Slender continua such as long ropes, cables and belts are used as tension and payload-carrying members in various engineering applications. They are deployed in terrestrial mine/underground equipment and high-rise building installations through to tethered offshore tension members, tethered space satellite systems and rotating momentum exchange tethers in Earth’s orbit. The slender continua are inherently non-linear and this leads to large non-linear responses with passages through resonances taking place when the time-varying natural frequencies of the system approach the frequency of the inertial load resulting from the dynamic loadings. In this paper the lateral nonlinear dynamic behaviour of long slender continua moving at speed in a tall host structures is analyzed. A mathematical model comprising nonstationary nonlinear ordinary differential equations is used to describe the dynamic behaviour of the system equipped with a multi-modal active stiffness controller. The active control is implemented by an axial motion of the support which results in substantial reduction of the response