We report the reversible reduction potentials of the purines and pyrimidines of DNA and RNA. These were determined in dimethylsulfoxide using cyclic voltammetry. The absolute electron affinities have been determined from these reduction potentials by calibration with the absolute electron affinities for acridine and anthracene measured in the gas phase. These are the first experimentally determined values of the electron affinities of these purines and pyrimidines and are: Guanine = 1.51 eV, Adenine = 0.95 eV, Uracil = 0.80 eV, Thymine = 0.79 eV and Cytosine = 0.56 eV.