The invention relates to a fuel cell system (100) having a fuel supply unit (8) and fuel cells (1, 2) having a cathode (4, 4′) and an anode (3, 3′), wherein the cathode (4, 4′) features a cathode feed line (40), the anode (3, 3′) features an anode feed line (30), and the flow in the anode (3, 3′) is connected with the flow in the fuel supply unit (8) via the anode feed line (30), in which a reforming apparatus (13) is arranged, and having an anode exhaust line (6) provided with at least one burner apparatus (22, 23). According to the invention, a first heat exchanger (16) is provided in the cathode feed line (40), and a second heat exchanger (29), which is arranged upstream of the reforming apparatus (13), is provided in the anode feed line (30), wherein the anode exhaust line (6) divides downstream of the burner apparatus (22, 23) into a first anode exhaust subsidiary line (6a) and a second anode exhaust subsidiary line (6b), each of which is connected to an exhaust gas outlet (21), and wherein the first anode exhaust subsidiary line (6a) leads through a warm side of the first heat exchanger (16), and the second anode exhaust subsidiary line (6b) leads through a warm side of the second heat exchanger (29), and the vaporizing arrangement (12) is able to be heated via the second anode exhaust subsidiary line (6b).