  Radiative QCD corrections significantly influence the theoretical predictions
for the decay rates of the $Z$ and the Higgs boson. The status of the QCD
calculations to the hadronic $Z$ width is reviewed. The role of mass
corrections from bottom quark final states is emphasized. An estimate of the
theoretical uncertainties is given. New results for quartic mass terms of order
${\cal O}(\alpha_s^2)$ are presented. The impact of secondary radiation of
bottom quarks on the determination of $\Gamma(Z\rightarrow b\bar{b})$ is
discussed. Second order QCD corrections to the partial decay rate
$\Gamma(H\rightarrow b\bar{b})$ are also presented in this talk. A recent
result for the flavour singlet contribution to this quantity is presented. It
includes quark mass effects and completes the otherwise massless calculations
of order $\ordas^2)$.
