Exhibit 13.1

                                  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 Annual Report on Form 20-F for the fiscal year ended
December 31, 2004, of Grupo Financiero Galicia S.A. (the "Company") as filed
with the U.S. Securities and Exchange Commission (the "Commission") on the date
hereof (the "Report") and pursuant to 18 U.S.C. ss. 1350, as adopted pursuant to
Section 906 of the Sarbanes-Oxley Act of 2002, I, Antonio Garces, Chief
Executive Officer of the Company, certify, that:

     (1)  the Report fully complies with the requirements of Section 13(a) or
          15(d) 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 26, 2005

                                         /s/ Antonio Garces
                                         ---------------------------------------
                                         Antonio Garces
                                         Chief Executive Officer

     A signed original of this written statement required by Section 906 has
been provided to Grupo Financiero Galicia S.A. and will be retained by Grupo
Financiero Galicia S.A. and furnished to the Commission or its staff upon
request.