The tool-holder turret for lathes or like machining centers has a fixed support member (1; 52) bearing a rotary member (4; 51) to which there may be attached a tool-holder plate designed to bear a plurality of tools, each of which can brought into the operating position by the rotation of the rotary member, a drive motor (12; 54) also being provided, which is connected to a geared differential transmission unit (15, 18, 20; 47, 18, 20; 57, 64, 66) having three members, the first member, called the driver (15; 47; 57), being connected to the motor and controlling, on one hand, the opening and closing of the turret and, on the other hand, the rotation of its rotary member, the second member, which can be driven in rotation, of the differential unit (18; 18; 64) being connected to the rotary member and the third member, which can be driven in rotation, of the differential unit (20; 20; 66) being connected, via interposed cam transmission means (21, 23; 71, 72), to a rotationally fixed and axially movable member for relative engagement between the fixed member and the rotary member (7; 73), rotational locking members (29; 80; 34, 35; 40, 41; 76, 77) being provided for one of the members which can be driven of the differential unit for the transmission of movement to the other member and to the components associated therewith for the sequential control of the disengagement of the fixed member and the rotary member, the rotation of the rotary member into the preselected position and the reengagement of the fixed member and the rotary member, structure (97, 116) associated with the axially movable and rotationally fixed member also being provided and actuating the coupling of means for the transmission of movement to a rotary tool in the operating position.