The biomass‐derived polyesters poly(1,3‐propylene 2,5‐furandicarboxylate) (PPF), poly(1,3‐propylene succinate) (PPS) and poly(1,3‐propylene 2,5‐furandicarboxylate‐co‐1,3‐propylene succinate) (PPFPS) have been synthesized via a two‐step process involving polycondensation and azeotropic distillation. The kinetic parameters were obtained by fitting the experimental data from a batch polymerization reactor to three different kinetic models for polyesterification reactions. The activation energies of the all monomer systems were obtained by Arrhenius plots. Given the increasing availability of biomass‐derived monomers their use in renewable polyesters as substitutes for fossil fuel derived chemicals becomes a distinct possibility. The kinetic modeling of the uncatalyzed polyesterification reactions will enable further integrative process simulation of the studied bioderived polymers and provide a reference for future practical study or industrial applications of catalyzed polyesterification reactions and other bioderived monomer systems. © 2016 The Authors. Journal of Polymer Science Part A: Polymer Chemistry Published by Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016, 54, 2876–2887