The disclosure relates to a clamping apparatus for fixing in a recess (38) of a component (40) and comprising a clamping sleeve which is connected to an inner component (52). A clamping mandrel (42) is movable relative to the clamping sleeve. The inner component (52) is guided at least partially in a housing and a workpiece carrier (60) may be attached on that side of the housing (22) which faces towards the recess (38). The housing (22) may be moved relative to the clamping mandrel (42) when the clamping sleeve is situated in a clamped position. The clamping mandrel (42) may be moved relative to the clamping sleeve by a first pressure medium for bracing purposes. The holding force of the clamping action may be adjusted by pressure in the first pressure medium. The housing (22) which carries the workpiece carrier (60) can be moved relative to the clamping mandrel (42) with the aid of a second pressure medium in the case of the clamping sleeve which is situated in the clamped position, that the force, with which the workpiece carrier bears against the component, can be regulated by way of a pressure in the second pressure medium, and that the pressures in the first and in the second pressure medium are regulated in such a way that the holding force is greater than the force for carrying out the relative movement between the housing (22) and the clamping mandrel (42).