EXHIBIT 23.1
 
                   CONSENT OF INDEPENDENT PUBLIC ACCOUNTANTS
 
    As independent public accountants, we hereby consent to the incorporation by
reference in this Form S-3 Registration Statement of Telephone and Data Systems,
Inc. of our report dated January 29, 1997 (except with respect to the matter
discussed in Note 16, as to which the date is February 4, 1997), on the
consolidated financial statements of Telephone and Data Systems, Inc. and
Subsidiaries incorporated by reference in the Telephone and Data Systems, Inc.
Form 10-K for the year ended December 31, 1996 and to the incorporation by
reference in this Form S-3 Registration Statement of our report dated January
29, 1997 (except with respect to the matter discussed in Note 16, as to which
the date is February 4, 1997), on the financial statement schedules of Telephone
and Data Systems, Inc., included in the Telephone and Data Systems, Inc. Form
10-K for the year ended December 31, 1996. We also consent to all references to
our Firm included in this Form S-3 Registration Statement.
 
            [SIG]
 
ARTHUR ANDERSEN LLP
 
Chicago, Illinois
October 17, 1997