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 \MSbs, 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 we find that in order \alpha_s^2 the supersymmetric relation \gamma_{qq}^{m}+\gamma_{gq}^{m}-\gamma_{qg} ^{m}-\gamma_{gg}^{m}=0 is violated
