A time-varying magnetic fields generator for a magnetic resonance apparatus has at least one gradient coil and one radio-frequency antenna, gradient coil being formed by two essentially hollow-cylindrical units that are axially separated from one another and that contain conductors of the gradient coil, and that each have at least one axial free space proceeding therethrough to accommodate a shim device, and at least one hollow conductor of the radio-frequency antenna is disposed between the units such that its hollow interior axially communicates with and continues at least one of the free spaces.