Calculations are presented on six-g-electron N-B-N- and B-N-B-substituted benzene rings, [C3BN2H6](+) and [C3NB2H6](-), and their isomers. These compounds display a wide range of thermodynamic stability in those molecules, with N-B-N connectivity favored strongly in the cation, B-N-B in the anion. That stability order is easily understood using the charge distribution in a benzene polarized by heteroatom substitutions or the underlying allyl anion and cation. Deprotonation at N in [C3BN2H6](+) leads to a set of BN-substituted pyridines. The calculations predicted three B-N-substituted pyridines clearly more stable thermodynamically than those synthesized so far. The order of stability of the B-N-B-substituted benzenoid systems, which are as yet not well known experimentally, shows similar features. We investigated in a preliminary way the reactivity and potential stabilization by substitution of the energetically most stable structures and by examining possible escape routes by dimerization. Our study suggests new N B N and B-N-B molecules that could be made.