Lathe

The invention relates to a lathe with a workpiece spindle (11) and a workpiece guide bush (8) which are displaceable relative to one another in the axial direction of the spindle, the workpiece guide bush (8) being mounted in a guide-bush carrier (7). So that workpieces which do not require support by a guide bush (8) in the vicinity of the machining point can also be machined on a lathe of this type, it is proposed to design the workpiece spindle (11) in the shape of a centre sleeve and to allow it to project from the headstock by at least the length of the relative displacement and to insert a workpiece-spindle guide bush into the guide-bush carrier (7) in place of the workpiece guide bush (8) so that the workpiece spindle (11) is able to be supported in the guide-bush carrier (7).