It has been shown that small-amplitude oscillations can augment the diffusional flux : across a cylindrical tube by several orders of magnitude through Taylor - Aris dispersion phenomena (Aris, 1960). This enhancement in mass transport is selective for species with different molecular diffusion coefficients. This article shows that by coupling fluid oscillations with a reversible absorption in a stationary phase, the transport of species, which have similar molecular diffusivities but different affinities for the stationary phase, can be enhanced selectively. We developed analytical and asymptotic solutions to the enhancement of mass transfer as a result of the interaction between reversible absorption and fluid oscillations ill a cylindrical tribe. These results were qualitatively confirmed by experiments with a model system. For purely oscillatory flow, the maximum selectivity (the ratio of the fluxes of the species to be separated) achievable is 4.4 for solute species with widely different affinities for the stationary phase. The superposition of a small-amplitude steady backflow, however, can greatly increase the selectivity, but at the expense of throughput. Analysis shows that this technique may offer improvements relative to conventional liquid membrane separations, if the solute affinities for the stationary phase do not greatly differ or if a thick membrane is required for stability.