Abstract We report herein experimental observation and mechanistic interpretation of the evolution and self-acceleration of constant-pressure, spherically expanding H2/O2/N2 flames, subjected to hydrodynamic and diffusional-thermal instabilities over a wide range of pressure, equivalence ratio and thermal expansion ratio. Results show the existence of three distinct stages of flame propagation affected by the development of the instability cells, namely smooth expansion, transition, and saturated states of cell development. The onset of the instabilities is primarily controlled by the diffusional-thermal instability, while characteristics of the subsequent transition to and maintenance of the saturated state is controlled by the hydrodynamic instability. The acceleration exponent for the fully developed saturated instability is found to be around 1.2–1.4, which is smaller than 1.5, the suggested value for self-turbulization.