We describe nonlinear resonance absorption of compressional Alfv¿n waves in a model magnetosphere. It is shown that the ponderomotive force of excited standing shear Alfv¿n waves can lead to nonlinear saturation and spatial structuring of field line resonances and that in low-beta plasmas ponderomotive saturation may occur before other nonlinear saturation processes such as the Kelvin-Helmholtz instability. The effects of finite electron inertia are also considered, and it is shown that spatial structuring of field line resonances may occur with scale sizes compatible with those found in discrete auroral arcs. Results are discussed in the context of three-dimensional numerical solutions to the resistive magnetohydrodynamic equations and based on a simplified analytical model of nonlinear resonance absorption. ¿ 1998 American Geophysical Union