Dynamic modelling of a countercurrent multistage process is important not only for solving start-up and control problems but also for its possible use for performance analysis, specifically in a multicomponent non-linear extraction process. However, the respective differential equations are often stiff, complicated by non-linear equilibrium relations, and their numerical solution is very difficult. The problem is overcome by the proposed pulsed-flow model. In the model, each extraction stage is considered as a set of ideal mixers and the continuous process is represented by repeated sequences of pulsed flow and a batch mass transfer. Moreover, it is possible to introduce extraction efficiency into the pulsed-flow model. A typical example of the process with the above features is the extractive separation of the rare earth elements in a mixer-settler cascade. Adequacy of the pulsed-flow model was tested and its parameters were determined by dynamic experiments on a 6-stage cascade. The pulsed-flow model proved to be very useful for finding the steady-state operating conditions ensuring the required product purity in the rare earths separation using bis(2-ethylhexyl)phosphoric acid operating conditions ensuring (DEHPA) in a 30-stage extraction-stripping cascade with extract and raffinate refluxes. The model was also used for the prediction of responses to some disturbances and for the analysis of control configurations.