  We will give an outline of the computation of the QCD corrections to the spin
structure function g_1(x,Q^2) and the spin fragmentation function g_1^H(x,Q^2)
which are measured in deep inelastic electron-proton scattering and in
electron-positron annihilation respectively. In particular we show how to deal
with the gamma_5-matrix and the Levi-Civita tensor, appearing in the amplitudes
of the parton subprocesses, when the method of N-dimensional regularization is
used.
