Accretion-powered X-ray pulsars exhibit significant variability of the cyclotron resonance scattering feature (CRSF) centroid energy on pulse-to-pulse timescales, and also on much longer timescales. Two types of spectral variability are observed. For sources in group 1, the CRSF energy is negatively correlated with the variable source luminosity, and for sources in group 2, the opposite behavior is observed. The authors explore the hypothesis that the accretion dynamics in the group 1 sources is dominated by radiation pressure near the stellar surface, and that Coulomb interactions decelerate the gas to rest in the group 2 sources. They derive a new expression for the critical luminosity, ..., such that radiation pressure decelerates the matter to rest in sources with X-ray luminosity ... . The results confirm that the group 1 sources are supercritical and the group 2 sources are subcritical, although the situation is less clear for those highly variable sources that cross over the line ... . (ProQuest: ... denotes formulae/symbols omitted.)