This work reports the nondispersive solvent extraction (NDSX) of gold cyanide from aqueous alkaline cyanide media with LIX79 and stripping of gold from the organic complex simultaneously using two microporous hydrophobic polypropylene hollow-fiber contactors for extraction and stripping, respectively. Extraction was studied under different hydrodynamic conditions and mass-transfer correlations for shell and tube sides. The mass-transfer process was compared with experimental results. The HFNDSX was operated with 12-18% LIX 79 in n-heptane by contacting cyanide feed containing gold through the tube side and organic extractant through the shell side, which was recirculated between extraction and stripping hollow-fiber modules through the shell side countercurrently. In the second HF contactor, the stripping solution, 1M NaOH flowed through the tube side countercurrently. Modeling of the system identified rate-controlling steps under different experimental conditions. The interfacial chemical reaction rate at the dominant surface, and mass-transfer resistance caused by this reaction controlled the entire extraction process. Several experiments with synthetic solutions of different compositions of gold hydrometallurgical solutions established optimum conditions to achieve a clean separation of Au(I). It was possible to separate Au(I) in the presence of other metal cyanide salts, such as Fe(II), Cu(II), Ni(II), Ag(I), and Zn(II) (NaCN = 1,000 - 5,000 ppm), which was concentrated in the stripping phase containing NaOH.