An air conditioner for an occupant compartment of a vehicle having a forward vehicle space and a rearward vehicle space with right and left seat zones includes an air conditioning box, in which an evaporator and a heat exchanger are arranged, as well as a cold air space situated between the evaporator and the heat exchanger. A warm air space is arranged behind the heat exchanger and air mixing spaces are constructed for supplying the forward vehicle space and the rearward vehicle space with conditioned air. To provide a mutually independent temperature adjustment in the forward vehicle space and the rearward vehicle space, a separate air mixing space is assigned to each seat zone. The four air mixing spaces are connected with the warm and cold air spaces by one warm and one cold air flap respectively.