In a magnet system with two coil systems of different mean diameter arranged coaxially with respect to the longitudinal axis of the system defined by the direction of the field in the homogeneity region, which are rotationally symmetrical and are arranged symmetrically about the transverse median plane of the system perpendicular to the longitudinal axis and can carry exciting currents which result in overlapping magnetic fields that compensate, at least approximately, for the dipole fields of the two coil systems, an operating mode selector switch device (22) configured as a superconducting network is provided, by means of which the magnet system (10) can also be switched, as an alternative to the operating mode which provides considerable dipole-field compensation in the outer space of the magnet system (10), to that operating mode in which the magnetic fields generated by the two coil systems (11 and 12) at the center thereof are aligned in the same direction. In a special configuration, the ratio B.sub.0i :B.sub.0a between the values of the field strengths B.sub.0 1 and B.sub.a generated by the inner field coil (11) and the outer field coil (12) is equal to 3.