The analysis and design of structures for earthquake resistance requires reliable estimates of the ground shaking expected at the site. Current procedures for the evaluation of these seismic ground motion characteristics tend to be empirical and result in estimates that are restricted to the particular earthquake and site for which they were developed. The results of such analyses therefore may not be suitable for general seismic response analyses of structures. This research program addresses the task of establishing reliable estimates for the description parameters that influence the seismic motions at a site. The multitude of recorded earthquake data at SMART-1 (Strong Motion Array in Taiwan-1) and the newly developed techniques for decomposing the motions into their dominant wave components is used for this purpose. The analysis of the dominant wave characteristics at the site for a number of earthquakes provides a basis with which to evaluate general expressions for the stochastic characteristics of the seismic motions (power and cross spectral densities of the motions in three orthogonal directions, their rotational components and their spatial variability). The development of attenuation equations that relate the stochastic descriptions of the motions with the earthquake and site characteristics is being explored.