Planar N-x systems such as cyclo-N-5(-) and N-5(+) tend to be more stable than nonplanar systems such as the neutral cyclo-N-6. It is proposed that the key to stabilization is the separation of the sigma and pi electron systems. In both cyclo-N-5(-) and N-5(+), a six-pi-electron system is created upon either adding to or removing from the cyclo-N-5 radical one electron. Judicious addition of oxygen atoms to polynitrogen ring compounds such as cyclo-N-4 and cyclo-N-6 can increase their thermodynamic and kinetic stabilities, accompanied by only a small reduction in their efficiency as high energy density materials (HEDMs). The properties of some of these compounds are calculated and compared with the parent all-nitrogen compounds. Coordination of one or more oxygen atoms to the ring leads to effective separation of the sigma and pi electron systems helping to stabilize the systems. Natural bond analysis indicates that the exocyclic NO bonds can assume a single or double bond character, depending on the ring system.