An aircraft fuel system comprising 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, wherein the vent system comprises: a vent; an inward vent pressure check valve disposed between the vent and the at least one fuel tank and configured to enable a predetermined degree of negative pressure to be maintained within the fuel tank; and an outward vent pressure check valve disposed between the at least one fuel tank and the vent and configured to enable a predetermined degree of positive pressure to be maintained within the fuel tank; wherein, the aircraft fuel system further comprises an inward vent line for directing inwardly vented air from the vent to the at least one fuel tank and wherein the inward vent pressure check valve bypasses the inward vent line; characterized in that, the vent system further comprises a vent tank and the inward vent pressure check valve and outward vent pressure check valve are disposed between the at least one fuel tank and the vent tank, wherein, the fuel system further comprises a vent distribution duct extending through the at least one fuel tank and arranged to receive inwardly vented air from the vent system and distribute the inwardly vented air across the at least one fuel tank, the inward vent line extends from the vent tank to the vent distribution duct, wherein the inward vent line includes a mixing chamber and the inlet for introducing inerting gas deposits the inerting gas at the mixing chamber. 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, wherein the vent system comprises: a vent; an inward vent pressure check valve disposed between the vent and the at least one fuel tank and configured to enable a predetermined degree of negative pressure to be maintained within the fuel tank; and an outward vent pressure check valve disposed between the at least one fuel tank and the vent and configured to enable a predetermined degree of positive pressure to be maintained within the fuel tank; wherein, the aircraft fuel system further comprises an inward vent line for directing inwardly vented air from the vent to the at least one fuel tank and wherein the inward vent pressure check valve bypasses the inward vent line; characterized in that, the vent system further comprises a vent tank and the inward vent pressure check valve and outward vent pressure check valve are disposed between the at least one fuel tank and the vent tank, wherein, the fuel system further comprises a vent distribution duct extending through the at least one fuel tank and arranged to receive inwardly vented air from the vent system and distribute the inwardly vented air across the at least one fuel tank, the inward vent line extends from the vent tank to the vent distribution duct, wherein the inward vent line includes a mixing chamber and the inlet for introducing inerting gas deposits the inerting gas at the mixing chamber. a vent; an inward vent pressure check valve disposed between the vent and the at least one fuel tank and configured to enable a predetermined degree of negative pressure to be maintained within the fuel tank; and an outward vent pressure check valve disposed between the at least one fuel tank and the vent and configured to enable a predetermined degree of positive pressure to be maintained within the fuel tank; wherein, the aircraft fuel system further comprises an inward vent line for directing inwardly vented air from the vent to the at least one fuel tank and wherein the inward vent pressure check valve bypasses the inward vent line; characterized in that, the vent system further comprises a vent tank and the inward vent pressure check valve and outward vent pressure check valve are disposed between the at least one fuel tank and the vent tank, wherein, the fuel system further comprises a vent distribution duct extending through the at least one fuel tank and arranged to receive inwardly vented air from the vent system and distribute the inwardly vented air across the at least one fuel tank, the inward vent line extends from the vent tank to the vent distribution duct, wherein the inward vent line includes a mixing chamber and the inlet for introducing inerting gas deposits the inerting gas at the mixing chamber.