Experiments and quantitative evaluation are conducted upon the cellular morphology and self-acceleration in lean H-2-air expanding flames, trying to interpret the inherent relationship between them. Results confirm the existence of two distinct self-acceleration stages (transition and saturation). The transition between them happens when the aver- aged cell radius decreases to a minimum stable value. Self-similar laws exist both in the transition stage and the saturation stage, with the fractal excess of transition stage much greater than saturation stage. In the saturation stage, fractal excess slowly increases with pressure but is always smaller than 0.33. Basing on evolution profiles of cell radius, the physical interpretation of greater self-acceleration exponent in the transition stage is quantitatively confirmed by correlating the decreasing rate of cell wavelength with flaradius. Finally, the inconsistency of fractal excess in the saturation stage is interpretedme from the perspective of the discrete wavelength spectrum in cellular flames. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.