Novel linear and crosslinked polymers from non-modified and modified tung oil are reported. These materials are based on the exploitation of the Diels–Alder reaction using, on the one hand, the dienic character of the three conjugated double bonds of tung oil and their susceptibility to react with a dienophile, and, on the other hand, the bulk reaction of furfuryl amine at the ester moieties of tung oil to produce three fatty acid furan amides, still bearing the three conjugated double bonds, and their linear polymerization with bismaleimides.