The results of theoretical and experimental studies of spontaneous nonlinear oscillations produced at the liquid/liquid interface by surfactant transfer from a point source situated in one of the bulk phases are presented. The theoretical analysis is based on the direct numerical simulation of the system evolution. The experiments are performed for the heptane/water interface using middle-chain aliphatic alcohols as surfactants. The results for the oil/water interface are compared with the corresponding data obtained for the air/water interface. The presented results allow the conclusion that auto-oscillations at the air/liquid and liquid/liquid interfaces are governed by very similar mechanisms but their characteristics are strongly dependent on the properties of the two contacting media, in particular, on the surfactant partition coefficient.