Propagation of one-dimensional disturbances of solid concentration in liquid-solid and gas-solid fluidized beds of magnetic particles in an external magnetic field is considered. Linear disturbances are analysed and the criteria of magnetic stabilization of liquid-solid and gas-solid fluidized beds are derived. Propagation of non-linear long concentration waves is analysed. Burgers equation is shown to describe the propagation of long waves in a fluidized bed of magentic particles. Formation of domains with a sharp change in solid concentration ("shock" fronts) is analysed. The structure of the shock front (in particular the thickness of the front) is found to depend on the magnetic parameters of the solid particles. The obtained results can be used to explain the mechanism of supression of bubble formation in magnetically stabilized fluidized beds.