A sealing system of a turbomachine for sealing a rotor of the turbomachine relative to a stator of the turbomachine, having a rotor-side component rotating together with the rotor, a stator-side component that is stationary together with the stator, and a dry gas seal, which includes a rotor-side sealing component and a stator-side sealing component compressed via a spring element forming a sealing gap, and a cleaning device, via which detergent is conducted in the direction of the spring element for cleaning the same and/or in the direction of the sealing gap for cleaning the same.