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A resilient system comprised of a high-strength moment-resisting steel frame (HSMRF) and self-centering steel plate shear walls (SC-SPSWs) has been proposed to address the issue of frame expansion. The system’s steady-state dynamic responses were analysed using an analytical solution of a single-degree-of-freedom nonlinear oscillator under harmonic excitation, solved via the method of slowly varying parameters. A stability analysis was also conducted to assess the behaviour of singular points. The hysteretic model for the proposed structure is a combination of validated bilinear, self-centering, and pinching hysteresis, representing the high-strength frame, self-centering frame, and steel plate shear wall, respectively. The results indicate that increasing the proportion of bilinear hysteresis has minimal impact on resonance but can decrease nonlinearity for lower excitation intensities. However, for higher intensities, increasing the bilinear hysteresis can significantly decrease peak responses and reduce both the jump and unbounded phenomena. Most of the unstable responses can be divided into four zones, and the unstable regions are greatly influenced by the ratio of hysteretic models. This steady-state dynamic analysis suggests that a well-designed mixture of high-strength moment-resisting steel frames and self-centering steel plate shear walls can bring a favourable seismic performance.