<TABLE> <S> <C>
<ARTICLE> 6
<LEGEND>
THIS SCHEDULE CONTAINS SUMMARY FINANCIAL INFORMATION EXTRACTED FROM THE KEMPER
INTERMEDIATE MUNICIPAL BOND FUND ANNUAL REPORT FOR THE FISCAL YEAR ENDED
09/30/2000 AND IS QUALIFIED IN ITS ENTIRETY BY REFERENCE TO SUCH FINANCIAL
STATEMENTS.
</LEGEND>
<CIK> 0000055190
<NAME> KEMPER NATIONAL TAX-FREE INCOME SERIES
<SERIES>
<NUMBER> 006
<NAME> KEMPER INTERMEDIATE MUNICIPAL BOND FUND
<S> <C>
<PERIOD-TYPE> 12-MOS
<FISCAL-YEAR-END> SEP-30-2000
<PERIOD-START> OCT-01-2000
<PERIOD-END> SEP-30-2000
<INVESTMENTS-AT-COST> 19,606,841
<INVESTMENTS-AT-VALUE> 20,054,361
<RECEIVABLES> 332,189
<ASSETS-OTHER> 262,376
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 20,648,926
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 77,676
<TOTAL-LIABILITIES> 77,676
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 20,519,202
<SHARES-COMMON-STOCK> 115,457
<SHARES-COMMON-PRIOR> 236,205
<ACCUMULATED-NII-CURRENT> 3,540
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> (399,012)
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 447,520
<NET-ASSETS> 20,571,250
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 1,237,000
<OTHER-INCOME> 0
<EXPENSES-NET> 282,830
<NET-INVESTMENT-INCOME> 954,170
<REALIZED-GAINS-CURRENT> (136,875)
<APPREC-INCREASE-CURRENT> 9,643
<NET-CHANGE-FROM-OPS> 826,938
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> (55,179)
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 433,854
<NUMBER-OF-SHARES-REDEEMED> (1,670,330)
<SHARES-REINVESTED> 40,982
<NET-CHANGE-IN-ASSETS> (4,891,753)
<ACCUMULATED-NII-PRIOR> 0
<ACCUMULATED-GAINS-PRIOR> (262,000)
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 124,700
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 304,497
<AVERAGE-NET-ASSETS> 1,512,699
<PER-SHARE-NAV-BEGIN> 10.00
<PER-SHARE-NII> .36
<PER-SHARE-GAIN-APPREC> (.03)
<PER-SHARE-DIVIDEND> 0
<PER-SHARE-DISTRIBUTIONS> (.36)
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 9.97
<EXPENSE-RATIO> 1.77
</TABLE>
