Density-functional theory (B3LYP functional) is used to investigate the ionization potentials and electron affinities of the DNA and RNA nucleotide bases. For the first time, anions lying lower in energy than the neutral species have been calculated for both thymine and uracil (i.e., positive adiabatic electron affinities). Additionally, the calculations show that anion formation leads to significant geometrical changes to the nucleobases. This is a very important finding as previous calculations have indicated that the anions are very similar in geometry to the neutral species and reported negative valence adiabatic electron affinities.