Abstract: In flue gases or other humid exhaust gases which are relatively cold and contain SO.sub.2, NO.sub.2 and other gaseous pollutants, the SO.sub.2 content is oxidized to SO.sub.3 and the NO content is reduced by a catalytic treatment, the SO.sub.3 content is condensed as sulfuric acid and other gaseous pollutants are removed by being scrubbed with aqueous liquids at low temperatures. In order to heat up the flue gas to the temperature required for the catalysis, the flue gas is heated up in a first heating-up stage by an indirect heat exchange with the catalytically treated gas before the catalytic treatment, the heated-up gas is heated up further in a second heating-up stage to the temperature required for the catalytic treatment, the catalytically treated gas which has been cooled in the first heating-up stage is cooled further in an indirect heat exchanger below the dew point temperature of sulfuric acid and is subsequently fed to an SO.sub.3 condenser.