Exhibit 31.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

I, Terry S. Parker, certify that:

1. I have reviewed this annual report on Form 10-K of CellStar Corporation; and

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.

/s/ Terry S. Parker                                

Terry S. Parker, Executive Chairman

Date: September 24, 2004