Seismic response of primary-secondary structural system with the consideration of torsional coupling of the primary system is obtained for bi-directional earthquake excitations. Response quantities of interest are the relative displacement between the primary and the secondary system, and the absolute acceleration of the secondary system. Responses of the secondary system are obtained by the frequency domain spectral analysis using white noise input excitation in two orthogonal directions. The response behavior of the secondary system is examined under a set of important parametric variations. The parameters include the uncoupled lateral frequency of the primary system, , the natural frequency of the secondary system, @, the ratio of uncoupled lateral to rotational frequencies, /w, of the primary system, eccentricity ratios of the primary, epx/rand ep/r, and the secondary, e/r and e/r, systems in X and Y directions, damping ratios of the primary, ,, and the secondary, 5,, systems, and the mass ratio, m,/m,,, of the two systems.