Kemper U.S.
Mortgage Fund,  since no Class I shares were issued as of the respective  fiscal
year ends of the funds.

Kemper U.S. Government Securities Fund

                                                                       July 3 to
                                              Year ended October 31,    October
                                                                           31,
CLASS I                                     1998       1997      1996     1995
- --------------------------------------------------------------------------------
Per share operating performance
Net asset value, beginning of period        $8.81      8.74       8.92      8.88
- --------------------------------------------------------------------------------
Income from investment operations:
  Net investment income                       .59       .66        .64       .22
- --------------------------------------------------------------------------------
  Net realized and unrealized gain (loss)     .07       .06      (.17)       .04
- --------------------------------------------------------------------------------
Total from investment operations              .66       .72        .47       .26
- --------------------------------------------------------------------------------
Less distribution from net investment         .62       .65        .65       .22
  income
- --------------------------------------------------------------------------------
Net asset value, end of period              $8.85      8.81       8.74      8.92
- --------------------------------------------------------------------------------
Total return (not annualized)               7.75%      8.60       5.56      3.02
- --------------------------------------------------------------------------------
Ratios to average net assets (annualized)
Expenses                                     .57%       .60        .59       .53
- --------------------------------------------------------------------------------
Net investment income                       6.73%      7.52       7.35      7.07
- --------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                    Year ended October 31,
                                       1998        1997      1996       1995      1994
<S>                                <C>         <C>        <C>       <C>        <C>
- -----------------------------------------------------------------------------------------
Supplemental data for all classes
Net assets at end of year
  (in thousands)                   $3,442,212  3,642,027  4,163,157 4,738,415  4,941,151
- -----------------------------------------------------------------------------------------
Portfolio turnover rate                150%         261        391       362      1,000
- -----------------------------------------------------------------------------------------

</TABLE>

Note:  Total return does not reflect the effect of any sales charges.  Per share
data were determined based on average shares  outstanding  during the year ended
October 31, 1998.

<PAGE>


Kemper High Yield Fund
                                                                   December 29,
                                                                     1994 to
                                      Year ended September 30,    September 30,
CLASS I                              1998       1997      1996        1995
- --------------------------------------------------------------------------------
Per share operating performance
Net asset value, beginning           $8.50      8.23       8.01      7.55
  of period
- --------------------------------------------------------------------------------
Income from investment operations:
  Net investment income                .76       .78        .78       .66
- --------------------------------------------------------------------------------
  Net realized and unrealized        (.78)       .31        .23       .39
    gain (loss)
- --------------------------------------------------------------------------------
Total from investment operations     (.02)      1.09       1.01      1.05
- --------------------------------------------------------------------------------
Less distribution from net             .80       .82        .79       .59
  investment income
- --------------------------------------------------------------------------------
Net asset value, end of period       $7.68      8.50       8.23      8.01
- --------------------------------------------------------------------------------
Total return (not annualized)       (.66)%     13.96      13.32     14.37
- --------------------------------------------------------------------------------
Ratios to average net assets (annualized)
Expenses                              .60%       .62        .61       .61
- --------------------------------------------------------------------------------
Net investment income                9.38%      9.44       9.72     10.70
- --------------------------------------------------------------------------------

                                        Year ended September 30,
                             1998        1997      1996       1995       1994
- --------------------------------------------------------------------------------
Supplemental data for all classes
Net assets at end of year 
  (in thousands)          $4,784,262  4,939,302  4,096,939 3,527,954   3,152,029
- --------------------------------------------------------------------------------
Portfolio turnover rate       92%          91        102        99         93
- --------------------------------------------------------------------------------

Note:  Total return does not reflect the effect of any sales charges.

<PAGE>


Kemper Income and Capital Preservation Fund
                                                                   July 3 to
                                       Year ended October 31,      October 31,
CLASS I                              1998       1997      1996        1995
- --------------------------------------------------------------------------------
Per share operating performance
Net asset value, beginning           $8.53      8.45       8.61      8.52
  of period
- --------------------------------------------------------------------------------
Income from investment operations:
  Net investment income                .56       .59        .60       .19
- --------------------------------------------------------------------------------
  Net realized and unrealized          .15       .08      (.15)       .12
    gain (loss)
- --------------------------------------------------------------------------------
Total from investment operations       .71       .67        .45       .31
- --------------------------------------------------------------------------------
Less distribution from net             .57       .59        .61       .22
  investment income
- --------------------------------------------------------------------------------
Net asset value, end of period       $8.67      8.53       8.45      8.61
- --------------------------------------------------------------------------------
Total return (not annualized)        8.62%      8.26       5.45      3.65
- --------------------------------------------------------------------------------
Ratios to average net assets (annualized)
Expenses                              .66%       .70        .72       .62
- --------------------------------------------------------------------------------
Net investment income                6.52%      7.02       7.14      6.87
- --------------------------------------------------------------------------------

                                         Year ended October 31,
                             1998        1997      1996       1995       1994
- --------------------------------------------------------------------------------
Supplemental data for all classes
Net assets at end of year 
  (in thousands)           $694,057    613,470    572,998   649,427     510,432
- --------------------------------------------------------------------------------
Portfolio turnover rate      121%         164         74       182        163
- --------------------------------------------------------------------------------

Note:  Total return does not reflect the effect of any sales charges.

SPECIAL FEATURES

Shareholders of a Fund's Class I shares may exchange their shares for (i) shares
of Zurich Money Funds -- Zurich Money Market Fund if the shareholders of Class I
shares  have  purchased  shares  because  they are  participants  in  tax-exempt
retirement plans of Scudder Kemper and its affiliates and (ii) Class I shares of
any  other  "Kemper   Mutual  Fund"  listed  in  the   prospectus.   Conversely,
shareholders  of  Zurich  Money  Funds  --  Zurich  Money  Market  Fund who have
purchased shares because they are participants in tax-exempt retirement plans of
Scudder  Kemper and its  affiliates may exchange their shares for Class I shares
of "Kemper  Mutual  Funds" to the extent that they are  available  through their
plan.  Exchanges  will be made at the  relative  net asset values of the shares.
Exchanges are subject to the limitations set forth in the prospectus.




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