Abstract: A process and an apparatus for the purification of gases, particularly for the desulphurization of and NO.sub.x -elimination from flue gas by multistage adsorption and catalytic reaction in gravity-flow moving beds of granular, carbon-bearing materials contacted by a transverse steam of the gas, in which a minimum of two moving beds are arranged in series with reference to the gas route so that NO.sub.x -elimination takes place in the second or any downstream moving bed. Where large volumes of flue gas from industrial furnaces must be purified, purification is adversely affected by the formation of gas streaks with widely varying sulphur dioxide concentrations. This disadvantage is eliminated in that the prepurified flue gas leaving the first moving bed and having a locally variable sulphur dioxide concentration gradient is subjected to repeated mixing before ammonia is added as reactant for NO.sub.x -elimination.