Enthalpies of formation, Delta H-f(298.15 K), of 2-methyl-, 3-methyl-, 2-ethyl-, 2-vinyl-, 2,3-dimethyl-, 2,4-dimethyl-, and 3,4-dimethylfurans are computed with three compound quantum chemical methods, CBS-QB3, CBS-APNO, and G3, via a number of isodesmic reactions. We show that previously experimentally determined enthalpies of formation of furan itself, 2,5-dimethyl-, 2-tert-butyl-, and 2,5-di-tert-butylfurans are self-consistent but that for 2-vinylfuran is most probably in error. The formation enthalpies of over 20 furyl and furfuryl radicals have also been determined and consequently the bond dissociation energies of a number of C-H, C-CH3, C-F, C-Cl, and C-OH bonds. The ring-carbon-H bonds in alkylfurans are much stronger than previously thought and are among the strongest ever C-H bonds recorded exceeding 500 kJ mol(-1). The relative thermodynamic instability of the various furyl radicals means that bonds to methyl, fluorine, and chlorine are also unusually strong. This is as a consequence of the inability of the radical to effectively delocalize the unpaired electron and the geometrical inflexibility of the five-membered heterocyclic ring. By way of contrast the furfuryl radicals are more stable than similar benzyl radicals which results in weaker side-chain C-H bonds than the corresponding toluene derivatives (although stronger than the corresponding cyclopentadiene analogue). These results have implications for the construction of detailed chemical kinetic models to account for the thermal decomposition and oxidation of alkylfurans either in engines or in the atmosphere.