The aseismic design of large structures may need to account for the nonstationary and the multivariate aspects of strong ground motions. These aspects influence both the time and the spatial variation of the dynamic response of the structure. Current techniques for treating this problem have considerable limitations. An approach is developed in the thesis for addressing this issue based on energy considerations. Estimates of evolutionary seismic auto- and cross-spectra are obtained. It is assumed that the available accelerograms are realizations of broad-band stochastic processes. By analyzing the output of lightly damped linear systems excited by these processes, estimates are obtained for the associated auto and cross spectral density functions. The proposed estimation techniques have two main advantages. Firstly, the evolutionary auto- and cross-spectra can be estimated without having to assume a specific form for the evolutionary spectrum. Secondly, with the evolutionary auto- and cross-spectra determined, the moments of structural responses to these stochastic seismic models, which are functions of time, can be approximated from the spectra without having to resort to simulation. The proposed method is further extended to provide for situations where not enough data are available to accurately assess the stochastic character of the ground motion. Based on a stochastic interpretation of ground accelerations, a weighted least squares method is used to estimate the coefficients of a commensurate model from the responses of a lightly damped linear system excited by these accelerograms.