In a magnetic resonance apparatus a gradient coil system in which "return" arc conductors, which contribute substantially less to the gradient field formation because they are situated further outwards radially and/or axially from the center of the system, are positioned to compensate for stray fields of "effective" are conductors, which are more centrally situated and which contribute more substantially to the gradient field formation. Due to both radial and axial displacement of the return arc conductors relative to the effective arc conductors, the measuring space of the apparatus can be conically shaped, so that a higher patient accessibility is achieved or a smaller diameter can be imparted to a central portion.