Second order QCD contributions to polarized spacelike and timelike processes

We will give an outline of the computation of the QCD corrections to the spin structure function g1(x, Q2) and the spin fragmentation function g1H(x, Q2) which are measured in deep inelastic electron-proton scattering and in electron-positron annihilation respectively. In particular we show how to deal with the γ5-matrix and the Levi-Civita tensor, appearing in the amplitudes of the parton subprocesses, when the method of N-dimensional regularization is used. (author)