Gas-phase structures of two isomers of dimethyl-substituted 1,5-diazabicyclo[3.1.0]hexanes, namely, 3,3-dimethyl- and 6,6-dimethyl-1,5-diazabicyclo[3.1.0]hexane molecules, have been determined by gas electron diffraction method. A new approach based on the Monte Carlo method has been developed and used for the analysis of precision and accuracy of the refined structures. It was found that at 57 °C 3,3-dimethyl derivative exists as a mixture of chair and boat conformers with abundances 68(8)% and 32(8)%, respectively. 6,6-Dimethyl-1,5-diazabicyclo[3.1.0]hexane at 50 °C has only one stable conformation with planar 5-ring within error limits. Theoretical calculations predict that the 6,6-dimethyl isomer is more stable in comparison to the 3,3-dimethyl isomer with energy difference 3-5 kcal mol(-1). In order to explain the relative stability and bonding properties of different structures the natural bond orbitals (NBO), atoms in molecules (AIM), and interacting quantum atoms (IQA) analyses were performed.