A stabilization device for bone parts or vertebrae includes two bone anchoring devices for anchoring in the bone parts or vertebrae. At least one of the bone anchoring devices includes an anchoring element with an anchoring section for anchoring in a bone part or a vertebra and a head, and a receiving part for receiving a stabilization rod. The receiving part has a seat for receiving the head so that the head can pivot with respect to the receiving part. The stabilization device includes a first pressure element which is movable in the receiving part so that it can be pressed onto the head to lock the angular position of the head. The stabilization device includes at least two stabilization rod sections, and at least two guiding channels within the receiving part which have a distance from each other for guiding through the at least two stabilization rod sections so that the rod sections do not touch each other.