A parametric study where the torsional response of base-isolated structures when eccentricities are set in the isolation system is presented. Nonlinear dynamic analyses were used to study peak responses for different static eccentricity ratios between the center of mass and the center of rigidity at the isolation system (eb), due to asymmetries in the stiffnesses of the isolators. 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 for the base-isolated structures was considered in the present study. Bilinear isolator systems with yield forces of 5% of the weight of the complete structure (Vy/W=0.05) and a post-yield stiffness of 10% of 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 eb for those response quantities. Among other relevant issues, it may be concluded from the study that eccentricities in the isolation system lead to a torsional response that adversely affects the design of the isolation system. In general, the amplification factors for the maximum isolator displacement of the unsymmetric system with respect to the symmetric system increase as the eccentricity increases.