Quantum chemical calculations using ab initio methods at the CCSD(T)/def2-TZVPP level and density functional theory using BP86 and M06-2X functionals in conjunction with def2-TZVPP basis sets have been carried out on the title molecules. The calculated energies suggest that the N-oxides R₃NO with R = F, Cl are lower in energy than the amine isomers R₂NOR, but the latter form is more stable than the N-oxides when R = H, Me, Ph. In contrast, the phosphane oxides R₃PO are always more stable than the phosphanyl isomers R₂NOR except for the parent system with R = H, where the two isomers are close in energy. The energy decomposition analysis suggests that the best description of the N–O bond in N-oxides R₃NO depends on the nature of the substituent R. The halogen systems F₃NO and Cl₃NO and the triphenyl species Ph₃NO possess dative bonds R₃N→O, which are enhanced by R₃N←O π backdonation. The contribution of the π backdonation is only 10% of the total orbital interactions ΔE_orb in Ph₃NO, but it amounts to ∼22% of ΔE_orb in F₃NO and Cl₃NO. The N–O bonds H₃NO and Me₃NO are better described in terms of electron-sharing single bonds between charged fragments R₃N⁺–O⁻, which are supported by modest R₃N⁺←O⁻ π backdonation that comprise 13–16% of ΔE_orb. In contrast, all phosphane oxides R₃PO are best depicted with electron-sharing single bonds between charged fragments R₃P⁺–O⁻, which are significantly supported by R₃P⁺←O⁻ π backdonation contributing 22–32% of ΔE_orb.