Abstract: A clamping device for gripping a tool in a carrier. The clamping device has a hollow centering extension or spigot and an abutment surface surrounding it are provided on the tool. A tool receptacle provided in the carrier has a receiving bore matched to the centering extension and an end face surrounding the bore and against which the abutment surface can be pressed by a clamping arrangement. The clamping arrangement comprises a clamping sleeve movable coaxially with respect to the central axis and a clamping ring or collet movable in the opposite direction to the clamping sleeve, both of which are provided with clamping cones facing towards one another. The collet is movable axially on the clamping sleeve by means of a clamping nut screwable on the sleeve. A plurality of clamping jaws surround the clamping sleeve and the collet concentrically and are supported in each case by one end against their clamping cones.