A model for nonsteady metals separation using nondispersive solvent extraction presented explicitly accounts for selective separation of multicomponent solutions and concentration of separated components in a back-extraction phase. The separation process comprises extraction and back-extraction steps carried out in two different hollow-fiber modules, connected through the organic phase, together with three homogenization tanks. The model is based on a set of coupled differential equations describing mass balances of metallic solutes in the fluid phases. To be applied in its simplest form, if requires the knowledge of three characteristic parameters, two parameters related to the chemical reactions, and one mass-transport parameter. The latter describes the mass-transport rate through pores of the hollow-fiber membrane filled with the organic phase. The mathematical model was checked against the kinetic results of the separation of Cd/Ni mixtures working with high-concentration solutions and obtaining the characteristic parameters of this system.