A complex heat source apparatus comprising: first and second, i.e., a total of two, heat exchangers (1 1, 1 2); a first burner (2 1) for heating the first heat exchanger (1 1), and a second burner (2 2) for heating the second heat exchanger (1 2), both the first and the second burners (2 1, 2 2) being constituted by totally aerated combustion burners; a single fan for supplying primary air, said fan being interposed in a common air supply passage connected to both the first and the second burners (2 1, 2 2); a gas supply passage for supplying fuel gas wherein a downstream end of the gas supply passage is connected to that portion of the air supply passage which is on an upstream side or on a downstream side of the fan so that a mixture of the primary air and the fuel gas can be supplied through the air supply passage to both the first and the second burners (2 1, 2 2); and a flow control means interposed in the gas supply passage so as to vary the amount of fuel gas supply in proportion to the amount of primary air supply, thereby making the air-fuel ratio of the air-fuel mixture constant; wherein an on-off valve is provided at a first connection portion (2 1 a, 2 2 a) between one of the first and the second burners (2 1, 2 2) and the air supply passage, and a flow control valve is provided at a second connection portion (2 1 a, 2 2 a) between the other of the first and the second burners (2 1, 2 2) and the air supply passage; and wherein the apparatus is adapted such that an amount of air-fuel mixture supply to said one of the burners is adjusted by a rotational speed of the fan and the amount of the air-fuel mixture supply to the other of the burners is adjusted by the rotational speed of the fan and by the flow control valve. first and second, i.e., a total of two, heat exchangers (1 1, 1 2); a first burner (2 1) for heating the first heat exchanger (1 1), and a second burner (2 2) for heating the second heat exchanger (1 2), both the first and the second burners (2 1, 2 2) being constituted by totally aerated combustion burners; a single fan for supplying primary air, said fan being interposed in a common air supply passage connected to both the first and the second burners (2 1, 2 2); a gas supply passage for supplying fuel gas wherein a downstream end of the gas supply passage is connected to that portion of the air supply passage which is on an upstream side or on a downstream side of the fan so that a mixture of the primary air and the fuel gas can be supplied through the air supply passage to both the first and the second burners (2 1, 2 2); and a flow control means interposed in the gas supply passage so as to vary the amount of fuel gas supply in proportion to the amount of primary air supply, thereby making the air-fuel ratio of the air-fuel mixture constant; wherein an on-off valve is provided at a first connection portion (2 1 a, 2 2 a) between one of the first and the second burners (2 1, 2 2) and the air supply passage, and a flow control valve is provided at a second connection portion (2 1 a, 2 2 a) between the other of the first and the second burners (2 1, 2 2) and the air supply passage; and wherein the apparatus is adapted such that an amount of air-fuel mixture supply to said one of the burners is adjusted by a rotational speed of the fan and the amount of the air-fuel mixture supply to the other of the burners is adjusted by the rotational speed of the fan and by the flow control valve.