Device for dynamic interlaminar stabilization comprising: - at least one viscoelastic mean used as multiaxial shock absorber with an elastic return force, - A base comprising a lower hook fitting to the geometry of the laminar of the lower vertebra, - A rigid piston fixed to an upper hook, crossing a hollow cylindrical body by an opening 120, and leaning on the viscoelastic mean - A stiff upper hook connected to the rigid piston, fitting with the laminar of the superior vertebra characterized by the following properties: - A hollow cylindrical body, serving as protective cap of the viscoelastic means and as a stop in the displacement of the upper hook - The said viscoelastic mean with cylindrical shape presenting on its lower face a convex part centering itself in a cavity integrated into the base, - A functional room, defined between the lower face of the hook and the superior face of the hollow cylindrical body, particularly calibrated to the limited movement in compression of the upper hook, - A functional room, space defined between the internal walls of the hollow cylindrical body and the shape of the viscoelastic mean particularly calibrated to the deformity without coming into contact with the internal walls of the hollow cylindrical body. - A functional room, residual space in the shape of a tronconic ring defined between the diameter of the opening of the hollow cylindrical body and the diameter of the rigid piston particularly calibrated to the necessary movements between the hooks and, these means, after they are joined together, form the device which is in one piece, what prevents any risk of sliding, dismantling or dislocation between the different means and allows the free deformation of the viscoelastic mean inside the hollow cylindrical body, while insuring its integrity; even allowing that the lower and superior hooks and of the device are always attached to the vertebrae, securing the intervertebral movements and the shock absorption of the applied mechanical loads thanks to the polyaxial movements of the upper hook and to the security stop on the superior face of the hollow cylindrical body. - at least one viscoelastic mean used as multiaxial shock absorber with an elastic return force, - A base comprising a lower hook fitting to the geometry of the laminar of the lower vertebra, - A rigid piston fixed to an upper hook, crossing a hollow cylindrical body by an opening 120, and leaning on the viscoelastic mean - A stiff upper hook connected to the rigid piston, fitting with the laminar of the superior vertebra characterized by the following properties: - A hollow cylindrical body, serving as protective cap of the viscoelastic means and as a stop in the displacement of the upper hook - The said viscoelastic mean with cylindrical shape presenting on its lower face a convex part centering itself in a cavity integrated into the base, - A functional room, defined between the lower face of the hook and the superior face of the hollow cylindrical body, particularly calibrated to the limited movement in compression of the upper hook, - A functional room, space defined between the internal walls of the hollow cylindrical body and the shape of the viscoelastic mean particularly calibrated to the deformity without coming into contact with the internal walls of the hollow cylindrical body. - A functional room, residual space in the shape of a tronconic ring defined between the diameter of the opening of the hollow cylindrical body and the diameter of the rigid piston particularly calibrated to the necessary movements between the hooks and,