A general nonlinear theory for low-frequency electromagnetic field generation due to the action of non-uniform and non-stationary high-frequency electromagnetic radiation (ponderomotive force) in uniform multicomponent dusty magnetoplasmas is developed. The anisotropic thermal pressure of all species in slow and fast oscillations is taken into account. This theory permits us to consider the nonlinear action of all waves that can exist in such plasmas. As an example, the equations for dust particle velocities arising due to nonlinear electric fields induced by electromagnetic cyclotron waves travelling along an external magnetic field are obtained. The dust grains are considered to be magnetized as well as unmagnetized. Various regimes of dust grain dynamics depending on the spatio-temporal variation of a fast wave amplitude are discussed. It is shown that induced nonlinear electric fields can have both an electrostatic and an electromagnetic nature. In some cases these fields across the background magnetic field in warm plasmas are considerably larger than those in cold plasmas. The longitudinal nonlinear electric field remains the same in warm and cold plasmas in its order of magnitude. Regimes are found for which the transverse acceleration of dust grains is much larger than the longitudinal one.