A transmission system is provided with a superconductive cable having three phase conductors and a cryostat, surrounding the phase conductors, and encasing a hollow space, for conducting a cooling agent. For the three phase conductors, a common neutral conductor is provided, being made of electrically normally conducting material, carried out as insulating round conductor and placed outside the cryostat and next to it. The cryostat is made of a circumferentially enclosed, thermally insulated sheath.