Abstract: An automatic turret lathe has a main and a supplementary tool-carrying turret both being jointly movable in longitudinal and transverse directions with the turrets being indexable about an indexing axis. The supplementary turret is of smaller diameter than the main turret. Turning tools can be placed in the turrets so that a tool in one turret forms a pair with a tool in the other turret, and the turrets arranged so that both inside and outside machining of a workpiece can be carried out simultaneously. Tools can be placed in the carriers in the turrets to carry out a particular desired function. The supplementary turret can be removed for machining shafts. The turrets can be moved towards and away from as well as along the lathe axis.