The excited states of dinucleoside phosphates (dGpdG, dApdA, dApdT, TpdA and dGpdT) in their cationic radical states were studied using 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 using B3LYP/6-31G(d) method. Further, to take into account the effect of the aqueous environment surrounding the dinucleoside phosphates, the polarized continuum model (PCM) was considered and the excitation energies were computed using the TD-B3LYP/6-31G(d) method. From this study, we found that the first transition, in all the dinucleoside molecules involves hole transfer from base to base. DG •+ pdG and dApdA •+ 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 using CASSCF/CAS-PT2 level of theory. This TD-DFT work supports the experimental findings that sugar radicals formed upon photo-excitation of G •+ in γ-irradiated DNA and suggests an explanation for the wavelength dependence found.