An osteosynthesis plate system is particularly well adapted to securely fuse adjacent cervical vertebrae. The plates are for mounting upon the anterior or posterior surfaces of the vertebrae. Plates for mounting on the anterior vertebral surfaces have a concave bone contacting surface and a bone screw locking mechanism integral with each screw hole. Moreover, the bone contacting surface of the plate has a plurality of bone penetrating protrusions to more securely affix the plate to bone. Plates for mounting on the posterior vertebral surfaces also have bone penetrating protections on their bone contacting surfaces. Such plates are formed so as to have a curved bone contacting surface that is concave in the transverse axis of the plate and convex in the longitudinal axis of the plate. The screw holes of such plates are constructed so as to guide a bone screw along a desired angle to improve the anchoring of the screws in bone.