The excited states of dinucleoside phosphates (dGpdG, dApdA, dApdT, TpdA, and dGpdT) in their cationic radical states were studied with time-dependent density functional theory (TD-DFT). The ground-state geometries of all the dinucleoside phosphate cation radicals considered, in their base stacked conformation, were optimized with the B3LYP/6-31G(d) method. Further, to take into account the effect of the aqueous environment surrounding he dinucleoside phosphates, the polarized continuum model (PCM) was considered and the excitation energies were computed by using the TD-B3LYP/6-31G(d) method. From this study, we find that the first transition in all the dinucleoside molecules involves hole transfer from base to base. dG(center dot+)-pdG and dApdA(center dot+) were found to have substantially lower first transition energies than others with two diffent DNA bases. Higher energy transitions involve base to sugar as well as base to base hole transfer. The calculated TD-B3LYP/6-31G(d) transition energies are in good agreement with previous calculations with CASSCF/ CAS-PT2 level of theory. This TD-DFT work supports the experimental findings that sugar radicals formed upon photoexcitation of G(center dot+) in gamma-irradiated DNA and suggests an explanation for the wavelength dependence found.