A modified form of the generalized Darken's model of interdiffusion is presented in the case of solid solution oxides of the (A, B,..)O type, i.e., binary, ternary and higher oxides. The equations describing the interdiffusion process in the general case where the components' diffusivities vary with composition and the reactions of diffusing components at the interfaces are allowed are shown. The model allows to study the evolution of the composition in the multicomponent system occurring as a result of its thermal treatment and/or intercalation, e.g., allows to predict the concentration profiles of all elements in the vicinity of interfaces (at the reaction zone). We show the simulation of the evolution of composition of the NiO-CoO solid solutions at high temperatures. We will show that the generalized Darken model allows to obtain the quantitative data on the interdiffusion in open systems as well as describe the complex mass transport processes in solid solutions.