Vertebral osteosynthesis equipment comprising: - at least one connecting bar having a length such that it is capable to span several vertebrae to be treated, - at least one anchor member having an anchoring portion for anchoring on a vertebra be treated, of the "tulip" type, i.e., comprising a body and a head that forms an engagement duct for the connecting bar, this duct being intended to be closed, after placement of the connecting bar therein, by a threaded member capable to be screwed on the head; the anchor member is of the so-called "polyaxial" type, i.e., with said head articulated relative to said body; - the head forms, on its side turned toward the body, outside said duct, an articulation portion including a completely or partially spherical surface, and forms thereon a distal bearing surface; - the body forms an articulation cavity for receiving said completely or partially spherical surface of the articulation portion, this articulation cavity being defined by a bearing wall outwardly having a partially spherical shape; - the anchor member includes a ring located between the distal bearing surface formed by the head and the bearing wall comprised by the body, this ring having a partially spherical recessed surface for bearing against said bearing wall and being angularly mobile relative to the head; - the ring and said distal bearing surface comprise inter-engagement means (16, 21); - the ring has an axis and is pivotable relative to the head about this axis; - the head has an axis and the inter-engagement means (16, 21), in a first angular position of the ring, have a first inter-engagement position in which the ring is placed in a first position along the axis of the head, in which play exists between the ring and said bearing wall, such that the head is movable, in an articulated manner, relative to the body; the inter-engagement means (16, 21) have, in a second angular position of the ring, a second inter-engagement position in which they position and maintain the ring in a second position along the axis of the head, in which said play is eliminated and the ring presses against said bearing wall, such that the head is made immobile, or substantially immobile, relative to the body; and - the ring comprises movement means (26, 27) for its pivoting movement, located angularly away from the openings by which said engagement duct emerges outside the head, such that the ring can be pivoted, by these movement means, even when a connecting bar is placed in said engagement duct. - at least one connecting bar having a length such that it is capable to span several vertebrae to be treated, - at least one anchor member having an anchoring portion for anchoring on a vertebra be treated, of the "tulip" type, i.e., comprising a body and a head that forms an engagement duct for the connecting bar, this duct being intended to be closed, after placement of the connecting bar therein, by a threaded member capable to be screwed on the head; the anchor member is of the so-called "polyaxial" type, i.e., with said head articulated relative to said body; - the head forms, on its side turned toward the body, outside said duct, an articulation portion including a completely or partially spherical surface, and forms thereon a distal bearing surface; - the body forms an articulation cavity for receiving said completely or partially spherical surface of the articulation portion, this articulation cavity being defined by a bearing wall outwardly having a partially spherical shape; - the anchor member includes a ring located between the distal bearing surface formed by the head and the bearing wall comprised by the body, this ring having a partially spherical recessed surface for bearing against said bearing wall and being angularly mobile relative to the head; - the ring and said distal bearing surface comprise inter-engagement means (16, 21); - the ring has an axis and is pivotable relative to the head about this axis; - the head has an axis and the inter-engagement means (16, 21), in a first angular position of the ring, have a first inter-engagement position in which the ring is placed in a first position along the axis of the head, in which play exists between the ring and said bearing wall, such that the head is movable, in an articulated manner, relative to the body; the inter-engagement means (16, 21) have, in a second angular position of the ring, a second inter-engagement position in which they position and maintain the ring in a second position along the axis of the head, in which said play is eliminated and the ring presses against said bearing wall, such that the head is made immobile, or substantially immobile, relative to the body; and - the ring comprises movement means (26, 27) for its pivoting movement, located angularly away from the openings by which said engagement duct emerges outside the head, such that the ring can be pivoted, by these movement means, even when a connecting bar is placed in said engagement duct.