Static third-order hyperpolarizabilities gamma 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 gamma values for H2NO, H2CO, (CH3)(2)NO and (CH3)(2)CO are examined. It is found that Moller-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 gamma for H2NO, H2CO and (CH3)(2)CO, while higher-order correlation effects at the CCSD(T) level are crucial for qualitative descriptions of gamma of (CH3)(2)NO.