  We compute the supersymmetric contribution to the anomalous magnetic moment
of the muon within the context of $SU(5)\times U(1)$ supergravity models. The
largest possible contributions to $a^{susy}_\mu$ occur for the largest allowed
values of $\tan\beta$ and can easily exceed the present experimentally allowed
range, even after the LEP lower bounds on the sparticle masses are imposed.
Such $\tan\beta$ enhancement implies that $a^{susy}_\mu$ can greatly exceed
both the electroweak contribution ($\approx1.95\times10^{-9}$) and the present
hadronic uncertainty ($\approx\pm1.75\times10^{-9}$). Therefore, the new E821
Brookhaven experiment (with an expected accuracy of $0.4\times10^{-9}$) should
explore a large fraction (if not all) of the parameter space of these models,
corresponding to slepton, chargino, and squarks masses as high as 200, 300, and
1000 GeV respectively. Moreover, contrary to popular belief, the $a^{susy}_\mu$
contribution can have either sign, depending on the sign of the Higgs mixing
parameter $\mu$: $a^{susy}_\mu>0\,(<0)$ for $\mu>0$ ($\mu<0$). The present
$a_\mu$ constraint excludes chargino masses in the range $45-120\GeV$ depending
on the value of $\tan\beta$, although there are no constraints for
$\tan\beta\lsim8$. We also compute $a^{susy}_\tau$ and find
$|a^{susy}_\tau|\approx(m_\tau/m_\mu)^2\,|a^{susy}_\mu|\lsim10^{-5}$ and
briefly comment on its possible observability.
