The balancing system has a balancing body to be mounted on a rotor of a turbomachine and a sealing ring to be mounted on a stator of the turbomachine; the sealing ring is arranged around the balancing body so that the balancing body can rotate about a rotation axis, thus there is a clearance between the body and the ring; furthermore, there is an arrangement for changing an axial position of the sealing ring during operation of the turbomachine so that the clearance can be adjusted. The possibility of adjusting clearance during operation of the turbomachine, such balancing system provides a good balancing action with a small leakage and a small risk of mechanical interference at any time during operation of the turbomachine.