The influence of bi-directional earthquake-induced loading on eccentric (plan-asymmetric) building systems has been investigated. In the first part of the study, comparisons have been made with equivalent results from uni-directional studies. The results are important in developing analytical models appropriate to the formulation of design recommendations. It is concluded that for valid comparisons, both perpendicular horizontal earthquake components must be considered when using models with transversely-orientated elements. In the second part of the study, an assessment has been made of a simplified, unidirectional (lateral) design approach. For stiffness-eccentric systems, the latter approach gives accurate and reasonably conservative estimates of the critical flexible-edge deformation, but may under estimate the stiff-edge element ductility demand by a factor of two in the short-period range.