A machining head (36) is drivable along a vertical axis and two horizontal axes with respect to a workpiece held on a workpiece-holding device, and has, at progressively lower levels along said vertical axis, one or two high-speed spindles (44), one or two low-speed spindles (46) and one or two feed-out spindles (48), all arranged at right angles to said vertical axis and driven by one or more motors (42) mounted on the head. The machining head can bring the high-speed spindles to cooperate with a tool-changing magazine (52). The workpiece-holding device (54; 154) is adapted to carry two sets of workpieces on respective supports (56, 58; 170), and to shift said supports in succession between a working position near the head and a tool-changing position remote from the head.