Abstract: An open-end spinning machine, is operated by continuously advancing a yarn towards a take-up station at which it is wound onto a bobbin rotating at a predetermined speed, so that a yarn package forms on the bobbin and the latter eventually becomes full. As the bobbin approaches a condition of fullness, an empty bobbin is rotated adjacent to it and is accelerated until it reaches the speed at which the full bobbin rotates. The yarn which advances onto the full bobbin is then severed from the yarn package on the latter, to provide a free yarn end which is inserted into one axial end of the rotating empty bobbin, to be engaged and entrained by the latter whereby winding of the free yarn end onto the empty bobbin commences. The full bobbin is now removed from the station and is replaced with the rotating empty bobbin.