  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.
