  We consider the Minimal Gauge Mediated Model (MGMM) with either fundamental
or antisymmetric messenger multiplets and study consequences of
messenger-matter mixing. We find that in these models, unlike MGMM without
mixing, wide range of $\tan\beta$ is allowed. It is shown that existing
experimental limits on processes with lepton flavor violation, and on
$K^0-\bar{K}^0$, $D^0-\bar{D}^0$ and $B^0-\bar{B}^0$ - mixing place significant
constraints on relevant coupling constants and mixing parameters. On the other
hand, the contributions of the messenger-matter mixing to the rates of $\tau
\to e\gamma$, $\tau \to \mu\gamma$ and $b\to s\gamma$ may be well below the
present experimental limits depending on the value of $\tan\beta$. We also
point out the possibility of sizeable slepton oscillations in this model.

High Energy Physics - Phenomenology