Abstract: A straight wool-combing machine (10) has, instead of the conventional pair of detaching rollers, a pair of jaws (30, 32) for gripping the combed end of a tuft and for separating it, by a withdrawal movement, from the rest of the fibre sliver (M). The pair of jaws (30, 32) has a suction fan (31) for transporting the combed fibres pneumatically to a collecting store.