Most simulations of diffusion in ternary systems have been limited to systems where the component diffusivities are equal or else where there is one dominant component. The case of unequal diffusivities has proved more difficult because standard calculations can give non-physical results that violate a material balance constraint. Presented here is a solution technique that is similar computationally to the standard method yet allows diffusion coefficients to be set arbitrarily. The method has been partially verified by molecular dynamic simulations. The method gives results equivalent to the standard technique for the case of equal diffusivities and reduces to Fickian diffusion when the mixture is ideal. A two-dimensional simulation of an asymmetric polymer-polymer-polymer system reproduces an experimentally observed bimodal distribution of dispersed-phase particle sizes for a system where the component diffusivities differ by two orders of magnitude. The ripening exponent for the larger particles is near the expected value of 0.33, but that for the smaller particle only about 0.1. The method was applied to a polymer/polymer/solvent system where the solvent not only had a much higher diffusivity but also had different interaction parameters with the polymers,c₁₃=0.2 and c₂₃=0.5.