The Differential Scanning Calorimetry (DSC) technique is used for measuring isobaric (vapour + liquid) equilibria for two binary mixtures: {monocaprylin + palmitic acid (system 1) or methyl stearate (system 2)} at two different pressures P = (1.20 and 2.50) kPa. The obtained PTx data are correlated by Wilson, NRTL and UNIQUAC models. The original UNIFAC group contribution method is also considered and new binary interaction parameters for the main groups CH2, CCOO, OH and COOH are regressed, to account for the non-idealities found in these lipid systems. Established thermodynamic consistency tests are applied and attest the quality of the measured data. In terms of relevance of the selected components, system 1 can be found in the purification and deodorization steps during the production of edible oils, while, system 2 can be found in the purification steps of biodiesel. It should be noted that no such data could be found in the open literature, not only for the specific components selected but also for the combination of the classes of components considered; that is, acylglycerol plus fatty acid or fatty ester.