Strong particle acceleration in neutron-star environments may result in the upscattering of soft photons to gamma-ray energies. Sheared Alfven waves, which may be generated by several plausible disturbances in the stellar crust, can energize the charges to Lorentz factors in excess of 10 exp 5. However, a full understanding of the physics of these MHD waves is lacking due to the complications arising from the charge separation within the sheared region. Here, we present a detailed study of this mechanism, with particular attention to a comparison of the nonrelativistic and relativistic domains. We find that the charge separation is consistent with our previous classical MHD solutions and that it provides a natural description of the sheared current via a relativistic flow. These waves can apparently produce the particle distributions that are necessary to produce the gamma-ray fluxes observed in gamma-ray bursts, regardless of whether the sources are Galactic or extragalactic.