Double W/O/W emulsions consist in an inverse emulsion which is dispersed within a water continuous phase as direct emulsion droplets. The aim of this paper is to explore the basic rules that govern the stability of double emulsions. By associating both water- and oil-soluble surfactants in various concentrations, we produce W/O/W double emulsions. We identify two types of instabilities that are responsible for the evolution of double emulsions: (i) coalescence of the small inner droplets with the globule interface or (ii) coalescence between the small inner droplets within the oil globule. The first type of instability leads to a complete delivering of the small inner droplets toward the external phase whereas the second one does not. We show that the kinetics associated with the release of the small inner droplets due to this former instability is clearly related to the hydrophilic surfactant concentration in the external phase. Depending on the value of this concentration, multiple emulsions may be dest...