The Cremer-Pople ring puckering analysis and the Konkoli-Cremer local mode analysis supported by the topological analysis of the electron density were applied for the first comprehensive analysis of the interplay between deoxyribose ring puckering and intramolecular H-bonding in 2'-deoxycytidine, 2'-deoxyadenosine, 2'-deoxythymidine, and 2'-deoxyguanosine. We mapped for each deoxyribonucleoside the complete conformational energy surface and the corresponding pseudorotation path. We found only incomplete pseudorotation cycles, caused by ring inversion, which we coined as pseudolibration paths. On each pseudolibration path a global and a local minimum separated by a transition state were identified. The investigation of H-bond free deoxyribonucleoside analogs revealed that removal of the H-bond does not restore the full conformational flexibility of the sugar ring. Our work showed that ring puckering predominantly determines the conformational energy; the larger the puckering amplitude, the lower the conformational energy. In contrast no direct correlation between conformational energy and H-bond strength was found. The longest and weakest H-bonds are located in the local minimum region, whereas the shortest and strongest H-bonds are located outside the global and local minimum regions at the turning points of the pseudolibration paths, i.e., H-bonding determines the shape and length of the pseudolibration paths. In addition to the H-bond strength, we evaluated the covalent/electrostatic character of the H-bonds applying the Cremer-Kraka criterion of covalent bonding. H-bonding in the puric bases has a more covalent character whereas in the pyrimidic bases the H-bond character is more electrostatic. We investigated how the mutual orientation of the CH2OH group and the base influences H-bond formation via two geometrical parameters describing the rotation of the substituents perpendicular to the sugar ring and their tilting relative to the ring center. According to our results, rotation is more important for H-bond formation. In addition we assessed the influence of the H-bond acceptor, the lone pair (N, respectively O), via the delocalization energy. We found larger delocalization energies corresponding to stronger H-bonds for the puric bases. The global minimum conformation of 2'-deoxyguanosine has the strongest H-bond of all conformers investigated in this work with a bond strength of 0.436 which is even stronger than the H-bond in the water dimer (0.360). The application of our new analysis to DNA deoxyribonucleotides and to unnatural base pairs, which have recently drawn a lot of attention, is in progress.