An electric machine includes a stator device having axial first cooling channels, and second and third cooling channels. The third cooling channels are arranged in the first cooling channels and extend at least substantially along an entire axial length thereof. The stator device is configured for inflow and outflow of a liquid cooling medium at least partially through the second cooling channels and for the liquid cooling medium to be conducted through the third cooling channels. A rotor is arranged on a rotor shaft for rotation around a rotational axis. Limiting elements are mounted on the stator device axially on both sides to thereby bound an internal rotor space which is in communication with axial ends of the first cooling channels of the stator device to thereby establish an internal air-cooling circuit from the internal rotor space through the first cooling channels and back into the internal rotor space.