In this paper a model to describe the lateral dynamic behaviour of long moving ropes employed in high-rise vertical transportation is developed. The model takes into account the fact that the longitudinal elastic stretching of the ropes is coupled with their transverse motions (sway) which results in cubic nonlinear terms. The governing non-stationary nonlinear equations are solved numerically to investigate the passage through resonance conditions arising during the system operation. The active stiffness control of transverse vibrations of the ropes is discussed. This involves the application of a longitudinal action at the rope end. The results of numerical simulation tests demonstrate the ability of multimodal active control to reduce non-linear low frequency sway of the ropes during and after the passage through resonance