Nonlinear properties of water/oil interface with ionic surfactant were investigated. Dynamic interfacial tension oscillated when adsorption and desorption of di(2-ethylhexyl) phosphoric acid proceeded at water/oil interface. Calcium chloride was necessary in the aqueous phase. Characteristics of both tension oscillation and spontaneous interfacial flow due to the Marangoni effect were examined. The tension oscillation was able to be classified into two groups. One looked like a random oscillation, and another seemed to be dominated by a certain deterministic nature. A model based on a spinodal dynamics was proposed: Surfactant can react with other chemical species at water/oil interface, and homogeneous mixture of surfactant and the reaction product is thermodynamically unstable at the interface. Then, spinodal decomposition takes place to form domains with concentration fluctuation. We calculated what would be expected if adsorption and desorption of surfactant proceeds simultaneously with the spinodal decomposition. Some aspects of complicated oscillations of dynamic interfacial tension were explained by this model.