The transformation of the DNA base pairs from the Watson-Crick (WC) structures to its tautomers having imino-enol form can be achieved via two types of hydrogen atom transfer processes: (i) concerted, and/or (ii) stepwise (step by step). Here, we have studied and compared these two mechanisms in the cytosine-guanine (C-G) system. In the first mechanism there is the concerted movement of two hydrogen atoms along two of the three H-bridges that bond the bases, one from the cytosine to guanine and the other in the opposite direction. This movement must be coupled to an electronic reorganization, with some bond orders that pass from single to double and vice versa, in order to preserve the neutrality of these new structures. In the stepwise mechanism the movement of the hydrogen atoms and the electronic reorganization are not concerted, and it implicates the movement of a hydrogen atom at a time with the identification of two or more steps in this reaction. There are two possible neutral imino-enol structures in the C-G system, and both have been considered here. The principal result from this paper is that a different behavior is observed if the hydrogen transfer begins with a H of the guanine or of the cytosine and that a concerted (synchronic in the N-N and asynchronic in the N-O) double-hydrogen transfer can be activated only when the first H atom to move is that of the guanine, in particular. This is different from the A-T system(1) studied previously where the movement in a N-N bridge produces a zwitterionic structure and that in the N-O the concerted double-hydrogen transfer. In both cases a general conclusion can be given: the concerted double-hydrogen process begins with a hydrogen atom of a purinic base.