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.