Abstract: A motion damping means for the take-up section of a cable haul system in which one or more rail-mounted carriers support loops of cable, and where the carriers bunch together upon take-up of cable and move apart when cable is paid-out. The cable is fastened to a terminal clamp and at least the first carrier adjacent the clamp is acted upon by a force-exerting means for restraining motion of the carrier towards the clamp for storing at least part of the energy removed from the carrier in restraining this motion and for returning at least part of the energy to that carrier on payout of the cable. In specific embodiments of the invention, the force-exerting means is an elastic rope. Undue swinging of the loops of cable upon take-up is avoided by the restraining action on the carrier.