  The internal symmetry of composite relativistic systems is discussed. It is
demonstrated that Lorentz-Poincar\'e symmetry implies the existence of internal
moments associated with the Lorentz boost, which are Laplace-Runge-Lenz (LRL)
vectors. The LRL symmetry is thus found to be the internal symmetry universally
associated with the global Lorentz transformations, in much the same way as
internal spatial rotations are associated with global spatial rotations. Two
applications are included, for an interacting 2-body system and for an
interaction-free many-body system of particles. The issue of localizability of
the relativistic CM coordinate is also discussed.
