(57) A method for the combustion of a lower hydrocarbon fuel by the use of a catalyst system provided, relative to the flow of a flammable mixed gas comprising said lower hydrocarbon having 1 to 4 carbon atoms and molecular oxygen, on the inlet side thereof with a front-stage catalyst bed packed with a catalyst containing one active component selected from the group consisting of an active component formed of palladium and platinum and an active component formed of palladium, platinum, and nickel oxides and on the outlet side thereof with a rear-stage catalyst bed packed with a catalyst containing one active component selected from the group consisting of an active component formed of platinum and an active component formed of platinum and palladium, which method comprises feeding said flammable mixed gas to said catalyst system, allowing at least part of said lower hydrocarbon in said mixed gas to undergo catalytic combustion in said catalyst system, and enabling the temperature of resultant combustion gas to rise to a level enough to induce secondary combustion.