Today, base isolation of buildings is a conventional approach to earthquake resistance. The prominent goal is to reduce displacement of structure by movement of elastomeric bearings installed on the base of structures on the ground. Considering widespread construction of asymmetric buildings well as the intensity of damages to such types of structures resulting from earthquake, the present research covers study of interaction mechanics of asymmetric base-isolated structures, where motion equations are presented in two coordinates, one fixed on the building base (global coordinate) and the other on the torsional isolation level (local coordinate). In this conventional approach, the motion equations are calculated on linear form in the initial coordinate system, whereas in the new approach proposed in this research, motion mechanics analysis in the secondary coordinate system will lead to non-linear equations. Three types of structures are proposed with ratio of torsional-lateral correlated natural frequency on asymmetric natural frequency. Responses of both linear and nonlinear methods for the three types of structures under harmonic effects and earthquake are compared while analyzing time history and frequency. Some differences are observed between the linear and nonlinear methods. Then, some non-linear phenomena such as saturation, energy transfer between modes, and rigid displacement in such structures are also analyzed.