The present invention comprises the provision and use of a novel retainer which is slidably advanced to a desired fixation position within a bone tunnel, fixed in position within the bone tunnel (preferably by wedging and/or pinning) while applying a lateral force against the graft ligament so as to compressively hold the graft ligament against the sidewall of the bone tunnel, and which then, optionally, has the graft ligament secured thereto with a cap, whereby to secure the graft ligament to the retainer and hence additionally to the host bone. The present invention also comprises the provision and use of a novel retainer which is slidably advanced to a desired fixation position within a bone tunnel so as to apply a lateral force against the graft ligament so as to compressively hold the graft ligament against the sidewall of the bone tunnel, and which is then locked to the host bone as the graft ligament is simultaneously secured to the retainer, whereby to secure the graft ligament to the retainer and hence additionally to the host bone.