A system for air-conditioning the cabin of a passenger aircraft using externally provided fresh air as well as bleed air tapped from the engine of the aircraft includes at least one heat exchanger (4, 5), a blower (7), a compressor (8), an expansion turbine (9), a condenser (11), a reheater (10), a first high pressure water separator (13), and a second low pressure water separator (12). The several components are connected to each other by air lines such as air ducts, with control valves interposed therein. Two separate air-flow paths representing two different sub-systems are formed. A first air-flow path uses the high pressure water separator while a second air-flow path uses the low pressure water separator. These two air-flow paths or sub-systems can be operated separately and independently of each other by appropriately switching respective shut-off valves. In this manner, the operation of the air-conditioning system can be adaptively switched to achieve an optimal operation under different operating conditions of the aircraft and different air-conditioning requirements.