  We have investigated the next-to-next-to-leading order (NNLO) corrections to
inclusive hadron production in e^+e^- annihilation and the related parton
fragmentation distributions, the `time-like' counterparts of the `space-like'
deep-inelastic structure functions and parton densities. We have re-derived the
corresponding second-order coefficient functions in massless perturbative QCD,
which so far had been calculated only by one group. Moreover we present, for
the first time, the third-order splitting functions governing the NNLO
evolution of flavour non-singlet fragmentation distributions. These results
have been obtained by two independent methods relating time-like quantities to
calculations performed in deep-inelastic scattering. We briefly illustrate the
numerical size of the NNLO corrections, and make a prediction for the
difference of the yet unknown time-like and space-like splitting functions at
the fourth order in the strong coupling constant.
