A computational scheme recently proposed for ab initio calculations of electronic spectra of molecular systems is applied to the azabenzene molecules. The method has the aim of being accurate to better than 0.5 eV for excitation energies and is expected to provide structural and physical data for the excited states with good reliability. Applications are possible to molecules with up to about 20 atoms with good quality basis sets. The scheme is based on the complete active space SCF method (referred to as CASSCF), which gives a proper description of the major features in the electronic structure of the excited state, independent of its complexity, accounts for all near degeneracy effects, and includes full orbital relaxation. The remaining dynamic electron correlation effects are in a subsequent step added using second-order perturbation theory with the CASSCF wave function as the reference state. The approach is tested here in a calculation of the valence excited singlet states of the azabenzenes pyridine, pyrazine, pyrimidine, pyridazine, and s-triazine, using a (C,N,4s3p2d/H,3s2p) atomic natural orbital (ANO) basis. The pi-pi* excitation energies of the azabenzenes are computed with an average error of 0.14 eV. With the exception of one case, the n-pi* excitation energies are computed with an accuracy of 0.32 eV or better in all cases where a comparison with reliable experimental data can be made.