An apparatus for clamping a component on a rotating machine part, in particular a balancing machine, having a basic body, having a clamping mandrel, which is arranged in an axially displaceable manner within the basic body, and having a plurality of clamping devices, which can be moved between a release position and a clamping position by axial displacement of the clamping mandrel. In order to make it possible for components to be clamped centrally with repeated accuracy, the clamping devices are designed as clamping segments which can be displaced radially in relation to the center axis of the basic body above the latter.