  We compute the large-$m_t$ contributions to the $Zb\overline b$ vertex in the
Standard Model non-perturbatively using both the $1/\nc$ and the $1/\nf$
expansions. Triviality and its consequences for the perturbative result are
systematically analyzed. In particular, we point out that the effect of
triviality is already important at the two-loop level for a heavy Higgs
($600\gev<M_H<1\tev$) even when the top mass is below $200\gev$.
