Abstract: An electrical machine with a stator has a winding support, which has at least one radial cooling slot, and a rotor, which likewise has at least one radial cooling slot. The winding support of the stator has on its outer shell a number of axially running cooling ribs, along which an axially running first cooling flow can be directed. Furthermore, the rotor has axially running first cooling ducts, which open out into its at least one radial cooling slot, so that a second cooling flow can be directed in the axial direction along the axial cooling ribs of the stator through the axial first cooling ducts of the rotor, the at least one radial cooling slot of the rotor, the air gap between the rotor and the stator and the at least one radial cooling slot. In this way, the stator can be cooled by two different cooling flows.