A method and apparatus of spinning yarns on an open-end spinning machine having a plurality of spinning positions, in which trash waste separated from the fibers of the slivers during advancement through respective fiber opening zones to respective yarn spinning rotors is continuously removed from the opening zones by a low velocity suction current of air and pneumatically conveyed along respective passageways to a central waste collection zone. In order to prevent accumulation of trash in the passageways and possible blockage thereby, the passageways are periodically purged by momentarily increasing the flow of air therealong to create a predetermined relatively high velocity in the passageways. A common source of suction may be employed for removal of the trash waste from the opening zones and also for removal of fiber waste from the respective yarn spinning rotors of the machines.