Abstract: By introducing the yielding level factor and constructing the ductility demand spectrum,the characteristic of peak values and frequency contents of ground motions are considered separately.Taking advantage of nonlinear time history analysis results of a single-degree-of-freedom system with the hysteretic model of bilinear,conditional distribution type of ductility demand factors are verified by goodness-of-fit tests.The formulations of the conditional mean and standard deviation of ductility demand factor for soil type I and II are obtained by nonlinear regression.Utilizing these formulations and the conditional probabilistic density function of ductility demand factor,the calculation method of the statistics of ductility factor is proposed,and the probabilistic ductility demand spectrum and displacement response spectrum are established.