The inventive machine has at least one workpiece (23) clamping device (22) which can be driven around a first axis of rotation (A), and at least one tool spindle (18) which can be driven around a second axis of rotation (C). Three slides (5, 6, 7) can be moved independently of each other on a slide guide (4) by means of drive mechanisms, and are connected by guide rods (11, 12, 13) to a unit (17) which supports the tool spindle. As the slide is moved along the slide guide, so the workpiece (19) can be moved along an X-axis and a Z-axis, and turned in a certain area. The inventive machine has fewer drive mechanisms and especially slide guides than known machines of the same type and is easy to construct modularly. The masses which are moved in the inventive machine are also less than in known machines and the dynamics of the inventive machine are better as a result.