Kinetic Alfv¿n waves have been invoked in association with auroral currents and particle acceleration since the pioneering work of Hasegawa [1976>. However, to date, no work has considered the dispersion relation including the full kinetic effects for both electrons and ions. Results from such a calculation are presented, with emphasis on the role of Landau damping in dissipating Alfv¿n waves which propagate from the warm plasma of the outer magnetosphere to the cold plasma present in the ionosphere. It is found that the Landau damping is not important when the perpendicular wavelength is larger than the ion acoustic gyroradius and the electron inertial length. In addition, ion gyroradius effects lead to a reduction in the Landau damping by raising the parallel phase velocity of the wave above the electron thermal speed in the short perpendicular wavelength regime. These results indicate that low-frequency Alfv¿n waves with perpendicular wavelengths greater than the order of 10 km when mapped to the ionosphere will not be significantly affected by Landau damping. While these results, based on the local dispersion relation, are strictly valid only for short parallel wavelength Alfv¿n waves, they do give an indication of the importance of Landau damping for longer parallel wavelength waves such as field line resonances. ¿ American Geophysical Union 1996