A premixing apparatus for mixing fuel gas supplied through a gas supply passage having interposed therein a flow control valve with air to supply thus obtained air-fuel mixture, through a fan, to a burner, wherein a downstream end of the gas supply passage is connected to a gas suction section disposed in an air supply passage on an upstream side of the fan, the premixing apparatus 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; 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 a downstream side of the flow control valve, wherein the air resistance changeover means is constituted by a butterfly valve disposed in that section of the air supply passage which is on the upstream side of the gas suction section, the butterfly valve being rotated by a stepping motor into an opened posture parallel with a longitudinal direction of the air supply passage or into a closed posture at right angles to the longitudinal direction of the air supply passage, wherein the gas resistance changeover means is constituted by a changeover valve disposed in the gas supply passage in an openable and closable manner; an interlocking mechanism causing the changeover valve to open or close in interlocking with the rotation of the butterfly valve into the opened posture or the closed posture, the interlocking mechanism being so arranged that, until the butterfly valve has been rotated from the closed posture toward the opening side by a predetermined angle, the changeover valve is maintained in the closed state, characterized in that the premixing apparatus is adapted such that, when the butterfly valve is rotated from the closed posture into the opened posture, a driving frequency of the stepping motor is made higher, until the butterfly valve has rotated from the closed posture toward the opening side by a predetermined set angle, than the driving frequency during the time at which the butterfly valve rotates from the said set angle to the opened posture. 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; 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 a downstream side of the flow control valve, wherein the air resistance changeover means is constituted by a butterfly valve disposed in that section of the air supply passage which is on the upstream side of the gas suction section, the butterfly valve being rotated by a stepping motor into an opened posture parallel with a longitudinal direction of the air supply passage or into a closed posture at right angles to the longitudinal direction of the air supply passage, wherein the gas resistance changeover means is constituted by a changeover valve disposed in the gas supply passage in an openable and closable manner; an interlocking mechanism causing the changeover valve to open or close in interlocking with the rotation of the butterfly valve into the opened posture or the closed posture, the interlocking mechanism being so arranged that, until the butterfly valve has been rotated from the closed posture toward the opening side by a predetermined angle, the changeover valve is maintained in the closed state, characterized in that the premixing apparatus is adapted such that, when the butterfly valve is rotated from the closed posture into the opened posture, a driving frequency of the stepping motor is made higher, until the butterfly valve has rotated from the closed posture toward the opening side by a predetermined set angle, than the driving frequency during the time at which the butterfly valve rotates from the said set angle to the opened posture.