A transport system and a system for moving permanent-magnet-excited transport bodies by an inductively excited magnetic field includes induction coils, a movably supported first reluctance element, and an actuator. The induction coils are configured for a current to flow through the induction coils in order to drive the transport bodies in a plane without contact. The actuator is configured to bring the first reluctance element from a first position into a second position. The permanent magnetic field of a transport body located over the first reluctance element experiences a lower magnetic resistance in a magnetic circuit through the first reluctance element in the second position than in the first position.