It is suggested that a dynamical space-time symmetry group of a given non-linear relativistic theory is able to generate an internal symmetry group. It is shown that onlyO(2N-1, 1) andO(2N, 1) groups are admitted as simple dynamical symmetry groups, and they implyU(2 N −2) as the largest internal symmetry groups. The boson and fermion content of the considered models is determined and a new dynamical symmetry breaking mechanism, different from the spontaneous one, is introduced.