We compute the supersymmetric contribution to the anomalous magnetic moment of the muon within the context of SU(5) × U(1) supergravity models. The largest possible contributions to $a_{\mu }^{\mathrm{SUSY}}$ occur for the largest allowed values of $tan\beta$ and can easily exceed the present experimentally allowed range, even after the CERN LEP lower bounds on the sparticle masses are imposed. Such $tan\beta$ enhancement implies that $a_{\mu }^{\mathrm{SUSY}}$ can greatly exceed both the electroweak contribution (≅ 1.95 × ${10}^{-9\mathrm{}}$) and the present hadronic uncertainty (≅ ± 1.75 × ${10}^{-9\mathrm{}}$). Therefore, the new E821 Brookhaven experiment (with an expected accuracy of 0.4 × ${10}^{-9\mathrm{}}$) 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 $a_{\mu }^{\mathrm{SUSY}}$ contribution can have either sign, depending on the sign of the Higgs mixing parameter $\mu : a_{\mu }^{\mathrm{SUSY}}>0\mathrm{}(<0\mathrm{})\mathrm{}$ 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 $tan\beta \lesssim 8$. We also compute $a_{\tau }^{\mathrm{SUSY}}$ and find $\left|a_{\tau }^{\mathrm{SUSY}}\right|\approx {\left(\frac{m_{\tau }}{\frac{m}{\mu }}\right)}^2\left|a_{\mu }^{\mathrm{SUSY}}\right|\lesssim {10}^{-5\mathrm{}}$ and briefly comment on its possible observability.

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