Abstract: The invention relates to a clearance control system for adjusting a running clearance (L) between a rotor (12) having rotor blades (10) of a turbomachine (14), especially a gas turbine, and a casing (18) that surrounds at least sections thereof and comprises at least two segments (16a-d), with at least one adjusting gear unit (20), which can be coupled to at least one segment (16a-d) of the casing (18) and by means of which the at least one segment (16a-d) for adjusting the running clearance (L) can be moved radially in relation to a rotational axis (D) of the rotor (12), and with an adjusting element (22) that can be arranged around the rotor (12) and which is coupled to the at least one adjusting gear unit (20) and can be moved in relation to it for actuating the adjusting gear unit (20), whereby the adjusting element (22) can be moved axially in relation to the rotational axis (D) of the rotor (12) or can be pivoted with respect to the rotor (12) for adjusting the running clearance (L), and the at least on