The apparent excess of Z --> b (b) over bar events at CERN LEP may be
an indication of new physics beyond the standard model. However, in ei
ther the two-Higgs-doublet model or the minimal supersymmetric standar
d model any explanation would lead to an important new decay mode of t
he top quark and suppresses the t --> Wb branching fraction, which goe
s against what has been observed at the Fermilab Tevatron. In the two-
Higgs-doublet model, the branching fraction of Z --> b (b) over bar a light boson which decays predominantly into b (b) over bar would be
at least of order 10(-4).