Substituted biguanides are known for their biological effect, and a few of them are used as drugs, the most prominent example being metformin (1,1-dimethylbiguanide, IUPAC name: N,N-dimethylimidodicarbonimidic diamide). Because of the presence of hydrogen atoms at the amino groups, biguanides exhibit a multiple tautomerism. This aspect of their structures was examined in detail for unsubstituted biguanide and metformin in the gas phase. At the density functional theory (DFT) level {essentially B3LYP/6-311+G(d,p)}, the most stable structures correspond to the conjugated, push-pull, system (NR2)(NH2)C═N-C(═NH)NH2 (R = H, CH3), further stabilized by an internal hydrogen bond. The structural and energetic aspects of protonation and lithium cation adduct formation of biguanide and metformin was examined at the same level of theory. The gas-phase protonation energetics reveal that the more stable tautomer is protonated at the terminal imino C═NH site, still with an internal hydrogen bond maintaining the structure of the neutral system. The calculated proton affinity and gas-phase basicity of the two molecules reach the domain of superbasicity. By contrast, the lithium cation prefers to bind the less stable, not fully conjugated, tautomer (NR2)C(═NH)-NH-C(═NH)NH2 of biguanides, in which the two C═NH groups are separated by NH. This less stable form of biguanides binds Li+ as a bidentate ligand, in agreement with what was reported in the literature for other metal cations in the solid phase. The quantitative assessment of resonance in biguanide, in metformin and in their protonated forms, using the HOMED and HOMA indices, reveals an increase in electron delocalization upon protonation. On the contrary, the most stable lithium cation adducts are less conjugated than the stable neutral biguanides, because the metal cation is better coordinated by the not-fully conjugated bidentate tautomer.