Abstract: A wrapping device guides an unwinder of a film web from a film roll to be unwound along a revolving path about a body to be wrapped. A guide path is formed by at least two separate motion systems which in each case are able to move the unwinder in at least two directions. Each of the motion systems has an actuatable mounting device for engaging a mounting flange of the unwinder, and the unwinder has two separate mounting flanges. The wrapping device has a computer by way of which the guide path of the unwinder along a freely determinable revolving path is generatable. The unwinder after a partial revolution of a motion system is transferable to the next motion system, such that a full path of the revolving path is generatable by the motion systems.