Apparatus for connecting and stabilizing adjacent vertebral segments, comprising a flexible composite connecting rod extending between the segments, and connection devices for connecting the rod to the vertebral segments. The rod comprises a rod member formed of a flexible plastic material having a predetermined compression strength, and a high tensile strength, low stretch, flexible reinforcing element extending longitudinally through the entire length of the rod member. The reinforcing element may be in the form of a single cord, rope, braid or monofilament, a plurality of substantially parallel cords, ropes, braids or monofilaments, or a tubular cord, rope, braid or woven or wire mesh strain relief device extending through the rod member in slidable relation or bonded thereto.