The phenomenon of resonance absorption leads to a secular damping of surface waves propagating parallel to the local magnetic field in a region of strong perpendicular gradient in the local Alfv¿n speed. This damping results from the growth of other wave modes at the expense of the surface waves. Resonance absorption is an effective dissipation mechanism which may forestall the steepening of MHD waves in such regions, and is probably the dominant mechanism by which widely distributed MHD wave energy becomes concentrated in rather thin, resonant, ''energy-containing'' layers coinciding with regions of strong Alfv¿n wave speed gradients. However, based upon physical consideration of the impulsive radially propagating magnetosonic disturbances associated with substorms, we maintain that nonlinear steepening effects are likely to be important in the dissipation of their energy. ¿ American Geophysical Union 1988