This paper examines the influence of mass transfer on the composition trajectories during distillation of mixtures that exhibit distillation boundaries. Simulations for total reflux distillation of the systems methanol-iso-propanol-water and benzene-iso-propanol-n-propanol show that composition trajectories originating along the distillation boundary could end up in completely different corners of the composition triangle depending on whether or not diffusional interactions are taken into account. Using published experimental data it is concluded that for reliable design and simulation it is necessary to use a rigorous model for mass transfer based on the Maxwell-Stefan diffusion equations.