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Two new organic dye samples J and L with a large two-photon absorption (TPA) cross section have been reported.The linear absorption spectra show that there is no linear absorption at the wavelength from 650 to 1200 nm.The molecular TPA cross section was measured to be as high as 2.59×10-47 cm4.s and 2.98×10-47 cm4.s at 1064 nm for samples J and L, respectively. The input-output curves indicate that there is a clear optical power limiting behaviour when the input intensity is higher than 0.4 GW/cm2. Furthermore, the basic theory of the TPA process has been discussed.