A systematic stoichiometric and kinetic model was developed for the acid-catalysed polyesterification of unsaturated dicarboxylic acids and mixtures of dicarboxylic acids. The model was based on a rigorous treatment of the functional groups and their reactions: esterification, cis-trans isomerization and double-bond saturation through Ordelt reaction. The model was applied on the polyesterification of maleic and phthalic acids with ethylene glycol, propylene glycol, diethylene glycol and dipropylene glycol in a semi-batch reactor at 160-195 degreesC. Kinetic and thermodynamic parameters included in the model were estimated with non-linear regression. It was found that important simplifications can be introduced: the rate constants of the different esterification and isomerization reactions can be set equal, whereas it was necessary to treat the different double-bond saturation reactions with individual rate constants. A comparison of model predictions with experimental data revealed that the proposed kinetic treatment is relevant for polyesterification of complex mixtures.