Dynamoelectric machine having air/liquid cooling

A dynamoelectric machine includes a stator having a laminated core and a winding system, which forms winding heads on end faces of the stator, and a rotor having a laminated core and connected to a shaft in a rotationally fixed manner. The stator and the rotor are arranged in a housing, and the shaft is supported by bearings arranged in bearing shields. The laminated core of the stator and/or rotor has axially extending cooling channels. The bearing shields form with the housing a closed interior having at least one closed inner cooling circuit. The housing has an outer jacket and an inner jacket facing the stator and arranged at a distance from the outer jacket in some sections. The outer jacket and the inner jacket combined form a cooling jacket defined by an axial extension which equals at least the axial extension of the laminated core of the stator.