Abstract: Seismic response hazard curves of a structure represent the relationship between the seismic response of a structure and the intensity of earthquake. Using the probabilistic ductility demand spectrum, the seismic response hazard curves of a structure can be established conveniently. Displacement response analysis of nonlinear structures under stochastic seismic is attributed to nonlinear stochastic vibration. The statistic of stochastic displacement response of nonlinear single-degree-of-freedom systems can be simply and effectively obtained by the probabilistic ductility demand spectrum. Combined with nonlinear static analysis, probabilistic ductility demand spectrum can be applied to the analysis of stochastic seismic response of multi-degree-of-freedom systems. Furthermore, probabilistic ductility demand spectrum can be utilized in seismic structural reliability analysis.