A theoretical approach to the consideration of coupling between Alfv¿n and compressional modes in two-dimensionally inhomogeneous plasma has been developed. The conversion of a compressional mode, propagating along a high-density layer perpendicular to the magnetic field, into leaking shear Alfv¿n waves has been considered. The wave spatial structure along the layer is described in WKB approximation. A compressional-type disturbance effectively emitts Alfv¿n waves when a local resonant condition within the layer is fulfilled. In contrast with the common field line resonance theory, the excited Alfv¿n modes are assumed to be running away waves but not standing oscillations. The physical situations that correspond to the considered model can be met in the outer near-equatorial magnetosphere, in the exterior cusp region, and in the other magnetospheres such as Jupiter and Saturn. ¿ 1998 American Geophysical Union