It has recently been suggested that the nonlinear ponderomotive force of hydromagnetic waves in the magnetosphere may cause significant mass transport along the ambient magnetic field. To investigate this further, a two-dimensional nonlinear hydromagnetic computer code is applied to box magnetospheres with two different radial variations of &bgr;, the ratio of plasma pressure to magnetic pressure. It is found that the rate at which density structure develops is dependent on the local sound speed. For fundamental standing waveforms along the magnetic field both the size of maximum equatorial density enhancements and the time for enhancements to develop decrease with increasing sound speed. Density enhancements are limited at each radial position by the propagation of density fronts from the equator toward the ionospheres. The propagation is confined to a given field line, supporting the idea that the fronts propagate in the slow magnetosonic mode. Simple predictors Dsm (for the maximum relative density change) and tsm (for the time to reach maximum density) derived from second-order theory are tested against the numerical simulations and are found to give quite good results. A dipolelike magnetosphere model is then set up with plausible plasma and magnetic field parameters. Radial variations of Dsm and tsm are obtained for observationally reasonable models of cavity modes and Alfv¿n resonances. It is found that maximum density enhancements in the inner plasmasphere and in the plasma sheet are relatively small. However, large density enhancements are obtained in the outer plasmasphere and plasma trough. The size of these enhancements depends on the mean ion temperature and the effective ion mass in that region and is also likely to depend on how strongly slow magnetosonic waves are Landau damped.