Gradient coil arrangement for a magnetic resonance apparatus has multiple sub-coils formed by coil conductors on a common substrate, and the gradient coil arrangement has at least one damping producer that damps voltage overshoots occurring due to capacitive and/or inductive coupling between two sub-coils as a result of interfering frequencies in the wanted signal for at least one of the sub-coils affected. The damping producer is directly applied to the coil conductor of at least one of the sub-coils involved in the capacitive and/or inductive coupling.