The object of this paper is mainly on the clarification of the inelastic earthquake responses of space structures subjected to three components of ground motion and on the proposal of an aseismic design method considering the vertical responses of structural members. Effects of initial condition and dynamic axial force on the local responses of space structures and the frequency characteristics of input ground motion on the general vertical responses are discussed. Finally, fundamental periods of vertical and horizontal vibration are approximately formulated and the effect of vertical response on the aseismic safety of structures corresponding to the span length- height ratio and the number of story are summarized.