In a previous paper , a mathematical model of a nonlinear hysteretic vibration isolator, with amplitude- dependent parameters, was established based on experimental study. In this paper, the corresponding multi- harmonic steady-state response analysis is addressed. The computational method is based on the Galerkin/Levenberg-Marquardt approach, in which the frequency/ time domain alternation and FFT procedures, as well as numerical search in the transformed time domain, are introduced. The response features of this hysteretic model are identified. Then, the steady-state responses of base-isolated structures are analyzed by the proposed method with the use of modal partial decoupling. Analytical responses of a vibration-isolated frame are compared favorably with experimental findings.