By using the Z-scan method we studied the third-order nonlinear optical parameters of several aminobenziliden-1, 3-indandione (ABI) derivatives that have previously been shown to own second-order nonlinear optical properties. Measurements were carried out using two 1064 nm Nd: YAG lasers with picosecond (ps) and nanosecond (ns) pulse widths, respectively. When ns laser was employed in the Z-scan setup, a strong thermal lensing took place resulting in severe overestimation of optical Kerr coefficients. Due to this reason the ps laser was employed to evaluate correct magnitude of Kerr effect. For investigated organic molecules, experimental results show that two-photon absorption at 1064 nm is in correlation with molar extinction coefficient at 532 nm. Here we demonstrate good linear correlation between values of second-order molecular hyperpolarizability determined experimentally and those obtained by quantum chemical modeling.