The elastic torsional sti!ness of a structure has important in#uence on the seismic response of an asymmetric structure, both in the elastic and inelastic range. For elastic structures it is immaterial whether the sti!ness is provided solely by structural elements in planes parallel to the direction of earthquake or by a combination of such elements in parallel and orthogonal planes. The issue of how the relative contribution of structural elements in orthogonal planes a!ects the torsional response of inelastic structures has been the subject of continuing study. Several researchers have noted that structural elements in orthogonal planes reduce the ductility demands in both the #exible and sti! edge elements parallel to the earthquake. Some have noted that the bene"cial e!ect of structural elements in orthogonal planes is more pronounced when such elements remain elastic. These issues are further examined in this paper through analytical studies on the torsional response of single-storey building models. It is shown that, contrary to the "ndings of some previous studies, the torsional response of inelastic structures is a!ected primarily by the total torsional sti!ness in the elastic range, and not so much by whether such sti!ness is contributed solely by structural elements in parallel planes or by such elements in both parallel and orthogonal planes.