We present the third-order (NNLO) contributions to the timelike splitting functions governing the evolution of parton fragmentation functions in QCD. The hitherto missing quark-gluon and gluon-quark quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange DIS structure functions and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and supersymmetric limit. A numerically tolerable uncertainty remains in the quark-gluon case which does not affect the endpoint logarithms for small and large momentum fractions x. The stability of the perturbative expansion at small x is spoiled by large double logarithms up to alpha_s^n ln^{2*n-2} x. Much more stable results are obtained when the fixed-order results are combined with the new small-x resummation up to the next-to-next-to-leading (NNL) logarithms (the derivation of which is discussed in another contribution).