  We explore the one-loop electroweak radiative corrections in the context of
the traditional minimal $SU(5)$ and the string-inspired $SU(5)\times U(1)$
supergravity models by calculating explicitly vacuum-polarization and
vertex-correction contributions to the $\epsilon_1$ and $\epsilon_b$
parameters. We also include in this analysis the constraint from $b\rightarrow
s\gamma$ whose inclusive branching ratio $B(b\rightarrow s\gamma)$ has been
actually measured very recently by CLEO. We find that by combining these three
most important indirect experimental signatures and using the most recent
experimental values for them, $m_t\gtrsim 170 {\rm GeV}$ is excluded for
$\mu>0$ in both the minimal $SU(5)$ supergravity and the no-scale $SU(5)\times
U(1)$ supergravity. We also find that $m_t\gtrsim 175(185) {\rm GeV}$ is
excluded for any sign of $\mu$ in the minimal ($SU(5)\times U(1)$) supergravity
model.
