The complete curing of furfuryl alcohol (FA), was studied by chemorheological analysis and model-free kinetics under isothermal and non-isothermal modes. Polymerization of FA under acidic catalysis involves complex reactions, with several steps (such as condensations and Diels-Alder cycloadditions). To account for the polymerization complexity, kinetic analysis of DSC data was performed with a model-free isoconversional method. The obtained E(alpha)-dependencies were closely-correlated with the variation of complex viscosity during curing. Linear condensations are predominant during the early curing stage and are followed by two distinct stages of branching cycloadditions. Gelation and vitrification, identified by rheometric measurements, were associated with a decrease of the overall reaction rate that becomes controlled by diffusion of small oligomers. Before vitrification, the rate of crosslinking is limited by the mobility of longer polymer chains and diffusion encounters a large energy barrier due to the cooperative nature of the motions, leading to higher E(alpha) values.