The resonant excitation of Alfv¿n waves is considered in a resistive warm plasma embedded in a purely poloidal field. The magnetostatic equilibrium is invariant in the y direction. The driven problem is studied in the asymptotic state, so we can assume that all wave fields vary as exp[i(&lgr;y-&ohgr;t)>. Resistive solutions are derived in the vicinity of the resonance with the aid of an asymptotic expansion procedure. We find that the zeroth-order functions of the flux coordinate have to satisfy differential equations analogous to those obtained by Goossens et al. [1995> for the resistive one-dimensional systems. Applied to the two-dimensional box model for the Earth's magnetosphere, we recover the results found by Thompson and Wright [1993> in ideal MHD, but in addition, we obtain the behavior in the dissipative layer in the asymptotic state. ¿ American Geophysical Union 1995