A clamping device for axially clamping a disk-shaped tool on a flange of a spindle of a machine tool, includes a clamping disk which rests against the tool in a friction-fitting manner in the clamped state, a screw which is screwed into a threaded receiving opening in an end face of the spindle, an operating element which is connected to the screw in a rotationally fixed manner, and a first securing element which interacts with a corresponding second securing element provided on a flange such that when the screw is at least partly introduced into the receiving opening, the clamping disk is rotationally secured to the flange in a form-fitting manner, where the clamping disk can be rotated relative to the screw and the operating element. The first securing element can be rotated relative to the screw and is mounted in a rotationally fixed manner relative to the clamping disk.