A pot spinning machine holds a yarn rewinding tube in ready position during the spinning operation for immediate movement to an operative rewinding position in the event of a yarn break so that the broken end of yarn is not lost by winding onto the yarn cake already formed in the spinning pot and the yarn cake may then be properly rewound. The yarn break is detected with the aid of a yarn sensor which then emits a signal for immediately moving the rewinding tube into the rewinding position and clamping the yarn end. The rewinding operation can begin, even in the absence of a loose end of the yarn, if the yarn has assumed the form of a chord-like yarn segment extending substantially in the circumferential direction against the inner face of the yarn cake deposited onto the inside wall of the pot, which can be grasped and utilized to initiate the rewinding operation.