Nonlinear oscillations of electric potential differences caused by mass transfer of benzyldimethyltetradecylammonium chloride through a nitrobenzene liquid membrane containing picric acid are investigated. The physical chemistry of this liquid membrane oscillator is described in detail, and limitations of applicability of some physicochemical laws are pointed out. It is shown that the oscillations are of chemical origin. The role of the accompanying hydrodynamic effects is critically examined. In order to understand the oscillation mechanism at the molecular level, a new mechanistic scheme based on ion pairs mass transfer is proposed. Oscillations appear at the membrane-aqueous acceptor phase interface, and they are caused by the autocatalytic adsorption of surfactant molecules to this interface. Inclusion of cross-catalytic molecular events shows interesting coupling between diffusion fluxes and the two oscillating subsystems present. It is demonstrated that the proposed mechanistic scheme is quite general and versatile. Time evolution of the oscillator is described by using the laws of deterministic chemical kinetics. The results obtained by numerical integration of the corresponding system of first-order autonomous differential equations are in fairly good agreement with experimental time series. It is postulated accordingly that the nonlinear oscillations observed for liquid membrane systems are originating from molecular events and are further amplified by hydrodynamic effects.