NOVELTY - A residual gas burner (3) comprises a combustion chamber (11) bordered at the inlet end by a supply wall (10) and at the outlet end by a cross-current heat exchanger (4). The supply wall has a bypass zone (14) with bypass openings (19) for supplying bypass gas to the combustion chamber. The bypass zone is arranged in a section of the supply wall allocated to an area of the heat exchanger adjacent the paths at the inlet end so that the bypass gas or a bypass gas-burner exhaust gas mixture acts upon this area on the primary end during operation of the burner.    USE - A residual gas burner for a fuel cell system (claimed).    ADVANTAGE - The bypass zone has bypass openings to supply bypass gas to the combustion chamber. This bypass zone is arranged inside the supply wall such that the critical area of the heat exchanger subject to high thermal loads is acted upon by comparatively cold bypass gas. In this way, the thermal burden on the heat exchanger is reduced. The resulting unavoidable loss of efficiency in heat transfer is acceptable and more than balanced by the prolonged lifetime of the heat exchanger.    DETAILED DESCRIPTION - A residual gas burner (3) comprises a combustion chamber (11) bordered at the inlet end by a supply wall (10) and at the outlet end by a heat exchanger (4) and enclosed laterally by a burner wall. The heat exchanger is a cross-current heat exchanger having a primary (20) and a secondary (21) path. The burner exhaust can flow as the primary medium through the primary path in a primary direction (22). A secondary medium can flow through the secondary path in a secondary direction (23) oriented across the primary direction. The secondary path is linked to the primary path to allow heat transfer. The supply wall has a burner zone (13) with oxidizer gas openings (15) for supplying oxidizer gas to the combustion chamber and with combustion gas openings (16) for supplying combustion gas to the combustion chamber. The supply wall has a bypass zone (14) with bypass openings (19) for supplying bypass gas to the combustion chamber. The bypass zone is arranged in a section of the supply wall allocated to an area of the heat exchanger adjacent the paths at the inlet end so that the bypass gas or a bypass gas-burner exhaust gas mixture acts upon this area on the primary end during operation of the burner.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of a fuel cell system.    Burner (3)    Heat exchanger (4)    Anode input (5)    Cathode inlet (6)    Anode outlet (7)    Cathode outlet (8)    End plate (9)    Supply wall (10)    Combustion chamber (11)    Fuel cell (12)    Burner zone (13)    Bypass zone (14)    Oxidizer gas openings (15)    Combustion gas openings (16)    Oxidizer gas line system (17)    Bypass openings (19)    Primary path (20)    Secondary path (21)    Primary direction (22)    Secondary direction (23)    Reaction space (26)    Bypass space (27)    Oxidizer line (31)    Cooling gas line (32)