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                                                                    Exhibit 12.1

                                  CERTIFICATION

I, Antonio Garces, certify that:

1.   I have reviewed this annual report on Form 20-F for the fiscal year ended
     December 31, 2004, of Grupo Financiero Galicia S.A.;

2.   Based on my knowledge, this report does not contain any untrue statement of
     a material fact or omit to state a material fact necessary to make the
     statements made, in light of the circumstances under which such statements
     were made, not misleading with respect to the period covered by this
     report;

3.   Based on my knowledge, the financial statements, and other financial
     information included in this report, fairly present in all material
     respects the financial condition, results of operations and cash flows of
     the company as of, and for, the periods presented in this report;

4.   The company's other certifying officer and I are responsible for
     establishing and maintaining disclosure controls and procedures (as defined
     in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the company and have:

     (a)  Designed such disclosure controls and procedures, or caused such
          disclosure controls and procedures to be designed under our
          supervision, to ensure that material information relating to the
          company, including its consolidated subsidiaries, is made known to us
          by others within those entities, particularly during the period in
          which this report is being prepared;

     (b)  Evaluated the effectiveness of the company's disclosure controls and
          procedures and presented in this report our conclusions about the
          effectiveness of the disclosure controls and procedures, as of the end
          of the period covered by this report based on such evaluation; and

     (c)  Disclosed in this report any change in the company's internal control
          over financial reporting that occurred during the period covered by
          the annual report that has materially affected, or is reasonably
          likely to materially affect, the company's internal control over
          financial reporting; and

5.   The company's other certifying officer and I have disclosed, based on our
     most recent evaluation of internal control over financial reporting, to the
     company's auditors and the audit committee of the company's board of
     directors (or persons performing the equivalent functions):

     (a)  All significant deficiencies and material weaknesses in the design or
          operation of internal control over financial reporting which are
          reasonably likely to adversely affect the company's ability to record,
          process, summarize and report financial information; and

     (b)  Any fraud, whether or not material, that involves management or other
          employees who have a significant role in the company's internal
          control over financial reporting.

Date: May 26, 2005

                                          /s/ Antonio Garces
                                          --------------------------------------
                                          Antonio Garces
                                          Chief Executive Officer
                                          (principal executive officer)