In the known filling device, the handling unit is a distributor which is arranged at the bottom end of a vertical conveyor. It is borne by a carriage which travels along a bridge. Since the main components for automatic filling are easily accessible, there is the danger that they can be willfully or accidentally damaged. In order to protect the main components from accidental or willful damage, the handling unit is designed as a tank robot which is housed inside the tank island. The tank robot can reliably grab the filler nozzle by means of its grippers and easily guide it to the filler neck of any motor vehicle. The filling device is not only suitable for conveying fluid fuels but also for pressurized gases.