  We investigate the resummation of large logarithmic perturbative corrections
to the partonic cross sections for single-inclusive high-p_T hadron production
in collisions of transversely polarized hadrons. We perform the resummation to
next-to-leading logarithmic accuracy. Phenomenological results are given for
pbar-p collisions at center-of-mass energy of 14.5 GeV and for p-p collisions
at 62.4 GeV and at 10 GeV, which are relevant for possible experiments at the
GSI-FAIR, RHIC and J-PARC facilities, respectively. We find significant
enhancements of the spin-dependent and spin-averaged cross sections, but a
decrease of the double-spin asymmetry A_TT.
