An open-end spinning apparatus in a spinning machine for continuous spinning of textile fibers includes a spinning rotor having an axis. A cap covers the spinning rotor and is pivotably supported about a pivot axis oriented at right angles to the rotor axis. Delivery and opening devices are disposed in the cap for supplying textile fibers to the spinning rotor. A stationarily installed shaft extends longitudinally of the spinning machine for driving a multiplicity of opening devices. A worm transmission drives at least the opening device and has a driving worm on the stationarily installed shaft and a worm wheel with teeth on a drive shaft of the opening device. The worm wheel meshes with and plunges into the driving worm upon closure of the cap. The driving worm includes at least one thread having adjacent windings with end surfaces and with lateral surfaces having an additional shaping tapering the end surfaces to a point. Two of the adjacent windings have tips being spaced apart by a spacing being great enough to cause at least one of the teeth of the worm wheel to be forced between two of the windings upon plunging into the driving worm.