The simultaneous heat- and mass-transfer process occurring during the condensation of vapours of immiscible liquids has been analysed using the design method adopted from Sardesai and Webb, which is based on the classical treatments of Ackermann and Colburn and Drew. Experimental data are reported for condensation of vapour mixtures on the outside of a cooled horizontal copper tube. The mixtures studied were toluene-water, n-heptane-water, cyclohexane-water and trichloroethylene-water. These mixtures are rich in steam and are removed from the eutectic composition. The design method predicts the experimental overall rates of condensation within +/-20%. It is shown, both experimentally and theoretically, that when the composition of the vapour mixture is non-eutectic, situations are possible where only one vapour condenses and the other acts as a non-condensable gas.