The phase velocity of a single plane magnetohydrodynamic wave in a rotating liquid is independent of the amplitude. The nonlinear interactions between the components of the spectrum of a complex traveling disturbance vanish only in a nonrotating fluid without dissipation. A criterion for the approximate validity of the principle of superposition is given for small values of the Coriolis force and the dissipation. In a rotating medium in a magnetic field a disturbance will not necessarily travel along the magnetic field lines. The anisotropic group velocity for a wave packet is given. In solar physics the effects of anisotropic dispersion and nonlinearity are significant for disturbances with wave lengths of the order of a hundredth of the solar radius, if a dipole field with a polar strength of less than 25 gauss is assumed.