The second hyperpolarizabilities of bisimidazole- and bistriazole-benzene compounds have been calculated at different levels of approximation to unravel the effects of diradical character as well as of charge and spin multiplicity. The largest second hyperpolarizabilities are associated with intermediate diradical character, provided positive charging does not compensate for this effect. For the neutral diradical bisimidazole compound, the sin-let diradical species possesses a second hyperpolarizability two to three times larger than the corresponding triplet, demonstrating the possibility of spin state control of the third-order NLO responses for diradical species.