Control of the liquid-liquid extraction process using advanced neural-network-based algorithms was applied to control product compositions of a Scheibel agitated extractor of type I. The nonequilibrium backflow mixing cell model was used to model the extractor hydrodynamics and mass-transfer characteristics of the column. Two neural-network-based control algorithms were used to control the extractor, namely, the model predictive control and the feedback linearization control algorithms. The performance of the feedback linearization controller was compared to that of the model predictive controller. Both algorithms were capable of solving the set-point tracking control problem with a noticeable superiority of the model predictive algorithm. Despite the good set-point direction tracking for the feedback linearization controller, its performance was slow and suffered from steady-state offsets. The application of this controller is restricted to certain processes and cannot be generalized for all processes. The model predictive control algorithm was better in terms of set-point tracking accuracy and speed of response.