An actively shielded superconducting magnet coil system (1) for generating a magnetic field in a working volume (6), which is rotationally symmetric about a z-axis, comprising a radially inner main field winding (5) and a radially outer shielding winding (7), and an electrically highly conductive shielding cylinder (radially inner shielding cylinder) (8a/8b) which is disposed radially inside the main field winding (5) or between main field winding (5) and the shielding winding (7) is characterized in that at least one further electrically highly conductive shielding cylinder (9) is disposed radially outside the shielding winding (7). The inventive magnet coil system prevents generation of a fringe field flash in the outer region of the magnet coil system in case of a quench.