Gas-phase metal affinities of DNA and RNA bases for the Na+ and K+ ions were determined at density functional level employing the hybrid B3LYP exchange correlation potential in connection with the 6-311+G(2df,2p) basis set. All the molecular complexes, obtained by the interaction between several low-lying tautomers of nucleic acid bases and the alkali ions on the different binding sites, were considered. Structural features of the sodium and potassium complexes were found to be similar except in some uracil and thymine compounds in which the tendency of potassium ion toward monocoordination appeared evident. B3LYP bond energies for both metal ions were in agreement with the available experimental results in the cases of uracil and thymine for which the most stable complex was obtained starting from the most stable tautomer of the free nucleic acid base. For adenine, although the interaction of the ions with the most stable free tautomer generated the least stable molecular complex, the best agreement with experiment was found in just this case. For the remaining cytosine and guanine bases, our calculations indicated that the metal ion affinity value closest to experiment should be determined taking into account the role played by the different tautomers of the free bases with similar energy and all the possible complexes obtained by them.