The magnetic shielding constant of the different 13C and 1H nuclei of a deoxyribose are calculated for the C2' endo and C3' endo puckerings of the furanose ring as a function of the conformation about the C4'C5' bond. For the carbons the calculated variations are of several ppm, the C3' endo puckering corresponding in most cases to a larger shielding than the C2' endo one. For the protons the calculated variations of chemical shifts are all smaller than 1.3 ppm, that is of the order of magnitude of the variation of the geometrical shielding produced on these protons by the other units of a DNA double helix, with a change of the overall structure of the helix. The computations carried out on the deoxyribose-3' and 5' phosphates for several conformations of the phosphate group tend to show that the changes of conformation of the charged group of atoms produce chemical shift variations smaller than the two conformational parameters of the deoxyribose itself. The calculations carried out for a ribose do give the general features of the differences between the carbon and proton spectra of deoxynucleosides and nucleosides. The comparison of the measured and calculated phosphorylation shifts tend to show that the counterion contributes significantly, for some nuclei of the deoxyribose, to the shifts measured. The calculated magnitude of this polarization effect on carbon shifts suggests a tentative qualitative interpretation of carbon spectra of the ribose part of DNA double helices.