Abstract: A recuperator for a recuperator burner for preheating combustion air by means of exhaust gas heat in a recuperator burner is disclosed, wherein the recuperator is of a tubular shape with an inside and an outside, wherein a plurality of elevations or ribs and recesses are provided at least on the inside or on the outside thereof and wherein at least one cellular structure, preferably consisting of a cellular metal or an open-pored ceramic foam, is accommodated in one of the recesses, at least on the inside or on the outside. In this arrangement, the inlet air is preferably preheated twice in the burner head, namely, in a first inlet air duct section, by an exhaust duct coaxially surrounded thereby, using cocurrent flow, and additionally by a second inlet air duct section, which is coaxially surrounded by the exhaust duct, using counter-current flow.