  We study the resummation of large logarithmic perturbative corrections to the
partonic cross sections relevant for the process pp-> h X at high transverse
momentum of the hadron h, when the initial protons are longitudinally
polarized. We perform the resummation to next-to-leading logarithmic accuracy.
We present numerical results for center-of-mass energies of 19.4 GeV, relevant
for comparisons to data from the Fermilab E704 experiment, and 62.4 GeV, where
preliminary data from RHIC have recently become available. We find significant
enhancements of the spin-dependent cross sections, but a decrease of the
double-spin asymmetry for the process. This effect is less pronounced at the
higher energy.
