This equipment comprises at least one rigid connecting bar (2), first and second bone anchoring members (3, 4) and first and second connecting parts (5, 6), capable of connecting the connecting bar (2) to said bone anchoring members (3, 4). According to the invention, each second bone anchoring member is in the form of a flexible ligament (4) capable of being engaged around the lamina (101) or an apophysis of a vertebra (100) each second connecting part (6) comprises a conduit (11) receiving said ligament (4) and means (12) for blocking said ligament (4) in the conduit, with tensing of the ligament (4), and each contact member includes at least one rotating part (16 17) mounted in said second connecting part (6), capable of coming into contact with said connecting bar (2) by a point.
