Static third-order hyperpolarizabilities γ of some open-shell systems including nitroxide radical sites are investigated by ab initio MO method. The dependences of basis sets and electron correlation effects on γ values for H 2 NO, H 2 CO, (CH 3 ) 2 NO and (CH 3 ) 2 CO are examined. It is found that Møller-Plesset second-order perturbation (MP2) method using the extended basis set with diffuse p and d functions can provide reasonable descriptions of relative tendencies of γ for H 2 NO, H 2 CO and (CH 3 ) 2 CO, while higher-order correlation effects at the CCSD(T) level are crucial for qualitative descriptions of γ of (CH 3 ) 2 NO.