The even-even and even-odd nuclei 126 Xe-132 Xe and 131 Ba-137 Ba are shown to have a wellrealized SO 8 ⊃ SO 6 ⊃ SO 3 fermion dynamical symmetry. Their low-lying energy levels can be described by a unified analytical expression with two (three) adjustable parameters for even-odd (even-even) nuclei that is derived from the fermion dynamical symmetry model. Analytical expressions are given for wavefunctions and for E2 transition rates that agree well with data. The distinction between the FDSM and IBM SO 6 limits is discussed. The experimentally observed suppression of the the energy levels with increasing SO 5 quantum number τ can be explained as a perturbation of the pairing interaction on the SO 6 symmetry, which leads to an SO 5 Pairing effect for SO 6 nuclei.