Fuel cell system and operating process

A fuel cell system (1), especially in a motor vehicle, is provided with a fuel cell (2), which generates electric current during the operation from anode gas and cathode gas, with a residual gas burner (3), which reacts anode waste gas with cathode waste gas into burner waste gas during the operation; with an air delivery device (17), which feeds air as cathode gas to the fuel cell (2) via a fuel cell air line (12) during the operation; and with a first heat exchanger (14), which couples a waste gas line (13) removing burner waste gas from the residual gas burner (3) with the fuel cell air line (12) in a heat-transmitting operation. The start-up process of the system (1) is improved with an auxiliary burner (20), which reacts air with a fuel into an auxiliary burner waste gas during the operation; with a bypass air line (24), which is connected on the inlet side to the fuel cell air line (12) between the air delivery device (17) and the first heat exchanger (14) and which is connected to the fuel cell air line (12) on the outlet side between the first heat exchanger (14) and the fuel cell (2). A second heat exchanger (23) couples an auxiliary waste gas line (21) removing auxiliary burner waste gas from the auxiliary burner (20) with the bypass air line (24) in a heat-transmitting manner.