In complement to the hydrodynamic instabilities driven by surface tension gradients, enclosed in Sects. 5.4-5.7, we describe here the dynamics of the liquid-liquid interface, formed by two fluids of very limited miscibility, e.g., by water and 2-nitropropane. First reports on this type of dynamical systems have been published by Dupeyrat and Nakache [1,2], and later analogous studies were continued also by .A representative example of that type of the systems is the water-2-nitropropane system [3]. The key point is that each phase should contain the dissolved species that is significantly better soluble in the other phase. In this way the initial state of such system is far from equilibrium and the natural trend to decrease the free Gibbs energy is the flow of each dissolved species to the other phase. In the example described here, the aqueous phase contains initially the hexadecyltrimethylammonium bromide (or cetyltrimethylammonium bromide, CTAB) the large organic CTA + cation of which exhibits, due to its hydrophobicity, higher affinity to the organic phase. In turn, the phase of 2-nitropropane contains initially dissolved picric acid (HA), better soluble and also partly dissociating in water (pK a % 0.2).When these two phases are brought into contact, with the organic layer placed over the aqueous layer, the oppositely directed flows of CTAB and HPi begin. This transport is associated with subtle oscillations of various characteristics: pH of aqueous solution, interfacial potential drop (Fig. 6.1), and interfacial tension. The latter phenomena are easily detectable as visible oscillations of the meniscus at the interface of both liquids. It is interesting that under such non-equilibrium conditions the presence of surfactant (CTAB) does not depress the surface tension gradients, but on the contrary, it is responsible for their periodic temporal variations.Yoshikawa and Matsubara [3] have proposed the mechanism of these oscillatory phenomena. First, one should note that CTA + cations in both phases form micelles above certain critical CTA + concentrations. Those micelles exhibit inverted M. Orlik, Self-Organization in Electrochemical Systems II, Monographs in Electrochemistry,