Abstract: In flue gases or other humid exhaust gases which contain NO.sub.x and SO.sub.2, the NO.sub.x content is reduced and the SO.sub.2 content is oxidized to SO.sub.3 by a catalytic processing and the SO.sub.3 content is subsequently condensed as sulfuric acid. In order to prevent a clogging and deterioration of the catalyst and a contamination of the sulfuric acid the flue gas is subjected before the catalytic processing to a fine dedusting by a scrubbing with hot dilute sulfuric acid. In dependence on the water content of the flue gases the concentration of sulfuric acid in the dilute sulfuric acid and the temperature of the latter are adjusted so that no water will be transferred from the flue gases to the dilute sulfuric acid and no water or only a small amount of water will be transferred from the dilute sulfuric acid to the flue gas.