Systems containing a base or a base pair and 25 water molecules, as well as a helical stack and 30 water molecules per base pair, have been simulated. Changes in the base hydration shell structure, after the bases have been included into the pair and then into the base pair stack, are discussed. Hydration shells of several configurations of the base pair stacks are discussed. Probabilities of formation of the hydrogen-bonded bridges of 1, 2 and 3 water molecules between hydrophilic centres have been estimated. The hydration shell structure was shown to depend on the nature of the base pair and on the stack configuration, while dependence of the global hydration shell characteristics on the stack configuration has been proved to be rather slight. The most typical structural elements of hydration shells, in the glycosidic (minor in B-like conformation) and non-glycosidic (major) grooves, for different configurations of AU and GC stacks, have been found and discussed. The number of hydrogen bonds between water molecules and bases per water molecule was shown to change upon transformation of the stack from A to B configuration. This result is discussed in connection with the reasons for B to A conformational transition and the concept of "water economy". Hydration shell patterns of NH2-groups of AU and GC helical stacks differ significantly.