SUMMARYAn attempt has been made to explore the general trends in the seismic response of plan-asymmetric structures without any restrictions imposed by a particular code. Systems with structural elements in both orthogonal directions under bi-directional excitation were studied. Idealized single-storey models with bi-axial eccentricity were employed. The systems were torsionally sti and, in the majority of cases, mass-eccentric. The main ÿndings are: in general, inelastic torsional response is qualitatively similar to elastic torsional response. Quantitatively, the torsional e ect on the exible side, expressed as an increase of displacements due to torsion, decreases slightly with increasing plastic deformation, unless the plastic deformations are small. The response on the sti side generally strongly depends on the e ect of several modes of vibration and on the in uence of the ground motion in the transverse direction. These in uences depend on the structural and ground motion characteristics in both directions. Reduction of displacements due to torsion, typical for elastic torsionally sti structures, usually decreases with increasing plastic deformations. As an additional e ect of large plastic deformations, a attening of the displacement envelopes in the horizontal plane usually occurs, indicating that torsional e ects in the inelastic range are generally smaller than in the elastic range. The dispersion of the results of inelastic torsional response analysis is generally larger than that of elastic analysis.