Abstract: The invention relates to a process for reducing the outside diameter and wall thickness by rolling a cylindrical hollow ingot the front part of which is fed into an Assel rolling mill, in which connection, in front of the Assel rolling mill as seen in the direction of feed, a device is provided for reducing the diameter and/or wall thickness of the rear end part of the hollow ingot threaded onto a mandrel rod. In this process, the prereduction rolls are slowly and continuously pressed against the ingot at a predetermined point near the end of the ingot to produce a conically reduced end portion.