When an aqueous solution of cetyltrimethylammonium bromide is contacted with a nitrobenzene solution containing picric acid, large scale motion of the interface is sometimes observed, accompanied by interfacial electrical potential oscillations with a period of order 3-10 s. This behavior has been interpreted using a stability analysis of a two-phase system (alpha, beta) in which a solute A (in phase alpha) diffuses to the interface where it reacts with solute B (from phase beta) to form product P. Kinetics of the surface reaction are assumed to be infinitely fast. The stability of the system was examined with respect to small perturbations in the spirit of normal mode stability analysis. Both oscillatory and stationary regimes were identified. For the simplified case in which component A is insoluble in phase beta and components B and P are insoluble in phase alpha, the presence of three diffusing components considerably modifies the stability criteria relative to those for the diffusion of a single component across the interface. It is found that, over a narrow concentration range, an oscillatory instability with a period of order 1 s is predicted. This compares well with observed experimental results.