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 degrees 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 degrees 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.