Abstract: A system for aligning a drilling module on a jack-up rig with a drilling module support surface on a fixed rig wherein the angular disposition of the drilling module is varied by moving a portion of the jack-up rig on at least one of the legs of the jack-up rig to bring the angular disposition of the drilling module into alignment with the angular disposition of the drilling module support surface on the fixed rig prior to transferring the drilling module from the jack-up rig to the fixed rig. The system also includes a position assembly for positioning the drilling module on the drilling module support surface in a predetermined aligned position.