The fuel line consists of a fuel pipe (2) with an outer wall (3) and an inner wall (4). The inner wall is at least partly covered with a catalytic layer (5). The catalytic layer is catalytically active in the temperature range of 150-600 deg C. The surface (6) of the catalytic layer is made as small as possible and the layer may consist of palladium or of a palladium-platinum alloy. The fuel tube is heated after flushing with air, so that catalytic combustion of the fuel remaining in it takes place.