Four different complexes of two base pairs, an adenine-thymine and a guanine-cytosine one, have been studied in order to understand the modifications induced by the staking interaction between the two base pairs on the hydrogen atoms transfers between the bases in either base pair. The inclusion of these two kinds of interactions allows us to clarify if some properties, as the mechanism of hydrogen transfer, is exclusively a local effect of a base pair or can be modified by a more long-range interaction between the base pairs. The results on these four complexes are compared with those of the monomeric systems, the A-T and G-C base pair, and with those of the A-T and G-C dimers. The specificity of each complex and of each hydrogen bond has been analyzed.