An outdoor system of an air conditioner comprising two outdoor units , wherein the two outdoor units include: a first outdoor unit including a first compressor , a first outdoor heat exchanger , a first main four-way valve disposed at an inlet side of the first compressor , a first auxiliary four-way valve disposed at an outlet side of the first compressor , a first heat exchanger input/output line , and a first outdoor system connection line ; a second outdoor unit including a second compressor , a second outdoor heat exchanger , a second main four-way valve disposed at an inlet side of the compressor , a second auxiliary four-way valve disposed at an outlet side of the second compressor , a second heat exchanger input/output line , and a second outdoor system connection line ; a pair of two-stage compression lines extending to the outside of the outdoor units ; wherein the valves are configured to open and close the heat exchanger input/output lines , the outdoor system connection lines , and the pair of two-stage compression lines ; and wherein, when the outdoor unit is switched from any one of the one-stage heating mode and the two-stage heating mode to the other thereof, any one of the main four-way valve and the auxiliary four-way valve is switched, wherein in the one-stage heating mode, refrigerant flowing to the first heat exchanger input/output line and the second heat exchanger input/output line are compressed by the first compressor and the second compressor , flowing to the indoor unit along the first outdoor system connection line and the second outdoor system connection line , and in the two-stage heating mode, refrigerant flowing to the first heat exchanger input/output line and the second heat exchanger input/output line are sequentially compressed in the first compressor and the second compressor , thereby flowing to the indoor unit along the second outdoor system connection line . a first outdoor unit including a first compressor , a first outdoor heat exchanger , a first main four-way valve disposed at an inlet side of the first compressor , a first auxiliary four-way valve disposed at an outlet side of the first compressor , a first heat exchanger input/output line , and a first outdoor system connection line ; a second outdoor unit including a second compressor , a second outdoor heat exchanger , a second main four-way valve disposed at an inlet side of the compressor , a second auxiliary four-way valve disposed at an outlet side of the second compressor , a second heat exchanger input/output line , and a second outdoor system connection line ; a pair of two-stage compression lines extending to the outside of the outdoor units ; wherein the valves are configured to open and close the heat exchanger input/output lines , the outdoor system connection lines , and the pair of two-stage compression lines ; and wherein, when the outdoor unit is switched from any one of the one-stage heating mode and the two-stage heating mode to the other thereof, any one of the main four-way valve and the auxiliary four-way valve is switched, wherein in the one-stage heating mode, refrigerant flowing to the first heat exchanger input/output line and the second heat exchanger input/output line are compressed by the first compressor and the second compressor , flowing to the indoor unit along the first outdoor system connection line and the second outdoor system connection line , and in the two-stage heating mode, refrigerant flowing to the first heat exchanger input/output line and the second heat exchanger input/output line are sequentially compressed in the first compressor and the second compressor , thereby flowing to the indoor unit along the second outdoor system connection line . <EOS>