A fuel cell has an electrochemical process area having a cathode area, an anode area and an ion-exchanging membrane that separates these areas. The cathode area has a gas passage way having a gas inlet, a gas channel and a gas outlet, wherein the gas passage way is for an oxygen-containing gas to flow from the gas inlet through the gas channel to the gas outlet. The fuel cell includes further a humidity transfer area having a dehumidifying zone, a humidifying zone and a humidity transfer membrane that separates these zones. An exhaust channel connects the gas outlet to the dehumidifying zone, and an inlet channel connects the gas inlet to the humidifying zone. Humidity is extracted from the oxygen-containing gas in the dehumidifying zone, and added to the oxygen-containing gas in the humidifying zone via the humidity transfer membrane.