Stabilization systems for stabilizing one or more vertebral levels are provided. The systems include anchors engageable to the vertebrae and an elongate connecting member system that maintains distraction between the vertebrae while allowing at least limited vertebral motion of the stabilized vertebral levels. The stabilization systems can be employed alone in non-fusion procedure or in conjunction interbody fusion and/or postero-lateral fusion procedures. The connecting members are structured to maintain a constant or slightly variable distance between the anchors to which the connecting members are connected while the connections of the connecting members with the anchors allow motion.