The invention relates to a superconductive multi-phase, fluid-cooled cable system comprising a) a cable comprising at least three electrical conductors constituting at least two electrical phases and a zero- or neutral conductor, said electrical conductors being mutually electrically insulated from each other, and b) a thermal insulation defining a central longitudinal axis and having an inner surface and surrounding the cable, said inner surface of said thermal insulation forming the radial limitation of a cooling chamber for holding a cooling fluid for cooling said electrical conductors. The invention further relates to a method of manufacturing a cable system and to its use. The object of the present invention is to provide a simplified manufacturing and installation scheme for a fluid cooled cable system. The problem is solved in that said cable—at least over a part of its length—is located eccentrically relative to said central longitudinal axis when viewed in a cross section perpendicular to said longitudinal axis and where the eccentric location has the function of accommodating thermal shrinkage and expansion of the cable with respect to the thermal insulation.