We present a detailed study on dissociative electron attachment (DEA) to isolated gas-phase cytosine (C) and thymine (T). The experimental setup used for these measurements is a crossed electron/neutral beam instrument combined with a quadrupole mass spectrometer. Electron attachment to these biomolecules leads to dissociation into various fragments without a hint of any measurable amount of stable C or T parent anions. The fragment anions with highest abundance are (C-H)(-) and (T-H)(-), respectively. Quantum chemical calculations were performed to calculate the electron affinities and binding energies of the different isomers of the (T-H) fragment. Besides (C-H)(-) and (T-H)(-), we observed five other fragment anions formed by DEA to cytosine and eight additional product anions were detected in the case of thymine. Ion efficiency curves were measured for all fragment anions in the electron energy range from about 0 to 14 eV. For mixtures of T or C with SF6 or CCl4 in the collision chamber, additional resonances close to 0 eV were observed, resulting from ion molecule reactions of SF6- or Cl- with the respective biomolecule.