Ternary mixtures have been shown to have the properties conducive to achieving enhanced performance when used in absorption heat pumps. In this paper the linearized theory of Toor (A.I.Ch.E.J. 1964, 10, 448-455) is used to calculate solutions for coupled heat and mass transfer in a falling film on a vertical cylindrical tube which is a candidate for the geometry of an absorber in a heat pump. As with earlier work performed for binary mixtures it is shown that mass transfer takes place in a thin liquid layer near the liquid-vapor interface provided that a dimensionless parameter involving the combination of flow rate and Schmidt number is small. The concept of mass transfer resistance is quantified through the definition of a mass transfer driving parameter (B) over right arrow which is assumed to be small for the present problem. An analytical solution for the mass absorbed is obtained for a wide range of physical parameters. Application to mixtures employed in the design of heat pumps is indicated and the generalization of the ternary mixture results to the case of multicomponent mixtures is apparent. Explicit results are presented for the case of a single component vapor and the application of the present work to the desorption process is shown to be immediate.