We report Z-scan experiments performed on titanium bis-phthalocyanine (TiPc2)/toluene solutions as a function of the molar concentration. The TiPc2 cubic molecular hyperpolarizability, gamma(hyper), has been found to be (-70 +/- 30) x 10(-32) esu at 800 nm, approximately 10(5) times larger in magnitude than the third-order susceptibility of the standard reference molecule CS2. Given the non-proximity of the laser wavelength to the main electronic bands of this molecule and its unusual molecular structure, we compare our results with previous measurements in other phthalocyanine systems. We also discuss the most probable factors influencing the non-linear optical response of our molecular system. The results indicate that the large non-linear optical response observed for TiPc2 cannot be explained using optical-pumping, resonance-enhancement or electronic delocalization arguments. (C) 2002 Published by Elsevier Science B.V.