Abstract: The method of catalytic cleaning of exhaust gases from organics and carbon monoxide consists in that an exhaust gas is passed through a bed of deep oxidation catalyst. The process is carried out with a temperature of 250.degree.-700.degree. C. The catalyst is made up of two parts. The exhaust gas is passed through a first part of the catalyst bed, stirred and passed through a second part of the catalyst bed. The stirring is continued until the temperature drop in the stream of the gas which is being cleaned is not over 50.degree. C. at the entrance into the second part of the catalyst bed, and the flow of the gas is reversed at regular intervals during the cleaning.