Air-conditioning apparatus for a motor vehicle, having a refrigerant circuit which comprises - a compressor, - an internal heat exchanger arrangement which at the input end is connected to the output of the compressor via a first refrigerant line section and through which portions of an air flow which can be conducted into a passenger compartment of the motor vehicle can flow, comprising • a first air/refrigerant heat exchanger segment which can be operated as an evaporator of the refrigerant circuit, • a first expansion valve which can be connected upstream of the first air/refrigerant heat exchanger segment in the flow direction of the refrigerant, and • a second air/refrigerant heat exchanger segment which is connected upstream of the first expansion valve in the direction of flow of the refrigerant and which can be operated as a condenser of the refrigerant circuit, - a second expansion valve which is connected downstream of the internal heat exchanger arrangement in the direction of flow of the refrigerant, and - a coupling heat exchanger which at the input end is connected to the second expansion valve via a second refrigerant line section and is thermally connected to a heat source or heat sink, the output of the said coupling heat exchanger being connected to the input of the compressor via a third refrigerant line section, and - the output of the first air/refrigerant heat exchanger segment and the input of the compressor are connected to one another via a sixth refrigerant line section, characterized in that - the first and the second refrigerant line section (I/II) are connected to one another via a fourth refrigerant line section, - the input of the second air/refrigerant heat exchanger segment and the output of the coupling heat exchanger are connected to one another via a fifth refrigerant line section which contains a third expansion valve, and - adjustable valves (42, 43, 51, 52, 52, 53, 54) are arranged in a manner distributed in the refrigerant circuit in such a way that, depending on their switching position, refrigerant can flow through the first, the second and the third refrigerant line section (I/II/III), while throughflow of refrigerant is suppressed in the fourth, in the fifth and in the sixth refrigerant line section (IV/V/VI), in a heat pump mode, or refrigerant can flow through the fourth, fifth and sixth refrigerant line section (IV/V/VI), while throughflow of refrigerant is suppressed in the first, in the second and in the third refrigerant line section (I/II/III), in a cooling mode. - a compressor, - an internal heat exchanger arrangement which at the input end is connected to the output of the compressor via a first refrigerant line section and through which portions of an air flow which can be conducted into a passenger compartment of the motor vehicle can flow, comprising • a first air/refrigerant heat exchanger segment which can be operated as an evaporator of the refrigerant circuit, • a first expansion valve which can be connected upstream of the first air/refrigerant heat exchanger segment in the flow direction of the refrigerant, and • a second air/refrigerant heat exchanger segment which is connected upstream of the first expansion valve in the direction of flow of the refrigerant and which can be operated as a condenser of the refrigerant circuit, • a first air/refrigerant heat exchanger segment which can be operated as an evaporator of the refrigerant circuit, • a first expansion valve which can be connected upstream of the first air/refrigerant heat exchanger segment in the flow direction of the refrigerant, and • a second air/refrigerant heat exchanger segment which is connected upstream of the first expansion valve in the direction of flow of the refrigerant and which can be operated as a condenser of the refrigerant circuit, - a second expansion valve which is connected downstream of the internal heat exchanger arrangement in the direction of flow of the refrigerant, and - a coupling heat exchanger which at the input end is connected to the second expansion valve via a second refrigerant line section and is thermally connected to a heat source or heat sink, the output of the said coupling heat exchanger being connected to the input of the compressor via a third refrigerant line section, and - the output of the first air/refrigerant heat exchanger segment and the input of the compressor are connected to one another via a sixth refrigerant line section, - the first and the second refrigerant line section (I/II) are connected to one another via a fourth refrigerant line section, - the input of the second air/refrigerant heat exchanger segment and the output of the coupling heat exchanger are connected to one another via a fifth refrigerant line section which contains a third expansion valve, and - adjustable valves (42, 43, 51, 52, 52, 53, 54) are arranged in a manner distributed in the refrigerant circuit in such a way that, depending on their switching position, refrigerant can flow through the first, the second and the third refrigerant line section (I/II/III), while throughflow of refrigerant is suppressed in the fourth, in the fifth and in the sixth refrigerant line section (IV/V/VI), in a heat pump mode, or refrigerant can flow through the fourth, fifth and sixth refrigerant line section (IV/V/VI), while throughflow of refrigerant is suppressed in the first, in the second and in the third refrigerant line section (I/II/III), in a cooling mode.