A superconducting electrical machine includes a rotor with a rotor outer housing surrounding a winding support having a superconducting winding. The rotor has on a torque-transmitting side a first, rigid connection device between the winding support and the rotor outer housing and on the opposite side a second connection device which compensates for axial expansion of the winding support. The second connection device has an axially extending connection element which is on one end connected rigidly to the winding support and which has on the opposite free end an axially moving, radially force-fitting connection to a centering holding element of the rotor outer housing. The holding element includes a bushing through the rotor outer housing, through which the free end of the connection element of the second connection device passes. The superconducting winding is cooled and thermally insulated.