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 28, 1998 (except with respect to the matters
discussed in Note 5, "American Paging Merger"; and in Note 16, as to which the
date is February 18, 1998) 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, 1997
and to the incorporation by reference in this Form S-3 Registration Statement of
our report dated January 28, 1998, (except with respect to the matters discussed
in Note 5 "American Paging Merger"; and in Note 16, as to which the date is
February 18, 1998) 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, 1997. We also consent to the incorporation by
reference of our reports dated January 28, 1998 on the financial statements of
the United States Cellular Group, the TDS Telecommunications Group and the TDS
Group for the year ended December 31, 1997, our report dated January 28, 1998
(except with respect to the matters discussed in Note 10, as to which the date
is February 5, 1998) on the financial statements of the Aerial Communications
Group and our report dated January 28, 1998 (except with respect to the matters
discussed in Note 5 "American Paging Merger"; and in Note 16, as to which the
date is February 18, 1998) on the consolidated financial statements of Telephone
and Data Systems, Inc. and Subsidiaries for the year ended December 31, 1997,
included in the Telephone and Data Systems, Inc. Proxy Statement/Prospectus on
Form S-4, as amended. We also consent to all references to our Firm included in
this Registration Statement.
    
 
ARTHUR ANDERSEN LLP
 
   
Chicago, Illinois
May 12, 1998