The partial decay rate \mbox{Γ(Z→bˉb)} of
the $Z$-boson is significantly affected by
higher order QCD corrections.
Of particular interest is the influence of the non-\ vanishing bottom quark
mass. Radiative corrections to the quadratic mass term
of the partial Z-width are computed in perturbative QCD.
The calculation of the third order
O(α3sm2b/M2Z) contribution for the
vector induced rate and of the second order
O(α2sm2b/M2Z) correction
for the axial induced rate
is described. The numerical influence of the results and the theoretical
uncertainties are discussed.