Air conditioning with cold storage

The invention relates to comprises an air conditioning system (1) with cold accumulator for a motor vehicle having a refrigerant circuit, an evaporator (1), which serves for cooling air to be conditioned for the interior, wherein, in a cold storage (2) is provided contained cold storage medium, in the region of the evaporator (1) between refrigerant-carrying tubes (4) or discs and / or corrugated ribs (5) is arranged. In this case, the cold storage (2) is exclusively in an air outlet end region of the evaporator (1) and spaced from the air inlet side area of ​​the evaporator (1).