  We present the next-to-next-to-leading order (NNLO) contributions to the main
splitting functions for the evolution of longitudinally polarized parton
densities of hadrons in perturbative QCD. The quark-quark and gluon-quark
splitting functions have been obtained by extending our previous all Mellin-N
calculations to the structure function g_1 in electromagnetic deep-inelastic
scattering (DIS). Their quark-gluon and gluon-gluon counterparts have been
derived using third-order fixed-N calculations of structure functions in
graviton-exchange DIS, relations to the unpolarized case and mathematical tools
for systems of Diophantine equations. The NNLO corrections to the splitting
functions are small outside the region of small momentum fractions x where they
exhibit a large double-logarithmic enhancement, yet the corrections to the
evolution of the parton densities can be unproblematic down to at least x about
10^{-4}.
