  We present the analytical $\alpha_{s}^3$ correction to the $Z^{0}$ decay rate
into hadrons. We calculate this correction up to (and including) terms of the
order $(m_Z^2/m_{top}^2)^3$ in the large top quark mass expansion. We rely on
the technique of the large mass expansion of individual Feynman diagrams and
treat its application in detail. We convert the obtained results of six flavour
QCD to the results in the effective theory with five active flavours, checking
the decoupling relation of the QCD coupling constant. We also derive the large
charm quark mass expansion of the semihadronic $\tau$ lepton decay rate in the
$\alpha_{s}^3$ approximation.
