  We have calculated the splitting functions governing the evolution of the
unpolarized parton distributions of the photon at the next-to-next-to-leading
order (NNLO) of massless perturbative QCD. The results, presented here mainly
in terms of compact and accurate parametrizations, are consistent with our
previous approximations based on the lowest six even-integer Mellin moments.
Consequently the NNLO corrections are small in both the MSbar and the DIS_gamma
factorization schemes at momentum fractions x >~ 0.1.
