The invention relates to a method for operating a fuel cell system, in particular a PEM fuel cell system, in which an anode gas is supplied to an anode (1) of a fuel cell via a supply path (2), and is fed back via a recirculation path (3) connected to the anode (1), wherein hydrogen is used as the anode gas. According to the invention, during the start up of the fuel cell system, the anode gas is supplied to a drying device (4), in particular an adsorber, via at least one normally open valve (8, 9, 10), and water is extracted from the anode gas using the drying device (4). The invention also relates to a fuel cell system, in particular a PEM fuel cell system, which is suitable for carrying out the method.