In this paper

two horizontal components of earthquake-induced ground motions are considered to be stationary random processes.On the basis of the single-dimensional random model

the spatial correlation of ground motions in two horizontal directions is analyzed in time domain and the correlation function matrix of two-dimensional horizontal random earthquake ground motion model is established according to the concept of principal axes of motions.Considering the spatial correlation of earthquake ground motions

the correlation function matrix is not only related to the intensity ratio of ground motions in two horizontal directions but also related to the angle of position between structural axes and principal axes of ground motions.The correlation function matrix can be used as the inputs of ground motions of random response analysis for structures due to two-dimensional earthquake motions.The equation of motion of the structures subjected to two-dimensional horizontal seismic excitations is represented by the state equations in state space

and the complex vibration characteristics and responses are analyzed.The method of a complex mode superposition is used to deduce the covariance response matrix of linear time-invariant structures under excitation of two-dimensional random model.The statistic characteristics of the responses may be obtained directly from the correlation function response matrix in time domain.Finally

a two-story single-span frame structure is given for numerical illustration of this method and the effects of intensity ratio of two components inputs and position angle on structural responses are discussed.This method can be developed to analyze the stationary responses of the structures subjected to multi-dimensional inputs in practice and the results can provide a basis for reliability assessment of the seismic structures.