The molecular vibrations of 1,4,5,8-tetraazanaphthalene (1458-TAN), 2,3,6,7-tetraazanaphthalene (2367-TAN) and pteridine are analyzed using a combination of infrared and Raman spectroscopy, ab initio calculations at the HF/6-31G* and MP2/6-31G* levels of theory, and B3LYP/4-31G and B3LYP/6-31G* density-functional calculations. New spectra are reported, and almost all of the ground-state normal modes have been identified for 1458-TAN and pteridine; the analysis for 2367-TAN is less complete. Calculated B3LYP/6-31G* vibrational frequencies provide the best correlation between theory and experiment for these compounds, but corresponding calculations using the smaller 4-31G basis are also satisfactory. The spectra of 1458-TAN and pteridine spectra exhibit a substantial number of Fermi resonances which complicate but do not prevent a detailed analysis.