The nonlinear optical absorption of InSe, GaSe and GaxIn1-xSe amorphous films with varying thickness and doping has been studied by open-aperture Z-scan experiment with 4 ns and 65 ps pulse durations at 1064 nm wavelength and femtosecond pump-probe spectroscopy. Our results show that the dopant and film thickness (from 20 nm to 104 nm) results in switching from saturable absorption to nonlinear absorption for equal input intensities. This behaviour is attributed to increasing localized defect states with increasing film thickness and/or dopant. The experimental curves were fitted to the theory of open aperture Gaussian beam Z-scan based on the Adomian decomposition method incorporating one photon, two photon, and free carrier absorptions and their saturations. By preparing very thin amorphous thin films the saturation threshold has been lowered significantly.