An aircraft tank system includes a tank cell for receiving fuel, a fuel line that connects the tank cell to a fuel inlet connection, and an aeration/deaeration device that for aeration/deaeration of the tank cell connects the tank cell to the environment. A shut-off valve of the aeration/deaeration device is adapted in an open position to open a connection between the tank cell and the environment and in a closed position to interrupt the connection between the tank cell and the environment. The aircraft tank system further includes an exhaust air outlet connection, which is connected to the aeration/deaeration device and which is adapted during filling of the tank cell with fuel to be connected to an aeration/deaeration connection of a storage tank of a refueling unit.