The invention relates to a compressor unit (1), in particular for underwater operation, wherein the stator (16) of the motor (2) is connected to a separate cooling means (40). It is an object of the invention to provide a cooling means for the stator of the electric motor, which cooling means firstly affords excellent operational reliability and secondly does not require any exchange of materials with the surroundings during operation. To this end, there is provision for the cooling means (40) to be configured in such a way that there is a natural circulation of a cooling medium (56) in the cooling means (40) of the stator (16) under operating conditions. One decisive advantage of the compressor unit (1) according to the invention lies in the fact that the separate cooling means (40) of the stator (16) can be adapted precisely to the operating conditions of the latter and, in particular, firstly the high power loss and secondly the sensitivity of this component can be taken into consideration.