A gradient coil system comprises a gradient coil for generating a rapidly changing magnetic gradient field in a working volume of a magnetic resonance apparatus, with a current path guided in windings on the surface of a geometric body, the geometry of which results in the desired spatial dependence of the magnetic field of this gradient coil in the working volume. N current power supplies (NG1, NG2) can be controlled with an analog or digital control signal to each generate a time-dependent controlled electric current (i1, i2) proportional to the control signal. The current path is divided into several parallel conductor paths which are electrically insulated from one another, and which form a doubly or multiply wound transformer, wherein the inductances of the various conductor paths with respect to one another as well as the mutual inductances with respect to one another have approximately the same value L. The ends of each conductor path are each connected to one respective current power supply (NG1,NG2), and the current power supplies (NG1, NG2) can be controlled with control signals in such a manner as to supply the same current (i1, i2) to the conductor paths at all times. This enables operation of a gradient coil with several current power supplies in such a manner that, should the dependencies of the currents of the current power supplies not be precisely identical, generation of disturbing magnetic fields having a geometry which differs considerably from the desired geometry for the gradient coil is prevented.