The involvement of three-state conical intersections in the photophysics and radiationless decay processes of the nucleobases has been investigated using multireference configuration interaction methods. Three-state conical intersections have been located for the pyrimidine base, uracil, and the purine base, adenine. In uracil, a three-state degeneracy between the S-0, S-1, and S-2 states has been located at 6.2 eV above the ground-state minimum energy. This energy is 0.4 eV higher than vertical excitation to S and at least 1.3 eV higher than the two-state conical intersections found previously. In adenine, two different three-state degeneracies between the S-1, S-2, and S-3 states have been located at energies close to the vertical excitation energies. The energetics of these three-state conical intersections suggest they can play a role in a radiationless decay pathway present in adenine. The existence of two different seams of three-state conical intersections indicates that these features are common and complicate the potential energy surfaces of adenine and possibly many other aromatic molecules.