A rotatable turret for bringing any selected one of a plurality of tool holders into operative position relative to a workpiece, is characterized in that the turret can be rotated in either direction so that it need follow only the shortest path between the location of the old tool holder and the location of the new tool holder when changing from tool to tool. For this purpose, the turret has a rotatable hub with a plurality of blocks on its periphery slidable relative thereto in directions parallel to the axis of rotation, into and out of slots on a fixed member, the location of the slots corresponding to the operative locations of the tool holders. The blocks are all secured to the keeper ring of an annular electromagnet, whose strength is sufficient to retain the keeper ring attracted when the blocks are out of the slots, but whose strength is insufficient to retain the keeper ring when the blocks are in the slots. Springs act between the hub and the blocks to urge the blocks into the slots; and cam surfaces on the fixed member cam the blocks out of the slots against the action of the springs in one direction of rotation of the hub. A driving ring for the hub has abutment surfaces that contact the hub only in that one direction of rotation; whereas the same driving ring has abutment surfaces that contact only the blocks in the other direction of rotation, and then only when the blocks are withdrawn from the slots.