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We explore the one-loop electroweak radiative corrections in the minimal$SU(5)$ and the no-scale flipped $SU(5)$ supergravity models via explicitcalculation of vacuum polarization contributions to the $\epsilon_{1,2,3}$parameters. Experimentally, $\epsilon_{1,2,3}$ are obtained from a global fitto the LEP observables, and $M_W/M_Z$ measurements. We include $q^2$-dependenteffects which have been neglected in most previous ``model-independent"analyses of this type. These effects induce a large systematic negative shifton $\epsilon_{1,2,3}$ for light chargino masses ($m_{\chi^\pm_1}\lsim70\GeV$).In agreement with previous general arguments, we find that for increasinglylarge sparticle masses, the heavy sector of both models rapidly decouples, \ie,the values for $\epsilon_{1,2,3}$ quickly asymptote to the Standard Modelvalues with a {\it light} Higgs ($m_{H_{SM}}\sim100\GeV$). Specifically, atpresent the $90\%$ CL upper limit on the top-quark mass is $m_t\lsim175\GeV$ inthe no-scale flipped $SU(5)$ supergravity model. These bounds can bestrengthened for increasing chargino masses in the $50-100\GeV$ interval. Inparticular, for $m_t\gsim160\GeV$, the Tevatron may be able to probe throughgluino($\tilde g$) and squark($\tilde q$) production up to $m_{\tilde g}\approxm_{\tilde q}\approx250\GeV$, exploring at least half of the parameter space inthis model.Comment: 15 pages,(6 ps figures available upon request), TeX(harvmac),  CTP-TAMU-19/93, ACT-07/9

Precision electroweak tests of the minimal and flipped SU(5) supergravity models