The effects of annealing and Al dopant on the nonlinear absorption characteristics of amorphous ZnO thin films were studied experimentally and theoretically. The structural patterns of AZO thin films grown at various growth temperatures (80 degrees C, 90 degrees C, 100 degrees C) and Al doping ratios (%5, %10, %20) were determined by using x-ray diffraction. The results revealed that the crystallinity increased with increasing growth temperature and Al doping ratio. The optical band gap decreased from 3.91 to 3.78 eV and the transmittance of AZO thin films decreased from 90% to 55% with increasing Al molar ratio. The open aperture Gaussian beam Z-scan measurements indicated that all studied films exhibited nonlinear absorption behavior due to the defect states inside energy bandgap. The nonlinear absorption coefficients increased from 1.34 x 10(-4) to 6.12 x 10(-4) cm/W for 4 ns pulse duration with increasing of doping concentration. The experimental curves were fitted to the theory of open aperture Gaussian beam Z-scan based on the Adomian decomposition method to obtain nonlinear absorption coefficients along with saturation intensity thresholds. In order to investigate the effect of free carrier absorption, the OA Z-scan experiments were also performed for 65 ps pulse duration. The nonlinear absorption coefficients were found to be 0.58 x 10(-4), 1.81 x 10(-4) and 3.29 x 10(-4) cm/W for 65 ps pulse duration. For nanosecond pulse durations, the obtained nonlinear absorption coefficient values of thin films are bigger than the values of picosecond pulse durations due to the greater contribution of free carrier absorption. Increasing annealing temperature from 100 degrees C to 400 degrees C leads to decreasing nonlinear absorption coefficients owing to decreasing localized defect states.