The calculation of the two-loop spin splitting functions P-ij((1))(x)

We present the calculation of the two-loop spin splitting functions P-ij((1))(x)(i,j = q, g) contributing to the next-to-leading order corrected spin structure function g(1) (x, Q(2)). These splitting functions, which are presented in the <(MS)over bar> scheme, are derived from the order alpha(s)(2) contribution to the anomalous dimensions gamma(ij)(m)(i,j = q, g). The latter correspond to the local operators which appear in the operator product expansion of two electromagnetic currents. Some of the properties of the anomalous dimensions will be discussed. In particular our findings are in agreement with the supersymmetric relation gamma(qq)(m) + gamma(gq)(m) - gamma(qg)(m) - gamma(gg)(m) = 0 up to order alpha(s)(2).