In this study, we investigated the changes of the energetic, electron-topological, geometric, polar and charge parameters for the biologically important T·2AP*(w) ↔ T*·2AP(w) and G·2AP*(w) ↔ G*·2AP(w) tautomerisation reactions in detail via the double proton transfer (DPT) at each point of the intrinsic reaction coordinate (IRC) (mutagenic tautomers are marked by the asterisks). These tautomerisations of the wobble (w) T·2AP*(w) and G·2AP*(w) mispairs could produce the T* and G* enol tautomers, respectively, in view of the lifetimes of the terminal T*·2AP(w) and G*·2AP(w) base mismatches. These DPT reactions could be also considered as a preparatory stage before the wobble ↔ Watson–Crick tautomerisations involved in the origin of the point mutations induced by 2-aminopurine (2AP) (RSC Adv., 2016, 6, 108255–108264). Investigated reactions have been established to proceed via the asynchronous concerted mechanism of the DPT along the neighboring intermolecular H-bonds and could be characterized by the 9 key points, 2 of which (3^rd and 4^th) are accidentally degenerated. It was shown that the extrema of the reaction force function coincide with the key points 2 and 8.