The kinetics of thickness transitions of the film, separating two electrostatically stabilized emulsion droplets, is studied. The film evolution is considered as a random process in the two-dimensional space of the film radius and thickness. The analysis is based on the Smoluchowski equation for the time dependent probality for realization of a given configuration (film radius and thickness). The combination of attractive and repulsive (van der Waals and electrostatic) energies determines the potential energy term in the Smoluchowski equation, while the hydrodynamic resistance of film thining determines the diffusion tensor. The components of the latter are calculated. This approach allows one to obtain the average escape time from the secondary (common film) to the primary (Newton black film) energy minimum. This is equivalent to the common film lifetime. If there are not any short-ranged repulsions, to stabilize the thin (Newton black!film) the droplets fuse and the average escape time becomes that for coalescence. It is shown that the droplet deformability may have a great impact on the kinetics of film thickness transition. This is particularly important for emulsion systems with low interfacial tension and high electrolyte concentrations.