Apparatus for producing waste wraps and thread reserve windings on a bobbin tube which is placed onto a rotating bobbin chuck and at a face side of which there is provided a thread catching zone. For the purpose of producing the waste wraps there is provided a first lever which is arranged to be pivotable with a delay and for producing the thread reserve wraps a second pivotable lever arranged axially offset with respect to the first lever as seen from the face side. Both levers are pivotable in such a manner that they are consecutively pivoted away by the thread caught by the rotating package tube and with different delays while wraps are wound beginning at the face side with the thread tending to move along a thread guide edge towards a central position.