In a machine tool having at least one tool spindle which is displaceable in relation to a device for holding workpieces in at least one of three spatial directions and in which the tools (W1-W7) for processing the workpieces can be chucked, there are provided a machine magazine (36) in which tools (W1-W7) provided for exchange in the tool spindle (23) are kept in store and a background magazine (31) in which tools (W1-W7) provided for exchange in the machine magazine (36) are kept in store. In the machine magazine (36), not more than four storage places (42, 43, 44, 45) for accommodating tools (W1-W7) are provided (FIG. 2).