An electrical machine with cryogenic cooling having a superconducting exciting winding secured to the rotor shaft and accommodated in a cavity in the rotor filled with a coolant. At the places where the superconducting winding is secured to the rotor shaft, there are provided grooves which communicate with a channel for the supply of the coolant, extending along the axis of the shaft at one of its ends, and with a channel for the removal of the coolant, extending along the axis of the shaft at its opposite end. The coolant is removed from the rotor cavity through channels provided at both ends of the rotor shaft. The rotor shaft accounts for an improved thermal protection of the superconducting exciting winding which is cooled only by the liquid phase of the coolant at a temperature of about 4.5 K.