We investigate linear MHD wave mode coupling in the cold plasma limit when the equilibrium density (&rgr;) varies along the equilibrium magnetic field (B). Our numerical simulations indicate that efficient fast/Alfv¿n mode coupling persists even when (B⋅∇)&rgr;≠0. The time-dependent picture we develop asymptotes to a normal mode for large t and also recovers the (B⋅∇)&rgr;=0 singularity qualitatively. When applied to waves in the magnetotail, we find that Alfv¿nic disturbances will have an extended structure across the magnetic field and that Alfv¿nic wave packets should be excited on plasma sheet boundary layer (PSBL) or mantle field lines. Alfv¿n waves driven on PSBL field lines are probably the most observable signature at Earth of wave coupling in the distant tail. ¿ 1998 American Geophysical Union