We show that dynamical localization of electrons in a thin semiconductor superlattice irradiated by a TM electromagnetic wave can lead to the formation of multistable states of the high-frequency field, which is accompanied by significant distortions of the reflection characteristics of superlattices. This effect is caused by the phenomenon of nonlinear plasma resonance and the related significant increase in the component of an alternating electric field, parallel to the superlattice axis, in the case where the real part of the corresponding component of the tensor of nonlinear dielectric permittivity becomes zero. It is found that the generation efficiency of odd harmonics of the radiation increases considerably under resonance conditions.