Generalized van Vleck perturbation theory (GVVPT2) for molecular electronic structures is applied to examine the azabenzene series: benzene, pyridine, pyrazine, symmetric triazine and symmetric tetrazine. The spectra of azabenzenes are complex with large numbers of excited states at low energies comprising n -> pi* and pi -> pi excited states and also doubly excited states of the n,n -> pi*,pi* type. The calculations are complicated due to strong correlation effects in the nitrogen lone-pair orbitals and the pi electrons: This study is the first to use GVVPT2 on conjugated systems. Comparison is made with experimental data and complete active space second-order perturbation theory, equation of motion coupled cluster and similarity transformed equation of motion coupled cluster theory data. Using polarized valence double split basis sets for benzene and pyrazine (cc-pVDZ) and pyridine (ANO-S) and polarized triple split basis sets (ANO-L) for triazine and tetrazine, the n -> pi* and pi -> pi* states are computed with an average error of 0.28 eV in comparison with available experimental data.