In a previous paper we argued that the damping of obliquely propagating kinetic Alfv¿n waves, chiefly by resonant mechanisms, was a likely explanation for the formation of the dissipation range for interplanetary magnetic field fluctuations. This suggestion was based largely on observations of the dissipation range at 1 AU as recorded by the Wind spacecraft. We pursue this suggestion here with both a general examination of the damping of obliquely propagating kinetic Alfv¿n waves and an additional examination of the observations. We explore the damping rates of kinetic Alfv¿n waves under a wide range of interplanetary conditions using numerical solutions of the linearized Maxwell-Vlasov equations and demonstrate that these waves display the nearly isotropic dissipation properties inferred from the previous paper. Using these solutions, we present a simple model to predict the onset of the dissipation range and compare these predictions to the observations. In the process we demonstrate that electron Landau damping plays a significant role in the damping of interplanetary magnetic field fluctuations which leads to significant heating of the thermal electrons. ¿ 1999 American Geophysical Union