Device for managing the electrodes for electrical discharge machining machine tools using tool electrodes (22) intended to machine workpiece electrodes (6), the management device comprising at least one magazine (1) that has a series of individual housings (33) designed to accept and hold exchangeable elements (5) consisting of the said electrodes each mounted on an electrode holder (11a, 11b), and at least one changer device (2) equipped with at least one gripping member intended to move the exchangeable elements (5) from the said individual housings (33) towards an attachment system situated on the machine (44) and vice versa, characterized in that the management device comprises at least one first adapter piece (21) associated with each of the exchangeable elements (5), the said first adapter piece (21) being shaped so that it at least partially surrounds the electrode holder (11a, 11b) and so that it can be gripped at least partially around its periphery by a gripper (9) that forms the said gripping member so as to ensure that the exchangeable element (5) is held precisely by the gripper (9).