The propagation of solid concentration disturbances in fluidized beds in an external magnetic field is considered. Both solid particles and the liquid phase are assumed to be simultaneously magnetizable. The total fluid-particle interaction force is supposed to include the inertial component proportional to the relative acceleration of fluid and particles. The effect of simultaneous magnetization of particles and fluid as well as the influence of the inertial component of interphase interaction force on the resulting criterion of stability of the uniform fluidization are analysed. Consideration is given to the dispersion phenomena in the wave propagation process. The model of propagation of nonlinear waves is developed in approximation of small finite-amplitude waves. The basic equations are reduced to the Korteweg-de Vries-Burgers equation for the departure of solid concentration from the uniform state. Possible configurations of the concentration wavefront are studied, including the oscillating wavefronts and small-amplitude shocks. The conditions of realization of each possible configuration are obtained. The propagation of a long finite-amplitude nonlinear steady wave is considered. The conditions for the existence of the steady concentration wave are derived. The The structure of the wavefront is studied and the thickness of the front is calculated as a function of magnetic and other physical parameters and the concentrations ahead of and behind the front. The conditions across the concentration shock in the fluidized bed of magnetic particles are obtained. The shock speed is calculated. The obtained results can be used to analyse structures of boundaries of bubbles, slugs and solid clusters formed in magnetically stabilized fluidized beds. In conclusion the analogy between the basic equations of magnetic fluidized beds and equations of the "particle bed" model by Foscolo & Gibilaro is briefly discussed in order to analyse the possibility to apply the developed approach to the study of the considered classes of nonlinear waves in conventional fluidized beds.