Abstract: The object of the invention is an implantable intervertebral connection device comprising at least two pedicular screws (1, 2) provided in their upper portion with a hexagonal head (3) prolonged by a cylindrical bearing (4, 4′) and an inter-screw connection of adjustable length anchored at each end on said bearings, characterized in that said inter-screw connections constituted, on the one hand, by a ball (7, 7′) preferably of a resiliently deformable material threaded on each bearing (4) and, on the other hand, by two connection elements (E1, E2; E′1, E′2) in prolongation of each other and interconnected by a screw system (17, 18; 18′, 41, 42) for adjustment of spacing, the free ends of the elements being shaped as a cup (8, 9; 8′, 9′) which is concave and threadable on said bearing (4, 4′) and matching said ball (7, 7′) such that in line with each pedicular screw (1, 2; 1′, 2′) the ball will be sandwiched between two cups (8, 9; 8′, 9&p