The IPPP-CLOPPA method is applied to investigate the influence of a methyl group on the energy of the hydrogen bonds and the potential energy curve of the bridge protons in model compounds, which mimic the methylated and unmethylated cytosine-guanine base pairs. On the same grounds, this influence on the polarizability of the intermolecular hydrogen bonds of these compounds is also addressed, in order to determine whether this linear response property provides a significant proof of the electronic mechanisms that affect the stabilization of the hydrogen bonds. Results obtained show that the methyl electronic system delocalizes on the hydrogen bond region, and changes of these intermolecular hydrogen bonds are due to this effect of delocalization.