The machine tool has a machine bed having a first horizontal linear guide and a second horizontal linear guide arranged at right angles to the first linear guide. On the first linear guide is arranged, in an axially displaceable manner, a workpiece clamping fixture, which is swivelable about a swivel axis oriented parallel to the second linear guide and is rotatable about a rotation axis oriented at right angles to the swivel axis. On the second linear guide a toque motor driven swivel arm is axially displaceable, the swivel axis of which is arranged parallel to the first linear guide and which on its free end bears a tool spindle, the axis of which is oriented parallel to the first linear guide.