Abstract: In this paper, studied is the influence of ground-motion peak displacements on the dynamic, especially non-linear dynamic, responses of single-degree-of-freedom (SDOF) systems, under the condition that the response spectrum and the peak velocity of the input ground motion are fixed. Firstly, by the method of superimposing narrow-band time histories in the time domain, two groups of artificial ground-motion time histories are synthesized, whose response spectra and peak velocities are same, while the peak displacement of one group is double the other. Secondly, by utilizing the initial natural period and the yielding strength reduction factor to describe the stiffness and the degree of the non-linear mechanical behavior of an ideal elastic-plastic SDOF system, respectively, and by comparing the seismic responses invoked by these two groups of input ground motion, the influence of ground-motion peak displacements on the elastic-plastic seismic responses of a system is analyzed. It has been concluded that, under the condition that the response spectrum and the peak velocity of input ground motions are identical, if the non-linear mechanical behavior of the system gains enough development, the increase of ground-motion peak displacements would significantly increase the elastic-plastic velocity and displacement responses of long-period structures. And such effect is more distinct for the displacement response.