Abstract: A machine for automatically cutting and dividing of cylindrical sleeves guided and supported on a drawoff spindle by means of a plurality of coaxially arranged rotary knives. The machine includes a transport arrangement for transporting an uncut sleeve onto the drawoff spindle where it is cut by the rotary knives and then transporting the now-divided sleeve onto an adjustable carrier sled which is transversely movably mounted relative to the axis of the drawoff spindle. The transport arrangement includes a pair of end pressure members which are movable toward and away from each other and which are adapted to grip the cut and uncut sleeve therebetween. The carrier sled includes a pair of adjustable parallel sleeve-receiving troughs which are adapted to be reciprocally mounted between precisely-defined relative positions with respect to the carrier sled and a rotary knife-supporting beam.