The performance of lift (elevator) systems deployed in the modern tall built environment can be substantially affected by adverse environmental conditions suchs as seismic (earthquake) activities (as well as strong winds). The building motion (sway) which is induced by those environmental conditions excites the lift system elastic components such as suspension / compensating ropes, belts and cables. A complex dynamic situation arises when the building is excited near its natural frequency which in turn approaches the natural frequency of the ropes. In this scenario resonances interactions phenomena take place. These phenomena severely affect lightly tensioned compensating ropes, as well as travelling cables, that sway at the frequency of the building displaying non-planar responses. Thus, the lift system designers have to take into consideration the critical characteristics of the building structure before the lift installation is constructed and installed. In this presentation the excitation mechanism is explianed and the dynamic analysis of responses of lift ropes is discussed. Suitable control strategies can then be developed and applied to minimize the effects of adverse dynamic responses arising in the building – lift system.