The use of supercritical alcohols has been proposed as a non-catalytical method to produce biodiesel, overcoming some of the shortcomings related to conventional catalytic methods. In this work, the Cubic-Plus-Association equation of state is used to predict the vapor-liquid equilibria of several alcohol + fatty acid ester and alcohol + glycerol systems, in the temperature range 493-573K and pressure range 2-12 MPa. The resulting predictions reproduce accurately the experimental data, within their experimental uncertainty. The ability to predict these phase equilibria is of primary importance for designing, operating and optimizing biodiesel production at near or supercritical conditions. The CPA EoS is shown to be a powerful prediction tool for an adequate design of the operations involved in the biodiesel production with near or supercritical alcohols. (C) 2010 Elsevier B.V. All rights reserved.