  We present inelastic neutron scattering data on highly overdoped Bi_2 Sr_2 Ca
Cu_2 O_{8+\delta} single crystals with superconducting transition temperature
T_C=70 K and, for comparison, a nearly optimally doped crystal with T_C=87 K.
In both samples, magnetic resonant modes with odd and even symmetry under
exchange of the two CuO_2 layers in the unit cell are observed. In the
overdoped sample, the linewidth of the odd mode is reduced compared with the
optimally doped sample. This finding is discussed in conjunction with recent
evidence for intrinsic inhomogeneities in this compound. The data on odd and
even resonant excitations are otherwise fully consistent with trends
established on the basis of data on YBa_2Cu_3O_{6+x}. This confirms the
universality of these findings and extends them into the highly overdoped
regime of the phase diagram.
