The invention relates to a system which is used to fix a part to a bone element. The invention is essentially characterized in that it consists of: at least one hole which is disposed in part; a rigid rod comprising a first end, the rod being wound into a spiral along a first helicoidal curve; and a device for rotating the rod around the axis of the first helicoidal curve, such that the first end of the rod moves alternatively inside and outside the bone element and, during the rotation thereof, the first end of the rod moves at least once into the opening. The invention is particularly suitable for fixing intervertebral disks or fusion cages to the vertebral bodies of two consecutive vertebrae.