The invention relates to a combing machine comprising a circular comb (2) and an oscillating gripper device (7), the mouth of which, when swinging backwards, moves away from the circular comb thus reducing the duration and the intensity of combing. In order to counteract this, the distance of the enveloping curve (H) of the tips of the needles (5) of the circular comb from the rotational axis can be increased counter to the rotational direction of said comb. This is achieved by virtue of the fact that the increase in the distance of the mouth of the gripper from said enveloping curve, when swinging backwards, is compensated at least in part and the tuft is combed for a long, intense duration.