Direct numerical simulations of Moderate or Intense Low-oxygen Dilution combustion inside a cubical domain are performed. The computational domain is specified with inflow and outflow boundary conditions in one direction and periodic conditions in the other two directions. The inflowing mixture is constructed carefully in a preprocessing step and has spatially varying mixture fraction and reaction progress variable fields. Thus, this mixture includes a range of thermo-chemical states for a given mixture fraction value. The combustion kinetics is modelled using a 58-step skeletal mechanism including a chemiluminescent species, OH*, for methane–air combustion. The study of reaction zone structures in the physical and mixture fraction spaces shows the presence of ignition fronts, lean and rich premixed flames and non-premixed combustion. These three modes of combustion are observed without the typical triple-flame structure and this results from the spatio-temporally varying mixture fraction field undergoing turbulent mixing and reaction. The flame index and its pdf are analysed to estimate the fractional contributions from these combustion modes to the total heat release rate. The lean premixed mode is observed to be quite dominant and contribution of non-premixed mode increased from about 11% to 20% when the mean oxygen mole fraction in the inflowing mixture is reduced from about 2.7% to 1.6%. Also, the non-premixed contribution increases if one decreases the integral length scale of the mixture fraction field. All of these results and observations are explained on physical basis.