The invention concerns an air conditioning system for the conditioning of the air of a passenger compartment of a motor vehicle. The air conditioning system has a refrigerant circuit with a compressor, a refrigerant-coolant heat exchanger for desuperheating the refrigerant after the compression, a first refrigerant-air heat exchanger and a second refrigerant-air heat exchanger, and at least one coolant circuit. The coolant circuit has a heating heat exchanger for heating an air mass flow being supplied to the passenger compartment. The refrigerant-coolant heat exchanger is designed as a component of the coolant circuit having the heating heat exchanger. The air conditioning system is designed for an operation in refrigerator mode, in heat pump mode, and in afterheating mode for the heating, cooling, and dehumidification of the air being supplied to the passenger compartment. A valve arrangement switches the air conditioning system between the different operating modes.