<p>The elastic-plastic displacement response of structures under long-period ground motions including far-field long-period ground motions (FLGM) and near-fault pulse-like ground motions (NPGM), are significantly different from ordinary ground motions (OGM), and the post-yield stiffness ratio of structures is a crucial index that determines the residual displacements and repairability of structures after earthquakes. Studying the influence of the post-yield stiffness ratio on the maximum and residual displacements of structures under long-period ground motions is crucial for post-earthquake repairs. This paper selected 25 OGM, 25 FLGM, and 25 NPGM to calculate the elastic-plastic displacement response of single degree of freedom (SDOF) systems, analyzing the influence of ground motion types, post-yield stiffness ratio, natural periods, and strength reduction coefficients on normalized elastic-plastic displacement. And the influence of design parameters and loading paths on the post-yield stiffness ratio of components was analyzed by finite element analysis based on the method of calculating the post-yield stiffness ratio of components. The results show that the normalized maximum displacement decreases with the increase of the period, the increase of post-yield stiffness ratio and the decrease of strength reduction coefficient. Nevertheless, the variation degree of the normalized maximum displacement is distinguishing under different ground motions. The normalized residual displacement of SDOF system under the NPGM is the most significant and the variation of normalized residual displacement with post-yield stiffness ratio, strength reduction coefficient and natural period is different under different ground motions. Moreover, post-yield stiffness ratio of components is significantly influenced by design parameters and loading path.</p>