Reactor for catalytic primary reforming of hydrocarbons using steam at elevated pressure, having a cracking tube system and a firing chamber, - wherein the cracking tube system, as reaction chamber, possesses a multiplicity of vertical tubes which are arranged in rows and are suitable for being filled with catalyst and possesses appliances for feeding hydrocarbons that are to be reformed and steam to the reaction chamber, and also appliances for removing reformed synthesis gases from the reaction chamber, - in this case, additionally having in the upper region of the firing chamber a multiplicity of firing appliances arranged in parallel to one another, - each of which are arranged between the cracking tubes and which consist of a multiplicity of burners arranged in series, - wherein the burners can generate substantially downwards directed flames, - which are suitable for heating the abovementioned tubes, - the respective firing appliances are fed with heating gas and air via feed devices, wherein the air is withdrawn from the respective feeds, - a multiplicity of substantially horizontally arranged flue gas tunnels that proceed in parallel to one another and at right angles to the vertical cracking tubes and are made of ceramic materials for withdrawal of the flue gases through the openings in the side walls of the flue gas tunnels are located in the lower region of the firing chamber, - each of which are assigned to a series of firing appliances, and - the flue gas tunnels, at the exit of the firing chamber, open out into devices which are provided with heat exchangers (14, 15) for heat recovery, characterized in that - at the end side each individual flue gas tunnel in the direction of flow of the withdrawn flue gases has feed appliances for an additional gas which contains not only oxygen but also an incombustible gas, in such a manner that the additional gas passed into the flue gas tunnels passes through the flue gas tunnel along the entire length of the firing chamber, and - wherein each individual one of the feed appliances for the additional gas has devices for the regulation of the additional gas stream, and - wherein the feed appliances of air to the burner have elongations that open out into the feed appliances for additional gas into the flue gas tunnels. - wherein the cracking tube system, as reaction chamber, possesses a multiplicity of vertical tubes which are arranged in rows and are suitable for being filled with catalyst and possesses appliances for feeding hydrocarbons that are to be reformed and steam to the reaction chamber, and also appliances for removing reformed synthesis gases from the reaction chamber, - in this case, additionally having in the upper region of the firing chamber a multiplicity of firing appliances arranged in parallel to one another, - each of which are arranged between the cracking tubes and which consist of a multiplicity of burners arranged in series, - wherein the burners can generate substantially downwards directed flames, - which are suitable for heating the abovementioned tubes, - the respective firing appliances are fed with heating gas and air via feed devices, wherein the air is withdrawn from the respective feeds, - a multiplicity of substantially horizontally arranged flue gas tunnels that proceed in parallel to one another and at right angles to the vertical cracking tubes and are made of ceramic materials for withdrawal of the flue gases through the openings in the side walls of the flue gas tunnels are located in the lower region of the firing chamber, - each of which are assigned to a series of firing appliances, and - the flue gas tunnels, at the exit of the firing chamber, open out into devices which are provided with heat exchangers (14, 15) for heat recovery, characterized in that - at the end side each individual flue gas tunnel in the direction of flow of the withdrawn flue gases has feed appliances for an additional gas which contains not only oxygen but also an incombustible gas, in such a manner that the additional gas passed into the flue gas tunnels passes through the flue gas tunnel along the entire length of the firing chamber, and - wherein each individual one of the feed appliances for the additional gas has devices for the regulation of the additional gas stream, and - wherein the feed appliances of air to the burner have elongations that open out into the feed appliances for additional gas into the flue gas tunnels.