We show that a steep plasma pressure gradient can lead to radially localized Alfv¿n modes, which are damped through coupling to field line resonances. These have been called drift Alfv¿n ballooning modes (DABM) by [Chen and Hasegawa, 1991> and are the prime candidates to explain Pc4-Pc5 geomagnetic pulsations observed during the recovery phase of geomagnetic storms. A strong dependence of the damping rate of the azimuthal wave number m is established, as well as on the equilibrium profile. A minimum azimuthal mode number can be found for the DABM to be radially trapped. We find that higher m DABMs are better localized, which is consistent with high-m observations. ¿ American Geophysical Union 1994