The UV electronic transition energies and their oscillator strengths for two stacked dimers having B-DNA geometries and consisting of 5-bromouracil ((Br)U) and a purine base were studied at the MS-CASPT2/6-311G(d) level with an active space of 12 orbitals and 12 electrons. The calculated energy of the first vertical (π,π*) transitions for the studied dimers remain in fair agreement with the maxima in the difference spectra measured for duplexes with the 5'-A(Br)U-3' or 5'-G(Br)U-3' sequences. Our MS-CASPT2 results show that the charge transfer (CT) states in which an electron is transferred from A/G to (Br)U are located at much higher energies than the first (π,π*) transitions, which involve local excitation (LE) of (Br)U. Moreover, CT transitions are characterized by small oscillator strengths, which implies that they could not be excited directly. The results of the current studies suggest that the formation of the reactive uracil-5-yl radical in DNA is preceded by the formation of the highly oxidative LE state of (Br)U, which is followed by electron transfer, presumably from guanine.