In the framework of the diffusional-thermal flame model, an asymptotic nonlinear differential equation is derived for the evolution of a disturbed spherical flame front. A quantitative description is presented of the formation of cellular flame structure and the subsequent self-turbulization of the flame. A cellular flame may form only when the combustible mixture contains a sufficiently light reactant in small concentration. If there is an excess of the light reactant, the laminar flame front remains smooth. An explanation is given for the anomalous stability of a spherical flame in comparison with a plane flame. The existence of a regular hexagonal cellular structure is shown.