  Recently methods have been developed to extend the resummation of large-x
double logarithms in inclusive deep-inelastic scattering (DIS) to terms not
addressed by the soft-gluon exponentiation. Here we briefly outline our
approach based on fixed-order results, the general large-x structure in
dimensional regularization and the all-order factorization of mass
singularities, which is directly applicable also to semi-inclusive e+e-
annihilation (SIA). We then present some main results for the corresponding
timelike splitting functions and transverse and longitudinal fragmentation
functions. The close relation between DIS and SIA facilitates the determination
of additional third-order results for the latter function which is fully known
only at the next-to-leading order. Therefore all above quantities can be
resummed at next-to-next-to-leading logarithmic accuracy.
