A premixing apparatus (A) for mixing fuel gas with air to supply thus obtained air-fuel mixture, through a fan , to a burner , in which a downstream end of a gas supply passage having interposed therein a flow control valve for supplying fuel gas is connected to a gas suction section disposed in an air supply passage to be disposed on an upstream side of the fan , the premixing apparatus (A) comprising: an air resistance changeover means for changing over, between high and low, a ventilation resistance in that section of the air supply passage which is on an upstream side of the gas suction section ; and a gas resistance changeover means for changing over, between high and low, a ventilation resistance in that section of the gas supply passage which is on the downstream side of the flow control valve , wherein the air resistance changeover means is constituted by a butterfly valve rotatably disposed in that section of the air supply passage which is on an upstream side of the gas suction section , characterized in : that , in that section of the air supply passage which is on the upstream side of the gas suction section , an inner tube containing therein the butterfly valve is disposed while leaving a clearance to an inner circumferential wall surface of the air supply passage , and; that a subsidiary passage which is parallel with a main passage inside the inner tube is constituted by the clearance between the inner circumferential wall surface of the air supply passage and an outer peripheral surface of the inner tube . an air resistance changeover means for changing over, between high and low, a ventilation resistance in that section of the air supply passage which is on an upstream side of the gas suction section ; and a gas resistance changeover means for changing over, between high and low, a ventilation resistance in that section of the gas supply passage which is on the downstream side of the flow control valve , wherein the air resistance changeover means is constituted by a butterfly valve rotatably disposed in that section of the air supply passage which is on an upstream side of the gas suction section , characterized in : that , in that section of the air supply passage which is on the upstream side of the gas suction section , an inner tube containing therein the butterfly valve is disposed while leaving a clearance to an inner circumferential wall surface of the air supply passage , and; that a subsidiary passage which is parallel with a main passage inside the inner tube is constituted by the clearance between the inner circumferential wall surface of the air supply passage and an outer peripheral surface of the inner tube . that , in that section of the air supply passage which is on the upstream side of the gas suction section , an inner tube containing therein the butterfly valve is disposed while leaving a clearance to an inner circumferential wall surface of the air supply passage , and; that a subsidiary passage which is parallel with a main passage inside the inner tube is constituted by the clearance between the inner circumferential wall surface of the air supply passage and an outer peripheral surface of the inner tube . <EOS>