A cylindrical gradient coil arrangement is provided for a magnetic resonance device. The arrangement includes at least one conductive structure that forms at least one gradient coil and a cooling device that uses a cooling fluid to cool the at least one conductive structure. The arrangement includes an outer carrier structure and an inner carrier structure. The outer carrier structure includes two tubular, coaxial outer sections with different diameters. The inner, tubular carrier structure is arranged between and coaxially with the outer sections. The conductive structure is placed on the inner carrier structure. The inner carrier structure is spaced from the outer sections by a clearance. The clearance forms a cooling channel through which the cooling fluid of the cooling device may flow. The inner carrier structure is fastened to the outer carrier structure at least in a point-by-point manner.