Ab initio two-determinants GVB computations (required to get the appropriate representation of the lowest singlet states of such systems) have been carried out for (Cu+(NH3)(n))(2)-O-2 (n = 0-3) and [Cu2Cu-pydz)(2)(cnge)(2)](2+)-O-2. Different dioxygen binding modes (ranging from perpendicular to parallel with respect to the Cu-Cu direction) on these complexes have been examined. The results obtained show unambiguously that the parallel arrangements are always the less stable ones. In the especially important case of (Cu+(NH3)(3))(2)-O-2 complexes, both staggered and eclipsed conformations have been considered. They are found almost isoenergetic, and the optimized geometrical parameters are, for a perpendicular O-2 binding onto a staggered complex, in fine agreement with corresponding experimental data obtained from either oxyhemocyanin or its synthetic models. In the case of a (Cu+(NH3)(4))(2)-O-2 complex, taken as a model for Karlin’s [((TMPA)Cu)(2)-O-2](2+) complex, the computations tend to show that the experimental end-on (trans mu-1,2) O-2 binding is due to the presence of four nitrogens in the copper’s coordination shell. Regarding the complexes with [Cu-2(mu-pydz)(2)(cnge)(2)](2+), the results indicate that the dioxygen binding mode remains perpendicular even if the fixation of a third pyridazine is known to occur in a parallel manner on this complex.