Abstract: A clamping device, having a first and a second coupling part, for the tool of a machine tool. The first coupling part is eccentric and comprises small rails having angular off-sets in relation to each other and limiting surfaces for exactly positioning the second coupling part in the xy plane. The second coupling part comprises lateral faces having elastic lips which rest against the limiting surfaces, a connecting device is used to exactly position the first and the second coupling part in the z plane. The second coupling part consists of a piece having various strength values, ductility values and/or hardness, whereby the areas of the lips have higher strength values, ductility values and/or harnesses than the other areas of the lips and/or areas of the second coupling part.