This device has a stationary storage durm (2) onto which an intermediate yarn store is wound by a winding-on device (3) and from which the yarn (WY) is withdrawn spiralling around the withdrawal end of the storage drum. The device also has a plurality of yarn stopping devices (10) being arranged at angular intervals around the storage drum, said yarn stopping devices consisting of yarn stopping elements (14) and of actuator means (11) moving said stopping elements into and out of the path of the yarn being withdrawn, and an actuator control device (8) adjustable to desired yarn lengths to be withdrawn, said control device transmitting actuating signals to said plurality of yarn stopping devices. The control device (8) comprises storing means (20) for storing an information regarding the yarn stopping device actuated at the end of the next preceding yarn withdrawal cycle, and calculating means (20) for determining a selected series sequence of said yarn stopping devices to be alternately actuated and de-actuated consecutively during the yarn withdrawal cycle on the basis of said stored information and of an adjustable input information for the calculating means representing at least one significant parameter for the distance/time function of the weft yarn insertion process cycle. The calculating means (20) also determines the yarn stopping device to be kept actuated at the end of the present weft yarn withdrawal cycle at last one in said selected series sequence of alternately actuated and de-actuated yarn stopping devices, on the basis of said stored information and of an input information representing said desired yarn length.