A method and apparatus for twisting a yarn, such as a sliver of staple fibers, is disclosed, and wherein the yarn is advanced through a drafting zone and then through a twisting apparatus. The twisting apparatus includes two circular discs, with at least one of the discs being flexible. Also, in the preferred embodiment, two separate pressure applying members are mounted adjacent the back surface of the flexible disc, with the members being positioned on opposite sides of the plane defined by the axes of rotation of the discs. The two pressure applying members are adapted to be actuated concurrently, with one member defining a first twisting zone wherein S twist is imparted to the advancing yarn, and the other member defines a second twisting zone wherein Z twist is imparted. Means are also provided for controlling the degree of twist imparted at each of the zones, so as to obtain, for example, a twisted yarn composed of core fibers having minimal twist and which are bound by outer fibers of greater twist.