Abstract: To provide a predetermined pre-set twist or rotation about an angle corresponding at least approximately through the spiraling angle of strands (8) wrapped about a core wire or strand (48), the individual surrounding strands are passed through directionally orienting dies (20, 28) which may receive circular strands and impart an approximately truncated wedge-shape thereto, or directly receive pre-shaped strands. The orienting dies are angularly adjustable in a holder (26) which, in turn, is rotatable about an axis transverse to the axis of the die opening, all the dies being secured to a carrier plate which is axially adjustable with respect to the stranding die (7) of the apparatus.