THE CALCULATION OF THE 2-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 corre cted spin structure function g(1) (x, Q(2)). These splitting functions , which are presented in the <(MS)over bar> scheme, are derived from t he order alpha(s)(2) contribution to the anomalous dimensions gamma(ij )(m)(i,j = q, g). The latter correspond to the local operators which a ppear in the operator product expansion of two electromagnetic current s. Some of the properties of the anomalous dimensions will be discusse d. 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).