A theory of the propagation of nonlinear surface magnetostatic waves (MSW) in a ferromagnetic film with one periodically corrugated surface is presented. It is shown that the filter characteristics of this nonlinear periodic structure exhibit bistable or multistable properties above a threshold power so that, for a given input power of the wave, several values of output power are possible. A Fabry-Perot resonator is discussed for which the nonlinear magnetostatic waves are multistable. Magnetostatic waves that propagate in thin ferromagnetic film have strong nonlinear properties. These have been investigated both theoretically and experimentally. The theory of nonlinear MSW and the necessary conditions for the creation of MSW solitons, and the role of three- and four-magnon in stabilities of MSW has only recently been studied, so that is a relatively new field. Recent investigations of the propagation of optical electromagnetic waves in nonmagnetic, nonlinear, Fabry-Perot resonators, and dielectric waveguides with periodically changing values of the refractive index of the waveguiding medium have already shown that the electromagnetic waves can exhibit multistable properties. This is therefore to be expected in the microwave range where it will be just as important as it is in the construction of optical logic devices.