The paper presents a new approach to the modelling of heating and evaporation of dual-fuel droplets with a specific application to blends of biodiesel (represented by the widely used soybean methyl ester, SME) and Diesel fuels in conditions representative of internal combustion engines. The original compositions, with up to 105 components of Diesel and biodiesel fuels, are replaced with a smaller number of components and quasi-components using the recently introduced multi-dimensional quasi-discrete (MDQD) model. Transient diffusion of these components and quasi-components in the liquid phase and temperature gradient and recirculation inside droplets are taken into account. The results are compared with the predictions of the case when blended biodiesel/Diesel fuel droplets are represented by pure biodiesel fuel or pure Diesel fuel droplets. It is shown that droplet evaporation time and surface temperature predicted for 100% SME, representing pure biodiesel fuel, are close to those predicted for pure Diesel fuel. Also, it is shown that the approximations of the actual compositions of B5 (5% SME and 95% Diesel) and B50 (50% SME and 50% Diesel) dual-fuels by 17 quasi-components/components, using the MDQD model, lead to under-predictions in droplet lifetimes by up to 9% and 4%, respectively, under the same engine conditions. The application of the latter model has resulted in above 83% reduction in CPU time compared to the ease when all 105 components are taken into account using the discrete component model. (C) 2016 Elsevier Ltd. All rights reserved.