Abstract: A method is provided for filling a fuel storage system of a motor vehicle with fuel at a relatively high pressure. The fuel storage system has a main tank, which can be filled by way of a main filling line until a limit pressure has been reached, and an auxiliary storage device. If the filling line is connected to a supply station, which provides fuel at a pressure exceeding the tank limit pressure, a tank shut-off valve provided in the filling line will be closed in time before the limit pressure is reached in the main tank and an auxiliary tanking valve is opened in an auxiliary storage device filling line branching off from the main filling line upstream of the tank shut-off valve and leading to the auxiliary storage device. The auxiliary storage device is configured to receive fuel at a higher pressure than the above-mentioned tank limit pressure.