  We explore the radiative corrections to the process Z --> b b-bar in models
with extended Higgs sectors. The observables R_b (the Z hadronic branching
fraction to b b-bar) and the b-quark asymmetry A_b = (g_L^2 - g_R^2)/(g_L^2 +
g_R^2) are sensitive to these corrections. We find that in models containing
only Higgs doublets, singlets, or larger multiplets constrained by a custodial
SU(2) symmetry, the radiative corrections to R_b involving charged Higgs bosons
always worsen the Standard Model fit to electroweak data. Thus, the present R_b
data can be used to set lower bounds on the charged Higgs masses in such
models. Radiative corrections to R_b involving light neutral Higgs bosons in
models with enhanced couplings to b b-bar can improve the Standard Model fit to
present data. The Higgs sector alone cannot explain a significant deviation of
A_b from its Standard Model prediction. We present general formulas for the
corrections to R_b and A_b in an SU(2)xU(1) electroweak model with an arbitrary
extended Higgs sector, and derive explicit results for a number of specific
models.
