Triviality, perturbation theory and $Z\to b \overline b$

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 $200\gev$.