An aircraft fuel system including at least one fuel tank, a source of inerting gas, an inlet for introducing the inerting gas into the at least one fuel tank, and a vent system arranged to allow the inward and outward venting of air from the fuel tank. In embodiments, the vent system includes a vent, an inward vent pressure valve disposed between the vent and the at least one fuel tank and configured to enable the at least one fuel tank to increase by a predetermined pressure over ambient air pressure, and an outward vent pressure valve disposed between the at least one fuel tank and the vent and configured to enable the at least one fuel tank to decrease by a predetermined pressure below ambient air pressure.