An aircraft air conditioning system (10) comprises an ambient air supply line (12) allowing a flow of ambient air therethrough, an ambient air cooling device (28) connected to the ambient air supply line (12) and being adapted to cool the ambient air flowing through the ambient air supply line (12), and an ambient air discharge line (62) connected to the ambient air cooling device (28) and being connectable to an aircraft cabin (48). The aircraft air conditioning system (10) further comprises a compressed air supply line (30) allowing a flow of compressed air therethrough, a compressed air cooling device (38) connected to the compressed air supply line (30) and being adapted to cool the compressed air flowing through the compressed air supply line (30), and a compressed air discharge line (40) connected to the compressed air cooling device (38) and being connectable to the aircraft cabin (48). A refrigerating apparatus (68) comprises a refrigerant circuit (70) allowing the flow of a two-phase refrigerant therethrough and is designed to convert the two-phase refrigerant, upon flowing though the refrigerant circuit (70), from the liquid state of aggregation into the gaseous state of aggregation and thereafter again back from the gaseous state of aggregation into the liquid state of aggregation. The refrigerant circuit (70) of the refrigerating apparatus (68) is adapted to supply cooling energy to the ambient air cooling device (28) and the compressed air cooling device (38).