Abstract: A workpiece is clamped onto a worktable that can travel in at least three directions at right angles to each other relatively to each of several tools. The tools which are inserted each in an individually driven work spindle with only one of the spindles cutting at a time. The spindles are located in a stationary spindle support or in spindle supports permitting linear travel. The workpiece and the tools are brought into contact by numerically controlled movements in the Z-direction, in the X- and Y-directions or in the X- and Z-directions. An automatic tool changing device cooperates with the spindles and with at least one tool magazine. For changing tools, one or one each changer arm or comparable device can work in conjunction with a spindle and with at least one tool magazine.