EXHIBIT 32.1

      CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT
                                       TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Alaska Communications Systems Group,
Inc. (the "Company") on Form 10-Q for the period ending March 31, 2004 (the
"Report"), I, Liane Pelletier, Chief Executive Officer of the Company, certify,
pursuant to 18 U.S.C. Section 1350, as created by Section 906 of the
Sarbanes-Oxley Act of 2002, that:

(1)   The Report fully complies with the requirements of section 13(a) or 15(d),
      as applicable, of the Securities Exchange Act of 1934 as amended; and

(2)   The information contained in the Report fairly presents, in all material
      respects, the financial condition and results of operations of the
      Company.

Date: May 12, 2004                     /s/ Liane Pelletier
                                       ----------------------------------------
                                       Liane Pelletier
                                       Chief Executive Officer,
                                       Chairman of the Board and President
                                       Alaska Communications Systems Group, Inc.