Apparatus for friction false-twisting synthetic filaments is described wherein the yarn travels over coaxial hemispherical surfaces inverted with respect to each other and having a gap between them into which projects the edge of a disc. Parallel shafts, respectively carrying an element formed with the surfaces and the disc are carried by a bearing unit beneath which the shafts carry rollers with a driving belt travelling between them. To economize in machine space the bearing unit is mounted to turn about an axis displaced from the axis of one of the shafts towards the belt. The unit can be swivelled from a central position in which the rollers are clear of the belt to positions on each side thereof in which the rollers contact the belt. Means are provided for latching the bearing unit in each of these three positions. In operation, only one of the rollers is fixed to its shaft. Means are provided for locking or freeing each roller to its shaft as required by the nature of the required twist.