System for a global three-dimensional correction of the curvatures of the spine, comprising for each of a plurality of vertebrae of a section of the spine to be corrected: a first bone anchoring element configured to be anchored into a vertebra; a second bone anchoring element configured to be anchored into said same vertebra; both said first and second bone anchoring elements (10, 11) having an axial part for insertion into the vertebra and a head; said head of said first and second bone anchoring elements having pivotally connected thereto a first receiving part and a second receiving part (12, 50) respectively to which a first alignment elongate member and a second alignment elongate member (13, 19) extending along respective longitudinal axis are temporally attached by a proximal portion thereof, respectively, each receiving part (12, 50) defining a housing; said first alignment elongated member attached to said first bone anchoring element including a first longitudinal transversal slot allowing insertion there through, for each of first elongated member in the plurality of vertebrae of a section of the spine to be corrected, of a first corrective rod, said longitudinal slot connecting with said housing and allowing said first corrective rod to be displaced from the uppermost part of the transversal slot to the bottom until reaching said housing of said receiving part to become there implanted and reduce the spinal deformity; said second alignment elongated member attached to said second bone anchoring element including a second longitudinal transversal slot allowing insertion there through, for each of second elongated members in the plurality of vertebrae of a section of the spine to be corrected, of a second corrective rod, said second longitudinal slot connecting with said housing and allowing said second corrective rod to be displaced from the uppermost part of the transversal slot to the bottom until reaching said housing of said receiving part to become there implanted and reduce the spinal deformity; characterized in that said first receiving part connected to said head of said first bone anchoring elements is pivotable only in a single sagittal plane, by means of the arrangement of said first corrective rod in said housing of the receiving part; said second receiving part connected to said head of said second bone anchoring element is pivotable only in a transverse plane perpendicular to said sagittal plane, to allow for a correction of the concavity of the deformed spine occurring mainly in a sagittal plane as the bone anchoring member follows said second corrective rod, and said elongate member (13, 19) being removed once corrective rods (15, 21) are implanted, thereby a change in the vertebral rotation occurs, producing a correction of the axial vertebral deformity and a tridimensional correction of the spine deformity. a first bone anchoring element configured to be anchored into a vertebra; a second bone anchoring element configured to be anchored into said same vertebra; both said first and second bone anchoring elements (10, 11) having an axial part for insertion into the vertebra and a head; said head of said first and second bone anchoring elements having pivotally connected thereto a first receiving part and a second receiving part (12, 50) respectively to which a first alignment elongate member and a second alignment elongate member (13, 19) extending along respective longitudinal axis are temporally attached by a proximal portion thereof, respectively, each receiving part (12, 50) defining a housing; said first alignment elongated member attached to said first bone anchoring element including a first longitudinal transversal slot allowing insertion there through, for each of first elongated member in the plurality of vertebrae of a section of the spine to be corrected, of a first corrective rod, said longitudinal slot connecting with said housing and allowing said first corrective rod to be displaced from the uppermost part of the transversal slot to the bottom until reaching said housing of said receiving part to become there implanted and reduce the spinal deformity; said second alignment elongated member attached to said second bone anchoring element including a second longitudinal transversal slot allowing insertion there through, for each of second elongated members in the plurality of vertebrae of a section of the spine to be corrected, of a second corrective rod, said second longitudinal slot connecting with said housing and allowing said second corrective rod to be displaced from the uppermost part of the transversal slot to the bottom until reaching said housing of said receiving part to become there implanted and reduce the spinal deformity; said first receiving part connected to said head of said first bone anchoring elements is pivotable only in a single sagittal plane, by means of the arrangement of said first corrective rod in said housing of the receiving part; said second receiving part connected to said head of said second bone anchoring element is pivotable only in a transverse plane perpendicular to said sagittal plane, to allow for a correction of the concavity of the deformed spine occurring mainly in a sagittal plane as the bone anchoring member follows said second corrective rod, and said elongate member (13, 19) being removed once corrective rods (15, 21) are implanted, thereby a change in the vertebral rotation occurs, producing a correction of the axial vertebral deformity and a tridimensional correction of the spine deformity.