The ultrasonic NDE technique to characterize the ultrasonic nonlinear response of the cyclically load 7075-T6 aluminum is described in this thesis. In order to estimate the nonlinear relation of the ultrasonic waves due to material fatigue damage or degradation, the spectral analysis techniques such as the power spectrum, bispectrum, and bicoherence spectrum are applied. The ultrasonic nonlinearity parameters by Cantrell and Jhang are introduced and presented as a function of the material fatigue growth, the number of fatigue cycles. This thesis presents the effectiveness of the bispectral analysis for evaluating the nonlinear aspects of the ultrasonic wave propagation. The results show that the nonlinearity parameters by Cantrell and Jhang are responsive to the output amplitude of the received signal and vary for the various materials, and independent of the input frequency and the ultrasonic wave propagation distance. By using the bispectral analysis tools, particularly the bicoherence spectrum, the increase of the coupling levels between the fundamental, its harmonic, and subharmonic frequency components is presented as the number of fatigue cycles is increased. This thesis suggests that the application of the bicoherence spectrum based on the nonlinear wave coupling relations be more effective for estimating the level of the material fatigue life. / Master of Science