Methoxyfurans are known components in a number of biofuel synthesis processes and their thermochemical properties are important to the stability, reaction paths, and chemical kinetics of these species. Enthalpies (DeltaH degrees (f298)), entropies (S degrees (298)), and heat capacities (C(p)(T)) are reported for 2-methoxyfuran and 3-methoxyfuran, cyclic ethers with possible biofuel implications, and their radicals corresponding to loss of hydrogen atoms. Standard enthalpies of formation are calculated at the B3LYP/6-31G(d,p), B3LYP/6-311G(2d,2p), CBS-QB3, G3MP2B3, and G3 levels of theory with isodesmic reactions to minimize calculation errors. Structures, vibrational frequencies, and internal rotor potentials are calculated at the B3LYP/6-31G(d,p) density functional level and are used to determine the entropy and heat capacities. The recommended ideal gas phase enthalpy of formation, from the average of the CBS-QB3 and G3MP2B3 levels of theory, for 2-methoxyfuran is -45.0 kcal mol(-1) and for 3-methoxyfuran is -41.1 kcal mol(-1). Bond dissociation energies are also calculated. The C-H bonds of the furan ring are approximately 120 kcal mol(-1), which is consistent with recent data on several alkylfurans; they are significantly stronger than non-aromatic, stable heterocyclic structures. The bond energy decreases to 98 kcal mol(-1) for the methoxy-methyl C-H bonds making this methyl site a favorable abstraction target and an important site for initial decomposition paths during combustion. Group additivity for furan is discussed and groups for furan and methoxyfuran carbon radicals are derived.