We have investigated the kinetics of swelling of squalane-in-water emulsion drops by the addition of decane-in-water emulsion drops. Squalane is sufficiently insoluble in the aqueous continuous phase that it cannot transfer between oil drops. Decane is able to transfer between drops and swells the squalane drops. The mixed emulsions were stabilized by the nonionic surfactant n-dodecyl octaoxyethylene glycol ether (C12E8) and were stable with respect to drop coalescence. We have made a systematic series of experiments in which the swelling rates were determined as functions of the initial drop radii, volume fractions, and oil compositions of both types of emulsions. Using a theoretical model originally developed by Ugelstad et al., the entire data set was successfully fitted with a single adjustable parameter equal to the product of the solubility of decane (C-infinity) and its diffusion coefficient in the aqueous continuous phase (D). The measured value of CinfinityD was consistent with a mechanism of decane transport in which micelles of C12E8 act as carriers facilitating decane transport between emulsion drops. Also in agreement with this mechanism, it was observed that increasing the aqueous phase concentration of C12E8 increased the swelling rate. Ostwald ripening rates of the decane-in-water emulsions gave values of CinfinityD consistent with those derived from swelling experiments.