Method for stopping a flyer as a result of roving-break signals. The conversion of a roving-break signal into a shut-down signal triggering the stopping of the flyer is prevented in blocking zones of the path of movement of the bobbin carriage, so that the latter does not come to a standstill in critical end regions of its travel movements. In order to reduce on average the effects of the blocking zones on the bobbin fillings, at least one limit of each blocking zone is adjusted in position relative to the instantaneous position of the associated critical end region in dependence on a flier variable related to the bobbin-carriage speed.
