A novel extraction technique using an emulsion liquid membrane within a hollow-fiber contactor was developed and utilized to extract copper using LIX 84 extractant. Emulsion liquid membranes are capable of extracting metals from dilute waste streams to levels much below those possible by equilibrium-limited solvent extraction. Utilizing an emulsion liquid membrane within a hollow-fiber contactor retains the advantages of emulsion-liquid-membrane extraction, namely, simultaneous extraction and stripping, while eliminating problems encountered in dispersive contacting methods, such as swelling and leakage of the liquid membrane. Mathematical models for extraction in hollow-fiber contactors were developed. The models satisfactorily predict the outcome of both simple solvent extraction and emulsion-liquid-membrane extraction of copper by LIX 84 in a hollow-fiber contactor over a wide range of conditions. Emulsion-liquid-membrane extraction performs exceptionally well when the extraction is close to equilibrium limit. It is also capable of extracting a solute from very dilute solutions. Stability of the liquid membrane is not crucial when used in hollow-fiber contactors; the surfactant in liquid membrane can be reduced or even eliminated without severely impairing the performance.