Recent observations have indicated that in addition to the classical inverted-V type electron acceleration, auroral electrons often have a field-aligned distribution that is broad in energy and sometimes shows time dispersion indicating acceleration at various altitudes up the field line. Such acceleration is not consistent with a purely electrostatic potential drop and suggests a wave heating of auroral electrons. Alfv¿n waves have been observed on auroral field lines carrying sufficient Poynting flux to provide energy for such acceleration. Calculations based on the linear kinetic theory of Alfv¿n waves indicate that Landau damping of these waves can efficiently convert this Poynting flux into field-aligned acceleration of electrons. At high altitudes along auroral field lines that map into the plasma sheet boundary layer (PSBL), the plasma gradients are relatively weak and the local kinetic theory can describe this wave--particle interaction. At lower altitudes, the gradient in the Alfv¿n speed becomes significant, and a nonlocal description must be used. A nonlocal theory based on a simplified model of the ionospheric Alfv¿n resonator (IAR) is presented. For a given field-aligned current (FAC), the efficiency of the wave--particle interaction increases with the ratio of the thermal velocity of the electrons to the Alfv¿n speed at high altitudes. These calculations indicate that wave acceleration of electrons should occur at and above the altitude where the quasi-static potential drops form.