Push-pull imines with strong electron donor group(s) display exceptional basicity in the gas phase. Most of them do not exhibit prototropic tautomerism, and gas-phase acid-base equilibria have been already well described and reviewed. Some questions remain for tautomeric systems, particularly for their uncommon forms. As shown by quantum-chemical calculations, some often-neglected tautomers display higher basicity than the thermodynamically favored forms. However, their participation in tautomeric mixtures being in equilibrium is negligible, and their basicity can be impossible to measure in the gas phase by the equilibrium method. During this work, we examined the gas-phase proton basicity for some acyclic and cyclic push-pull organic bases containing the tautomeric amidine or guanidine group. By quantum-chemical calculations, we confirmed the existence of very low amounts of rare tautomeric forms, in particular, those bearing a methylidene (=CH