  We consider here a layered superconductor subject to an externally applied
moderately-strong electromagnetic field. We predict hysteretic jumps in the
dependence of the surface reactance of the superconductor on the amplitude of
the incident electromagnetic wave. This very unusual nonlinear phenomenon can
be observed in thin superconducting slabs at not very strong ac amplitudes, if
the frequency of the irradiating field is close to the Josephson plasma
frequency. Using the set of coupled sine-Gordon equations, we derive the
expression for the phase shift of the reflected wave and obtain the conditions
for the appearance of hysteresis.
