Abstract: Machine for the cylindrical turning, conical turning, heading and threading of sleeves (11) or suchlike, comprising at least a work station (13a, 13b, 13c) in which means (15) for holding the sleeve are present, of the gripper-type (16a, 16b), and at least a work unit (17b, 17c) configured to carry out a threading operation on the sleeve (11). The means (15) for holding the sleeve are configured to support the sleeve (11) substantially in cantilevered fashion, acting on its external surface and according to an orientation of the holding means (15) that is substantially orthogonal to the direction of movement (Y) of the work unit (17b, 17c), which direction substantially coincides with the longitudinal axis (X) of the sleeve (11).