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A mixed dual frame-wall resilient system, composed of a high-strength moment-resisting steel frame (HS-MRF) and self-centering steel plate shear walls (SC-SPSWs), was proposed to address the issue of frame expansion. To study the steady-state dynamic responses of the structural system, an analytical solution of a single-degree-of-freedom nonlinear oscillator under harmonic excitation was solved using the method of averaging. The steady-state responses of HS-MRF, self-centering frame and steel plate shear wall that are represented by the bilinear, self-centering and pinching hysteresis, respectively, were studied individually, followed by a full system study. A stability analysis was also carried out to evaluate the behaviour of the singular points. The results show that the hysteretic damping in the bilinear system can significantly reduce the resonance, and the responses are always stable. Jump phenomenon …