Abstract: An open-end spinning machine is provided which includes a plurality of commonly driven spinning units arranged in side-by-side relationship. Each of the spinning units includes a spinning rotor, an opening device for opening fibers, a fiber feed device for feeding fibers from the opening device to the spinning rotor, and vacuum producing means for generating an air current to act on the fibers to aid in the feeding through the fiber feed device. To accommodate start-up operations and restarting in the event of a shut-down spinning unit, piecing apparatus is provided which includes a thread end return device for returning a thread end into the rotor for piecing onto a fiber ring deposited inside of the rotor and for taking off the pieced thread. In preferred embodiments, the piecing apparatus is equipped with additional devices for controlling the rotor speed and the quantity of fibers fed during the piecing step.