In our article [
B. Gu, Y. X. Fan, J. Wang, J. Chen, J. P. Ding, H. T. Wang, and B. Guo, Phys. Rev. A 73, 065803 (2006)
] we have presented the theory of open-aperture Gaussian-beam Z-scan, based on the Adomian decomposition method, which is available only for the saturable absorption caused by single-photon absorption transition. In the present article, using the same technique (Adomian decomposition method, as a common technique), we develop an open-aperture Z-scan theory for evaluating the property of the saturable absorption originating from two-photon absorption (2PA) transition, when a spatial Gaussian beam is used as the excitation source. We find analytic polynomial expressions of the Z-scan traces for a continuous wave laser or a temporal Gaussian pulsed laser. As the experimental evidence, we investigate the saturable 2PA behaviors caused by the interband two-photon transition in the direct-gap II–VI semiconductors CdS, CdSe, ZnSe, and ZnTe, under the excitation condition of a femtosecond laser with a 140 fs pulse duration, a 1 kHz low repetition rate, and a 1.6 eV photon energy.