An interfolding machine (1) is described, including folding rollers (3). Such a roller has a cylindrical sleeve (3C) having a rotation axis (3A), an outer surface (3X) and an inner surface (3Y) defining an inner axial cavity (23) of the cylindrical sleeve (3C). The cylindrical sleeve includes, furthermore, a plurality of suction holes (41, 43) which extend from the outer surface (3X) to the inner surface (3Y) of the cylindrical sleeve (3C). The suction holes are arranged depending on longitudinal alignments (42, 44), parallel to the rotation axis (3A) of the cylindrical sleeve (3C) and angularly staggered in relation to one another. Inside a suction chamber (23A) in the cylindrical sleeve (3C), shutters are stationarily arranged having closing surfaces (37A) cooperating with the inner surface (3Y) of the cylindrical sleeve (3C) to selectively close the suction holes.