LES of gas and spray combustion in back-step flows are performed to investigate the mechanism underlying combustion instability and the effect of initial droplet diameter on combustion instability. Methane and kerosene are used as fuel for gas and spray combustion, respectively, and two-step global reaction models are used for the reactions. A dynamic thickened flame model is employed as the turbulent combustion model. The motions of evaporating droplets are tracked using the Lagrangian manner. The results show that in gas combustion, the pressure, heat release rate and streamwise velocity oscillate with the same frequency but different phases, and that the inlet velocity oscillation periodically generates a large vortex near the dump plane that drives combustion instability. In spray combustion, an oscillation of droplet evaporation rate is also observed. Whereas the difference in the initial droplet diameter slightly affects the mode of the pressure oscillation, it strongly affects the intensity of the pressure oscillation and causes a maximum value for a specific initial droplet diameter. This arises from the difference in the initial droplet diameter causing a difference in the droplet evaporation rate, which alters the relationship between the oscillations of the heat release rate and pressure near the dump plane. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.