[en] An analytical investigation is made of the dynamic response of two special classes of nonlinear hysteretic oscillators that model some of the basic phenomena involved in the response of complex nuclear power plant systems which are subjected to dynamic environments. Numerical studies as well as approximate analytical solutions for the response of the nonlinear oscillators under (a) harmonic and (b) random excitation are presented. The effects of various system parameters are evaluated and the range of validity of the approximate solutions is determined