Abstract: The present invention relates to a burner device (10) for a fuel cell system (100), having a burner housing (20) with a burner inlet (22) for admitting a fuel/air mixture (BL) and a burner outlet (24) for discharging a burner exhaust gas/air mixture (BAL), additionally having a catalyst body (30) within the burner housing (20) comprising a catalyst cavity (32) into which the burner inlet (22) opens, wherein the catalyst body (30) is gas-permeable and has a catalyst surface (34) with an at least partly catalytic coating (36), wherein a bypass volume (40) is formed between the catalyst surface (34) and the burner housing (20), said bypass volume opening into the burner outlet (24), wherein the catalyst body (30) additionally has a longitudinal axis (LA), and the catalyst surface (34) has a cross-sectional contour (QK) which deviates from a circular shape at least in some sections with respect to the longitudinal axis (LA).