An open end spinning machine includes a plurality of spinning units. Each spinning unit includes a first yarn breakage sensing device assuming a yarn sensing, operative position, in which it contacts the yarn, when the spinning unit is in a normal spinning operation and an inoperative position, in which it is not in contact with the yarn, when the spinning unit is in a transient condition either from or to the normal spinning operation, and a second yarn breakage sensing device assuming a yarn sensing position at least when the spinning unit is in the transient condition. Upon occurrence of yarn breakage when the spinning unit is in the transient condition, such breakage is detected by the second yarn breakage sensing device and the supply of fibers to the associated spinning unit is interrupted by the second yarn breakage sensing device.