Device for managing the electrodes for electrical discharge machining EDM machine tools comprises at least one magazine (1) that has a series of individual housings (33) designed to accept and hold exchangeable elements (5) consisting of electrodes (6, 22) mounted on an electrode holder (11a, 11b), and a changer device (2) equipped with a gripper (2) intended to move the exchangeable elements (5) from the individual housings (33) towards the machine and vice versa. A first adapter piece (21) is associated with each of the exchangeable elements (5). This adapter piece (21) surrounds the electrode holder (11a, 11b) and is gripped around its periphery by the gripper (9) of the changer (2) so as to guarantee that the exchangeable element (5) is held precisely. The device further comprises a second adapter piece (32) associated with each of the individual housings (33) of the magazine (1) that are likely to be used.