The torsional response of base-isolated structures when eccentricities are set in the superstructure is presented. Nonlinear dynamic analyses were used to study peak responses for different ratios of static eccentricities (es) between the center of mass and the center of rigidity for the superstructure. Unidirectional and bidirectional actions of selected ground motions typical of firm soils of the Mexican Pacific Coast were used in the study. An effective period range between 1.5 and 3.0 s (1.5 s≤TI≤3.0 s) for the base-isolated structures was considered in the present study. Bilinear isolator systems with yield forces of 5% and 10% the weight of the complete structure (Vy/W=0.05 and Vy/W=0.10) and a postyield stiffness of 10% their elastic stiffness (k2/k1=0.10) were considered. Peak dynamic responses such as maximum isolator displacements and peak displacement ductility demands were studied and compared to the ones obtained for symmetric systems of reference for the different ground motions under consideration, assessing the importance of the relative value of es on those response quantities.