The extraction of Cu2+ ions from sulfate solutions across a hollow-fiber membrane containing LIX64N carriers dissolved in kerosene has been studied, in which Cu(II) was then back-extracted to a stripping-phase containing HCl. Experiments were conducted as a function of the initial feed concentration of Cu2+ (1-10 mol/m(3)), feed pH (2-6), the carrier concentration (0.1-0.4 mol/dm(3)), and stripping acidity (0.4-4 mol/dm(3)). A mass-transfer model was developed to predict the extent of Cu2+ extraction from aqueous feed in hollow-fiber contactors. The calculated time profiles of Cu2+ concentrations were in reasonable agreement with the experimental data (average standard deviation 9% in both extraction and back-extraction modules). The rate-controlling step(s) of such dispersion-free extraction processes were identified. It was shown that the extraction was governed by combined interfacial reaction and aqueous diffusion under the ranges studied, whereas the back-extraction was limited by combined membrane diffusion and aqueous diffusion.