The present invention provides a complex machining machine tool (1) having a single frame in which a chip collecting space (4) is provided at the center portion, a first and a second spindle stocks (5,6) on the frame (2) being relatively free to move in a Z axis direction and being located on respective sides of the chip collecting space 14) workpiece spindles (5b,6b) on said spindle stocks (5,6), free to rotate and arranged mutually facing each other, and tool rests (7,9). The tool rests (7,9) have respective turrets (7a,9a) which can assume various kinds of movement forms. Furthermore, complicated and various kinds of machinings can be performed in such a manner that the rotation control forms of the workpiece spindles (5b,6b) and the spindle stocks (5,6) are combined. The invention also provides a specific machining method.