Abstract: An apparatus for making a cold-pilger-rolled tube has two grooved pilger work rolls rotatable in a roll frame about respective axes to compress a tubular workpiece moving in a travel direction around a mandrel extending in the direction between a nip formed between the grooved rolls and anchored upstream of the nip in a thrust block. An outside diameter of the workpiece is measured downstream in the direction from the rolls as the workpiece passes through the nip, and an actuator engaging one of the rolls relative the other of the rolls shifts it transversely to the travel direction as the workpiece passes through the nip in accordance with the measured outside diameter for maintaining a uniform outside diameter of the workpiece.