In known air-conditioning systems of the generic type, an external heat exchanger is provided in the cooling air circuit which is arranged in front of the radiator of the engine and in vehicles with a front part with a modern shape (reduced end face) also leads to thermal problems with the cooling of the engine. The solutions according to the invention avoid the need for an external heat exchanger which is cooled by the slipstream by virtue of the fact that either fresh air is guided via the compressor (14) and the pressure reducing machine (16) or outlet air is guided via the pressure reducing machine (46) and the compressor (44) in each case with the intermediate connection of an internal heat exchanger (18 and 48). Passenger vehicle constitute the preferred field of application. <IMAGE>