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Exhibit 31.1

CERTIFICATION PURSUANT TOSECTION 302 OF THE
SARBANES-OXLEY ACT OF 2002

I, Kenneth Hicks, certify that:

1. I have reviewed this quarterly report on Form 10-Q of
Argentex Mining Corporation;

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 small business issuers other certifying officer(s) 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)) and
internal control over financial reporting (as defined in Exchange Act Rules
13a-15(f) and 15d-15(f)) for the small business issuer 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 small
business issuer, 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) Designed such internal control over
financial reporting, or caused such internal control over financial reporting to
be designed under our supervision, to provide reasonable assurance regarding the
reliability of financial reporting and the preparation of financial statements
for external purposes in accordance with generally accepted accounting
principles;

(c) Evaluated the effectiveness of the
small business issuer'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

(d) Disclosed in this report any change
in the small business issuer's internal control over financial reporting that
occurred during the small business issuer's most recent fiscal quarter (the
small business issuer's fourth fiscal quarter in the case of an annual report)
that has materially affected, or is reasonably likely to materially affect, the
small business issuer's internal control over financial reporting;

5. The small business issuers other certifying officer (s) and
I have disclosed, based on my most recent evaluation of internal control over
financial reporting, to the small business issuer's auditors and the audit
committee of the small business issuer'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 small
business issuer'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
small business issuer's internal control over financial reporting.

Date: September 12, 2008

/s/ Kenneth Hicks Kenneth Hicks President and
Director (Principal Executive Officer)

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