Heats of formation, entropies, Gibbs free energies, relative tautomerisation energies, tautomeric equilibrium constants, relative proton affinities, dipole moments, and ionisation potentials for the fourteen possible tautomers of xanthine have been studied using semiempirical AM1 and PM3 quantum-chemical calculations at the SCF level in the gas and aqueous phases, with full geometry optimisation. The COSMO solvation model was employed for aqueous solution calculations. The calculations show that the two diketo tautomers X1,3,7 and X1,3,9 are the predominant species at room temperature in the gas and aqueous phase. But, the first more stable tautomer is the dioxo-7H tautomer, X1,3,7. Comparison with available experimental data provides support for quality of results derived from theoretical computations. The entropy effect on the Gibbs free energy of the xanthine is very small and there is little significance for the tautomeric equilibria of the base. The enthalpic term is dominant also in the determination of the equilibrium constant.