Abstract: On the basis of the dispersion curves of the Lamb waves propagating in the composite solid layers and the approach of modal expansion analysis for guided wave excitation, the physical process of generation of the primary Lamb wave time-domain pulse and the corresponding second-harmonic time-domain pulse has been discussed. Considering the measurement function of the Ritec-SNAP system, the physical meaning of integral of the envelope of second-harmonic time-domain pulse has been detailedly analyzed. This integral can describe the efficiency of second-harmonic generation accompanying the primary Lamb wave time-domain pulse, as well as the dispersion degree between the primary and the double frequency Lamb waves. Within the specific frequency range where the phase velocities of the primary Lamb waves exactly or approximately equal that of the double frequency Lamb waves, the second-harmonic signals without overlapping of multi-modes of the double frequency Lamb waves have been clearly observed. This phenomenon shows that the strong nonlinearity does occur in the primary Lamb wave propagation process. For the three different adhesive joints, the experiment results show that both the stress wave factors of the nonlinear Lamb waves firstly introduced in the present paper, and the frequency values corresponding to the peaks of the amplitude-frequency curves of the second-harmonic signals can effectively characterize the properties of the adhesive joints.