Mass transfer in the laminar, coccurent flow of two fluids in a rectangular channel is investigated. Distribution of concentrations and the local mass-transfer coefficients are calculated for the ideal flow, the Couette flow and for the flow with parabolic profile. Analytical and approximate solutions for finite and semi-infinite flows in a two-phase system are presented. The results obtained show that the formal mathematical solutions for one- and two-phase systems are similar. In the latter case, the diffusional resistance to the mass transfer is greater by a factor which is close to the value of the distribution coefficient.