Molecules containing only nitrogen atoms have been extensively studied as possible candidates for high energy density materials (HEDMs). An all-nitrogen molecule N-x can dissociate to N-2 with the release of a large quantity of energy. To be a viable HEDM, a molecule must resist dissociation well enough to serve as a stable fuel. Recent studies of acyclic N-8 and N-10 molecules suggest that these even-numbered molecules lose N2 too easily to be HEDMs. However, another study of acyclic N-9 suggests that N-9 may be stable enough. In the current study, the dissociation pathways of acyclic N-9 and N-2 1 are examined extensively by theoretical calculations to determine the stability of these acyclic odd-numbered N-x molecules. Dissociation barriers for N-9 and N-11 are calculated using Hartree-Fock (HF) theory, perturbation theory (MP2 and MP4), and coupled-cluster (CCSD and CCSD(T)) theory. The correlation-consistent basis sets of Dunning are employed. The results indicate that N-9 and N-11 can dissociate as easily as N-8 and N10, thereby contradicting the previous conclusion regarding N-9.