  We consider the scenarios of the GMSB models in which the dominant signal for
supersymmetry at the Tevatron are the events having two or three $\tau$ leptons
with high $p_T$ accompanied by large missing transverse energy. This signal is
very different from the multijet or multileptons (involving $e$ and/or $\mu$
only) in the usual supergravity models or the photonic signals in the GMSB
models (where the lightest neutralino is the next to lightest supersymmetric
particle (NLSP)). The parameter space where the lighter stau is the NLSP allows
this possibility. We find that such a signal could be observable at the
Tevatron Run II.
