Various all-nitrogen molecules have been examined as candidates for high energy density materials (HEDM), because of the energy release that would accompany the dissociation of such a molecule down to N-2 molecules. Numerous molecules N. have been shown to dissociate too easily to be a viable HEDM, including small N, all-nitrogen cages. One possible solution to the instability of small N, cages is oxygen insertion into the N-N bonds. Conversion of N-N bonds into N-O-N bonding groups would relieve much of the ring strain in small N-x cages, thereby stabilizing the molecule and possibly making the NxOy molecule a good HEDM. Several cage isomers of N8O4 are examined by theoretical calculations to evaluate their suitability as potential HEDM. Calculations are carried out with Hartree-Fock theory and Mphiller-Plesset perturbation theory (MP3 and MP4), using the CC-PVDZ basis set of Dunning. The relative thermodynamic stability of the isomers is discussed, along with dissociation energies for the various N8O4 cages.