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                                                                    Exhibit 23.1
 
                   CONSENT OF INDEPENDENT PUBLIC ACCOUNTANTS
 
    As independent public accountants, we hereby consent to the incorporation by
reference into this Registration Statement on Form S-3 of our report dated
February 6, 1998 (except with respect to the matters discussed in Note 17, as to
which the dates are February 17, 1998, June 8, 1998 and June 17, 1998), included
in TeleTech Holdings, Inc.'s Current Report on Form 8-K filed on July 28, 1998,
and to the incorporation by reference of our report dated February 6, 1998
(except with respect to the matter discussed in Note 17, as to which the date is
February 17, 1998), included in TeleTech Holdings, Inc.'s Annual Report on Form
10-K for the year ended December 31, 1997 and to all references to our Firm
included in this Registration Statement on Form S-3.
 
                                          ARTHUR ANDERSEN LLP
 
Denver, Colorado
September 25, 1998
