A method 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. Temporally before being shrunk onto the shaft, the at least one cam disc is clamped by a clamping device such that a tension force acts on the recess wall region, which defines the cam-disc recess, 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 takes place when the cam disc is clamped by the clamping device.