Disclosed is a furnace whose NOx emission may be reduced to a minimum degree so far unattainable in any prior art furnaces by optimumly controlling the ratio of exhaust gas mixed with the combustion air to be supplied to the burners to the exhaust gas to be mixed with the two-stage combustion air which is admitted through air nozzles into the combustion chamber and also by optimumly controlling the distribution of the two-stage combustion air in the combustion chamber depending upon the operating conditions. The present invention may be applied to any types of furnaces.