Winding device with which a tube produced in a rolling installation can be wound up outside the rolling installation. The tube which has already left the rolling installation is coiled or wound up in such a winding device for transport purposes. The disclosed device and method make it possible for the tube in the finished shaped condition to be put into a transportable state downstream of the roll stand while still other portions of the tube are at the stage of the tube shell or are just being shaped. For that purpose a winding device for a tube produced in a rolling installation has a bending device for curving the tube so that it can be wound in a spiral shape around a first axis, and a holding frame, wherein the bending device is mounted to the holding frame pivotably about a second axis substantially perpendicular to the first axis.