A cableway system has a conveying cable that is guided via a head wheel pulleys in the two terminal stations of the system. Vehicles, such as gondolas or chairs, are coupled to the conveying cable between stations, and they are guided through the stations by way of travelling-gear mechanisms. In the stations, the vehicles are moved by way of tire wheels or control tires, and the tire wheels are driven by at least one supporting roller for the conveying cable. The supporting roller is located in the relevant station. The at least one of these supporting rollers for the conveying cable via which the drive power of the control tires is derived from the conveying cable is adjustable in the vertical direction.