Spinal stabilization mechanisms act to prevent lateral bending, extension, and rotation at the disc space. Two or more anchors at each vertebral level, and links at each level to both anchors at the other level result in a cross-braced arrangement that enhances compression and promotes fusion. In the preferred embodiment, the mechanism uses screws for placement in the vertebral bodies and cables are used to connect the screws. The cables pull the screws together, applying compression across the disc space. Bone graft, cages, or distracting plugs and the device to enhance fusion area would fill or cross the disc space. The bone graft, cages, etc. within the disc space are preferably used to resist compression. The device may be used in the cervical, thoracic, or lumbar spine. The device is preferably placed anteriorly, but could also be used posteriorly, with the screws directed through the vertebral body pedicles. The various components may be constructed of titanium, stainless steel, polymers, or a combination of such materials. The anchors preferably include a post protruding from the vertebra, and a cable-holders which fits over the post. The post may be threaded, in which case a nut would be used to tighten the holders, or the cable holders may be allowed to rotate, depending upon the position and/or application of the fasteners. The cable holders may use tunnels, tubes or outer grooves to the hold the cables in position. Devices may also be added to keep the links from crossing one another where they cross.