The Jeffery-Hamel problem for laminar, radial flow between two nonparallel plates has been extended to the case of two immiscible fluids in slender channels. The governing continuity and momentum equations were solved numerically using the 4th order Runge-Kutta method. Solutions were obtained for air-water at standard conditions over the void-fraction range of 0.4 to 0.8 (due to its practical significance) and the computations were limited to conditions where unique solutions were found to exist. The void fraction, pressure gradient, wall friction coefficient, and interfacial friction coefficient are dependent on the Reynolds numbers of both fluids and the complex nature of this dependence is presented and discussed. An attempt to use a one-dimensional two-fluid with simplified assumptions succeeded in producing a qualitatively similar form of the void-fraction dependence on the two Reynolds numbers; however, quantitatively there are significant deviations between these results and those of the complete model.