A process is disclosed for producing a strip-shaped superconductor with several conductor cores made of a high-Tc superconducting material and surrounded by a normal conducting material. A conductor blank (2a) produced from a fabricated conductor should be rolled flat at least once. For that purpose, the conductor blank is fed into the gap (7) between two rollers (8, 9) of which the rolling surfaces (8a, 9a) describe a concave, at least approximately elliptical contour at least in the rolling region (8a). The strip-shaped multi-core conductor produced in this way advantageously contains superconducting cores made of a bi-cuprate embedded in an Ag matrix.