A spinning apparatus has a flyer which is rotated about its axis by a belt drive at one axial end of a spindle carrying the flyer. Received within the flyer and rotatable relative thereto is a yarn-package holder comprising a plush-lined cup snugly receiving a coreless package of glass-fiber yarn, and a takeup tube whose mouth lies within the package. A thread brake is provided within the takeup tube and the yarn holder is prevented from rotating with the flyer. The yarn of one or more threads is drawn off the inside of the package into the mouth of the nonrotating takeup tube, thence enters the end of the rotating spindle, passes radially out through the flyer under the yarn-package holder, and thence axially out through the rotating sleeve of the flyer. The tube of the flyer is formed by a pair of nested tubes connected by a corrugated stiffening element.