R_b in supersymmetric models

We compute the supersymmetric contribution to $R_{b}\equiv \Gamma (Z\to b{\bar b})/\Gamma (Z\to {\rm hadrons})$ in a variety of supersymmetric models. In the context of supergravity models with universal soft-supersymmetry-breaking and radiative electroweak breaking we find $R^{\rm susy}_b\lsim0.0004$, which does not shift significantly the Standard Model prediction ($R^{\rm SM}_b=0.2157$ for $m_t=175\GeV$; $R^{\rm exp}_b=0.2204\pm0.0020$). We also compute $R_b$ in the minimal supersymmetric standard model (MSSM), and delineate the region of parameter space which yields interestingly large values of $R_b$. This region entails light charginos and top-squarks, but is {\em strongly} restricted by the {\em combined} constraints from $B(b\to s\gamma)$ and a not-too-large invisible top-quark branching ratio: only a few percent of the points with $R^{\rm susy}_b>0.0020\,(1\sigma)$ are allowed.