A process for allowing the attachment of drive or coupling elements, such as cams, gears, crank webs or bearing elements, such as friction bearing bushes, or complete roller bearings on tubes or tubular portions by hydraulic expansion, for the purpose of producing assembled cam shafts, transmission shafts, crank shafts or the like, with the expansion of the tubes taking place exclusively in the region of the respective elements beyond the limit of elasticity of the tubes, against a permanent elastic prestress in the elements. To relieve the load on the seals limiting the regions to be expanded, a counter pressure which is higher than the ambient pressure is applied to the intermediate or end regions.