A clamping device for manufacturing an assembled camshaft for valve-controlled internal combustion engines, in which at least one cam disc with a base circle region and cam region is machined on the running surface and has a cam-disc recess, includes shrinking the cam disc onto a corresponding shaft designed with a defined dimensional overlap by cooling the shaft and heating the cam disc. Before being shrunk onto the shaft, the at least one cam disc is clamped by the clamping device such that a tension force acts on the recess wall region, the tension force corresponding to a predetermined extent to the state of stresses and/or deformation state of the recess wall region after the operation of shrinking the cam disc onto the corresponding shaft. The running-surface machining of the at least one cam disc occurs when the cam disc is clamped by the clamping device.