TheU-spin is defined for the higher-symmetry models based on theG2 andC2 algebras. Some relations concerning the masses and electromagnetic properties of the particles are derived and compared with the experimental situation. TheG2 model is found to be in contradiction with experiment especially for electromagnetic processes. A conservation law for an additional spin, theI*-spin, is shown to be a consequence of bothC2 andG2 symmetries. ForC2, this rule forbids at least one process which occurs in nature.