An anchoring device adapted for anchoring to a structure an element to be anchored having a distal side and a proximal side, the anchoring device comprising: - anchoring stages, each anchoring stage comprising a base and at least one anchoring element articulated on the base so as to be movable between a folded position and a position deployed radially with respect to the element to be anchored; and - a wedging member movable along the element to be anchored in the direction of the distal side so as to cause movement of the anchoring element(s) from the folded position towards the deployed position, wherein the anchoring stages include an end stage towards the distal side and at least one anchoring stage other than the end stage, wherein the base of each anchoring stage other than the end stage is movable along the element to be anchored, the movement of the wedging member in the direction of the distal side causing an approach of the bases to one another, wherein the base of the end stage may be coupled on the element to be anchored so as to be prevented from moving in the direction of the distal side during the movement of the wedging member which causes the deployment of the anchoring element(s), and wherein the base of an anchoring stage comprises a first guide element and at least one anchoring element of a neighbouring anchoring stage comprises a second guide element, the first and second guide elements (42, 50) cooperating with one another during the movement of the wedging member in the direction of the distal side to prevent the rotation of said anchoring member around the member to be anchored. - anchoring stages, each anchoring stage comprising a base and at least one anchoring element articulated on the base so as to be movable between a folded position and a position deployed radially with respect to the element to be anchored; and - a wedging member movable along the element to be anchored in the direction of the distal side so as to cause movement of the anchoring element(s) from the folded position towards the deployed position, wherein the anchoring stages include an end stage towards the distal side and at least one anchoring stage other than the end stage, wherein the base of each anchoring stage other than the end stage is movable along the element to be anchored, the movement of the wedging member in the direction of the distal side causing an approach of the bases to one another, wherein the base of the end stage may be coupled on the element to be anchored so as to be prevented from moving in the direction of the distal side during the movement of the wedging member which causes the deployment of the anchoring element(s), and wherein the base of an anchoring stage comprises a first guide element and at least one anchoring element of a neighbouring anchoring stage comprises a second guide element, the first and second guide elements (42, 50) cooperating with one another during the movement of the wedging member in the direction of the distal side to prevent the rotation of said anchoring member around the member to be anchored. wherein the anchoring stages include an end stage towards the distal side and at least one anchoring stage other than the end stage, wherein the base of each anchoring stage other than the end stage is movable along the element to be anchored, the movement of the wedging member in the direction of the distal side causing an approach of the bases to one another, wherein the base of the end stage may be coupled on the element to be anchored so as to be prevented from moving in the direction of the distal side during the movement of the wedging member which causes the deployment of the anchoring element(s), and wherein the base of an anchoring stage comprises a first guide element and at least one anchoring element of a neighbouring anchoring stage comprises a second guide element, the first and second guide elements (42, 50) cooperating with one another during the movement of the wedging member in the direction of the distal side to prevent the rotation of said anchoring member around the member to be anchored.