The results of an all-electron STO-6G valence-bond study of the origin of the long, weak N-N bond of asym-N2O3 are reported. Attention is given to the valence-bond structures which differ in the locations of eight electrons among five overlapping nitrogen and oxygen atomic orbitals, designated as <(pi)over bar>(1), h(2), and <(pi)over bar>(3) for NO2, and h(4) and <(pi)over bar>(5) for NO These orbitals accommodate the electrons of the N-N sigma-bond and oxygen lone-pair electrons prior to any delocalization of the latter electrons. The calculations are parametrized so that UHF/cc-pVQZ estimates of the atomic spin densities for NO2 and NO are approximately reproduced when their odd electrons are assumed to occupy these overlapping atomic orbitals. The origin of the N-N bond lengthening is thereby shown to be associated with (a) the orientation of the h(4) atomic orbital, and (b) some delocalization of oxygen <(pi)over bar> electrons into the nitrogen h(2) and h(4) atomic orbitals when the latter orbitals are initially singly occupied. Covalent-ionic resonance (O2N-NO <-> O2N-NO+ <-> O2N+NO-) is calculated to be needed in order to stabilize the N2O3 relative to the NO2 and NO dissociation products.