In this study, two critical Peclet numbers, Pe(c) for the onset of cracks on the flame surface, and, Pe(cl), for the onset of fully developed cellular flame leading to flame acceleration, of hydrogen air flames were experimentally evaluated. The dependency of Pe(cl) on Ma(b), the Markstein number for flame speed, and Ka(cl), the critical Karlovitz number, were discussed and compared with previous experiments for various fuel-air mixtures. In this study, we investigated the correlation between Pe(cl) and Ma(b) rather than that between Pe(cl) and Ma(sr), Markstein number for the burning velocity strain rate. The results demonstrated that the values of Pe(c) and Pe(cl) increased with an increase in Ma(b), because the transitions to cellularity were gradually affected by the intensity of the diffusional-thermal instability. The linear correlation observed between Pe(cl) and Ma(b) qualitatively agreed with the results of previous works on other types of fuels. The dependency of Ka(cl) on Ma(b) was estimated. The values of Ka(cl) rapidly decreased with an increase in Ma(b). Empirical correlations were derived to estimate the critical conditions for the onset of flame acceleration due to cellular flame instabilities. These empirical expressions approximatively correlated well with the experimental data.