A system for providing dynamic stabilization and balance control at a vertebral motion segment has first and second bridge elements and at least one bias element. The bridge elements anchor to adjacent vertebrae with polyaxially adjustable anchoring members, and the bias elements attach to each bridge element to span between them. Each bias element has two fixation portions and a bias body extending between the fixation portions. Each bias element may comprise an elastically deformable material to provide dynamic stabilization with motion, or may comprise rigid material to provide rigid stabilization, and both bias element types may be included in one system. The bias elements are attachable to the bridge elements at discrete attachment locations, or at non-discrete attachment locations. Alternate embodiments may include three or more bridge elements on adjacent vertebrae, and multiple bias elements. A tensioning tool may provide adjustable tension to an elastically deformable bias element.