Spinal osteosynthesis system comprising a vertebral rod, a vertebral anchoring member, a connector between the vertebral rod and the vertebral anchoring member, and pressure means for selectively blocking together the vertebral rod, the vertebral anchoring member and the connector, in which: - the connector comprises a body having receiving means for receiving the vertebral anchoring member oriented in a first axial direction (I-I), - the body comprises a substantially cylindrical receiving seat intended to receive the vertebral rod and extending in a second axial direction (II-II) substantially perpendicular to the first axial direction (I-I), - the receiving seat has a lateral opening defining two edges (10a, 10b) and allowing the vertebral rod to be introduced into the receiving seat transversely or radially with respect to the second axial direction (II-II), the lateral opening having a width at least equal to the diameter of the vertebral rod, - the connector has a locking member, which is movable with respect to the body of the connector, the locking member having a release position, in which the locking member allows the vertebral rod to pass through the lateral opening of the receiving seat, - the pressure means make it possible to selectively oppose a movement of the locking member to its release position, characterized in that: - the locking member is movable with respect to the body of the connector from its release position to a retention position, in which the locking member elastically opposes the passage of the vertebral rod through the lateral opening of the receiving seat by elastic return means which press the locking member such that it bears against the vertebral rod contained in the receiving seat, with a first predetermined clamping force, - the pressure means make it possible to selectively bias the locking member to a locking position, in which the locking member is pressed so as to bear against the vertebral rod contained in the receiving seat, with a second clamping force, which is greater than the first predetermined clamping force exerted by the elastic return means. - the connector comprises a body having receiving means for receiving the vertebral anchoring member oriented in a first axial direction (I-I), - the body comprises a substantially cylindrical receiving seat intended to receive the vertebral rod and extending in a second axial direction (II-II) substantially perpendicular to the first axial direction (I-I), - the receiving seat has a lateral opening defining two edges (10a, 10b) and allowing the vertebral rod to be introduced into the receiving seat transversely or radially with respect to the second axial direction (II-II), the lateral opening having a width at least equal to the diameter of the vertebral rod, - the connector has a locking member, which is movable with respect to the body of the connector, the locking member having a release position, in which the locking member allows the vertebral rod to pass through the lateral opening of the receiving seat, - the pressure means make it possible to selectively oppose a movement of the locking member to its release position, - the locking member is movable with respect to the body of the connector from its release position to a retention position, in which the locking member elastically opposes the passage of the vertebral rod through the lateral opening of the receiving seat by elastic return means which press the locking member such that it bears against the vertebral rod contained in the receiving seat, with a first predetermined clamping force, - the pressure means make it possible to selectively bias the locking member to a locking position, in which the locking member is pressed so as to bear against the vertebral rod contained in the receiving seat, with a second clamping force, which is greater than the first predetermined clamping force exerted by the elastic return means.