  We report on our calculation of the order \alpha_s^4 axial singlet
contributions for the decay rates of the Z-boson as well as the vector singlet
contribution to the cross section for electron-positron annihilation into
hadrons. Together with recently finished O(\alpha_s^4) calculations of the
non-signlet corrections [1,2], the new results directly lead us to the first
complete O(\alpha_s^4) predictions for the total hadronic decay rate of the
Z-boson and the ratio R(s).
