Electronic structures of cationic states (2(+) and 3(+)) of 1,3,5-triazine (TA) and its derivative hexahydro-1,3,5-triazine (HTA) are discussed with the ab initio molecular-orbital method including the electron correlation by the Moller-Plesset (MP) perturbation treatment. It has been found that sigma-radical spins give rise to low- and high-spin states in both TA and HTA. The present calculation at the MP3 level predicts that the spin multiplicity of the ground state of dicationic TA is a high-spin state triplet while that of tricationic TA is a doublet. On the other hand, low- and high-spin states are almost degenerate in both the dicationic and the tricationic states of HTA. This result will hopefully lead to the discovery of a high-spin state occurring from sigma-radical spins in molecules containing heteroatoms as the spin accommodators.