A cable railway system has two or more stations and at least one carrying cable and a conveying cable extending between the stations and guided in the stations by way of deflection pulleys. At least one of the pulleys is driven. Vehicles, such as cable cars or chairs, may be boarded or disembarked from in the stations by the passengers. The system may also have one or more fixed carrying cables along which the cars are moved by way of one or more hauling cables. At least one device is associated with the vehicles along the section of the cable railway system, by way of which device the pendulum movements that the vehicles are subject to transversely relative to the direction of movement of the vehicles are detectable and its output signals are conducted to a device that controls the drive of the cable railway system. The drive is thereby controllable in dependence on the extent of the pendulum movements.