Abstract: The process removes acid components including sulfur oxides and nitrogen oxides from the exhaust gases of industrial furnaces and includes oxidizing the nitrogen oxide contained in the exhaust gases with the oxygen contained in the exhaust gases at a exhaust gases temperature between 300.degree. and 900.degree. C. before entry of the gases into a first absorption stage, with an addition to the exhaust gases of an organic compound, preferably methanol, as a radical former. After oxidation of nitrogen oxides the exhaust gases undergo a two-stage absorption using aqueous ammonium salt solutions as absorption liquid, whose pH-value is continuously adjusted to less than 5 by addition of aqueous ammonia solution. The mol ratio of NO.sub.2 to SO.sub.2 in the exhaust gases introduced to the second absorption stage is maintained between 0.01 and 0.5 by diverting a portion of the exhaust gases prior to the first absorption stage to the second absorption stage.