PURPOSE: To provide an efficient and economic method for eliminating combustibles contained in offgas of air and/or waste gases by means of using the heat value in offgas, without limitations and demerits of existing methods.

CONSTITUTION: The method described is a method for eliminating combustibles contained in offgas of air and/or waste gases by catalytic combustion of the combustibles. The method comprises the steps of compressing the offgases in a compressor 10, heating the compressed offgas to a temperature required for subsequent catalytic combustion of the combustibles in the offgas, combusting and eliminating the combustibles in the compressed and heated offgas by contacting a combustion catalyst arranged in a combustion chamber, and expanding the combusted offgas to atmospheric pressure in a gas expansion turbine 16.