The present invention relates to a fastening or unfastening system (1, 10) including: an actuating device (2, 20), which has a plurality of actuating elements (22, 220) made of magnetic, magneto-sensitive or magnetically inert material; and a device to unlock or lock (3, 30, 3′), which includes a first element (4, 40, 4′), a second element (5, 50, 5′) and a first plane (7, 70), between said first element (4, 40, 4′) and said second element (5, 50), and a second plane (8, 80=between the second element (5, 50, 5′) and the third element (6, 60, 6′). Said first element (40, 4, 4′) and said second element (5, 5′ 50) present a plurality of housing couples (41, 51, 410, 510) corresponding to said plurality of actuating elements (22, 220) of said actuating device (2, 20), provided with centering means (9, 90) said centering means (9, 90) being made of magnetic, magneto-sensitive or magnetically inert material, able to lock or unlock the movement in respect to said first plane (7, 70).Said device (3, 30, 3′) has a single housing (400, 4000) comprised of a first further housing (42, 420), a second further housing (52, 520) and a third further housing (62, 620), respectively obtained in said first, second and third elements.Said single housing (400, 4000) provides, inside, at least at least two prevent and release means (91, 92, 910, 920) each sliding mutually, and a thrust element (63, 630) acting on said prevent and release means (91, 92, 910, 920). Further, said system (1, 10) can take a first configuration, wherein said prevent and release means (91, 92, 910, 920), block the movement of said elements (4, 40, 4′, 5, 50, 5′, 6, 60, 6′) in respect to said planes (7, 70, 8, 80), and a second configuration wherein said prevent and release means (91, 92, 910, 920) and said thrust element (63, 630), in a compressed form, allow the movement of said first (4, 40, 4′) and second (5, 50, 5′) element in respect to said planes (7, 70, 8, 80).Finally, coupling and movement of actuation device (2, 20) allows the movement from said first to said second configuration.