A solution of the problem of low flux, multicomponent, mass transfer in single, circulating liquid drops is presented in this work. The prediction from fundamental theory of single-component mass transfer for drops travelling at intermediate Reynolds numbers (10 less than or equal to Re less than or equal to 250), reported by the authors (Uribe-Ramirez & Korchinsky (2000) Chemical Engineering Science, in press), is extended to the case of several solutes transferring simultaneously. The same limitations of the previous paper apply here. These include (i) the neglect of the mass transfer occurring in the wake, (ii) that mass transfer during drop formation will previously have been accounted for, and (iii) that complete mixing occurs beyond the narrow boundary layer adjacent to the drop surface. The multicomponent diffusion equation, with velocities estimated as for the single component transfer case, is uncoupled using the linearized theory of Toor (1964a, b) and Stewart and Prober (1964). Each of the uncoupled differential equations is then solved, using a transformation of variables, for the pseudo-concentration profiles near the boundary in both phases, and for the bulk solute concentration changes in the drop. Multicomponent mass transfer coefficients are also calculated. Results for the quaternary system, toluene-acetone-acetaldehyde-water, are predicted to illustrate the application of the theory. Experimental data are required to check predictions.