We discuss the results of coupled Monte-Carlo/Fokker-Planck simulations of the thermal/nonthermal radiation and electron acceleration and cooling in the case of accretion onto a magnetized neutron star. Most of the energy release into thermal/nonthermal electrons is assumed to happen in a thin shell near the Alfve´n radius, where the radiation from the neutron star surface is reprocessed into thermal/nonthermal high-energy (hard X-ray—&ggr;-ray) emission. We explore the parameter space defined by the accretion rate, stellar surface field and the level of wave turbulence in the shell. Our results are relevant to the emission from atoll sources, transient X-ray binaries containing weakly magnetized neutron stars, and to recently suggested models of accretion-powered emission from anomalous X-ray pulsars. ©2001 American Institute of Physics.