Signatures of Gauge Mediated Supersymmetry Breaking Models at the Tevatron

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.