Abstract: The exhaust air from the tenterframe (1) conveyed by a fan (7) is fed as combustion air to the burner (13) of a steam boiler (21). The burner (13) is operated with a variable and high excess of air of .lambda.=1,5 to .lambda.=3,5. The boiler output is regulated by the fuel supply. The excess of air is increased at low boiler load. The boiler exhaust gas is cooled down below the dew point via three heat exchangers (29,30,31). Thus complete combustion of the organic noxious substances in the tenterframe exhaust air and at the same time recovery, which can be readily utilized, of the tenterframe waste heat and a lowering of the fuel requirement of the steam boiler are achieved. The same method is also suitable for purifying the exhaust air from singers.