Detonation properties including relative specific impulses (RIs), detonation velocities ( V D) and pressures ( P D), heats of detonation (HOD), heats of formation (HOF) in gas phase, and crystal densities of furazans and furoxans are calculated by quantum chemistry, molecular mechanics and Monte Carlo methods. The molecular stabilities of mono-furazans and mono-furoxans are discussed using homolysis energy analyses. As a result, 3,4-dinitrofurazan and 3-nitro-4-nitroaminofurazan are recommended to be promising energetic compounds on a comprehensive account. All calculated results show: (1) the crystal densities, detonation properties and sensitivities of most nitro furazans and furoxans are high; (2) it is not an efficient way to enhance detonation properties by increasing furazans or furoxans. Therefore, the smaller molecules are preferentially recommended; (3) the kinds, orders and quantities of the linking groups in poly-furazans and poly-furoxans can affect the above-mentioned properties.