Minimum energy conformations of Gua and/or Cyt deoxydinucleoside monophosphate anions, dDMPs, and structure of their Na⁺ complexes were obtained by DFT/PW91/DZVP method using geometries of B DNA as starting points. The predicted conformations show both sugar ring puckerings and sugar-phosphate torsions resembling those of B-family DNA duplexes. All the sugar rings of the Na⁺ complexes pertain to C2?-endo type, while sugar moieties of the anions exhibit C1?-exo and C3?-exo puckerings as well. Nearly all the geometry parameters for Na⁺ complexes fall into the experimentally observed regions while those of dDMP anions vary in wider limits. The heterocyclic rings of the bases retain a nearly planar configuration (all the endo cyclic torsions being within 5°) while amino groups become essentially non-planar and their configurations depend on nucleoside sequence. Hydrogen bond is formed between Gua and Cyt when the deoxydinucleoside contains both bases. Average dihedral angles between the base rings vary from 4.9 to 30.8 degrees, the largest angle observed for dGpdG anion. Interestingly, some sugar-phosphate torsion angles of this anion differ substantially from the corresponding angles of the other calculated structures. The obtained conformations show various patterns of mutual arrangement of bases, from rather extensive ring-on-ring overlap to practically non-overlapping cases. Nearly parallel arrangement of bases takes place in all conformations despite of the extent of their overlap. This suggests the major sugar-phosphate contribution to the stability of B-like single-stranded conformations whereas the base-base interactions play a minor role in the formation of these spatial structures. The dDMPs with the 5? end G and their Na⁺ complexes demonstrate extensive stacking overlap of the base rings, while in the dDMPs with the 5? end C and their Na⁺ complexes the base-ring stacking is practically absent. This observation correlates well with Pur-Pur, Pur-Pyr, and Pyr-Pur arrangement in crystals of B-DNA duplexes. The reference calculations employing 6-31G(d,p) basis set and other functionals, including B3LYP, performed on selected structures, suggest that the main conclusions of this work do not depend on the choice of the particular DFT functional.