In this Letter, weak-turbulence theory is used to investigate interactions among Alfvén waves and fast and slow magnetosonic waves in collisionless low-beta plasmas. The wave kinetic equations are derived from the equations of magnetohydrodynamics, and extra terms are then added to model collisionless damping. These equations are used to provide a quantitative description of a variety of nonlinear processes, including parallel and perpendicular energy cascade, energy transfer between wave types, "phase mixing," and the generation of backscattered Alfvén waves.
