Ab initio scattering calculations for low-energy electron collisions with gas-phase DNA pyrimidine bases (cytosine and thymine) are performed using the R-matrix method. The low-lying resonant states of the anions, formed due to electron capture by the bases, are identified using different levels of theory, including static exchange, static exchange plus polarization, and close-coupling approximations. For both the bases, all of our scattering models find three shape resonances of 2A″ (π) symmetry lying below 10 eV, in accordance with other calculations and experimental observations. In addition to these, a fourth 2A″ resonance is found in all models for thymine and in our best model, i.e. the uncontracted close-coupling approximation, for cytosine. This model places the fourth 2A″ resonance in both systems in the 6–7 eV range. No evidence is found for the presence of low-lying Feshbach resonances in either system. Integral cross sections for electronically elastic and inelastic collisions are also presented.