Abstract: A control device controls the air ratio in a combustion apparatus constructed so that combustion fuel supplied via a combustion fuel supplying pipe is burned with oxygen-enriched air obtained by drawing air through an oxygen permeable selective membrane by means of a vacuum pump provided at the downstream side of the oxygen permeable selective membrane and supplied via an air supplying pipe. The control device has an air flow meter and an oxygen concentration analyzer, both provided at the air supplying pipe, and a fuel flow meter provided at the combustion fuel supplying pipe. The air ratio is calculated from the values of the flow rate of of air, the oxygen concentration and flow rate of the combustion fuel. The amount of air drawn by the vacuum pump is controlled so that the actual air ratio is equal to an predetermined air ratio.