@ In a widely-used type of ring spinning or twisting machine, each spindle (8, 9) of the machine is provided at its upper end with a spinning head (22). This head (22) is engaged by yarn to be wound onto a cop spool (5) carried on the spindle (8, 9), the yarn passing from the spinning head (22) to the ring traveller (3) associated with that spindle. Due to the engagement of the yarn with the spinning head (22) it is generally not possible to employ known types of automatic cop removal devices with such machines. To overcome this problem, cop-raising means (18) are provided which, at the end of each cop-forming process and prior to operation of the cop-removal device, serve to raise the cop spools (5) above the level of the upper ends of the spinning heads (22) whereby to disengage the yarns therefrom. The cop-raising means (18) comprise, for example, a mechanism arranged to displace upwardly the so-called ring nuts (6, 14) associated with each spindle.