A superconducting electrical cable is specified, which is surrounded by a cryostat (3), which comprises two concentric metallic tubes (4, 5) which enclose thermal insulation between them and is used to carry a cooling medium. The cable has at least one superconductor (1), which is composed of superconducting material, as well as a normal electrical conductor (7), which is composed of normally conductive material and is electrically conductively connected to the superconductor. The normal conductor (7) is arranged outside of but resting on the cryostat (3).