mahdi@cc.iut.ac.ir Most of researches on elastic and inelastic earthquake response of asymmetric buildings have performed using single-storey models idealized with simple lateral load resistant shear-beam elements. These researches have led to different and sometimes contradictory results emerging from their initial assumptions. On the other hand, some practical issues related to the ductility demand of asymmetric buildings with dual lateral load resistant systems have not been considered. The effect of resisting planes perpendicular to the earthquake excitation for different asymmetric buildings under multicomponent ground motions along with the multi-story effect on inelastic torsional behavior of these structures are not fully understood. In the present study, aimed towards the understanding these critical issues, the inelastic seismic response of eccentric multi-story dual lateral load resistant R/C buildings is investigated subjected to an assemblage of ordinary and near-fault ground motions. Symmetric frame basis of these models were developed using the generic structures algorithm. Then asymmetric buildings were created by adding shear walls in both two principal directions. The nonlinear behavior of beam elements is idealized using moment-curvature theory, while fiber model is utilized to represent the interaction among tension/compression axial force and biaxial bending in column elements and shear walls modeled by panel elements. This approach of modeling is more accurate for multistory dual lateral load resistant structures, because it redefines the stiffness from the strength in each time step. The concept of stiffness eccentricity is modified and used to evaluate the torsional responses of the models. The torsional responses of models including the ductility demands for stiff and flexible edges elements are normalized to the corresponding values of the symmetric cases. The distribution of the normalized ductility demands along the height of the structure is used to assess the torsional effects in multistory structures.