A theoretical model to analyze the nonlinear circumferential guided wave (CGW) propagation in a composite circular tube (CCT) is established.The response features of nonlinear CGWs to early damage [denoted by variations in third-order elastic constants (TOECs)] in an inner layer of CCT are investigated.On the basis of the modal expansion approach,the second-harmonic field of primary CGW propagation can be assumed to be a linear sum of a series of double-frequency CGW (DFCGW) modes.The quantitative relationship of DFCGW mode versus the relative changes in the inner layer TOECs is then investigated.It is found that the changes in the inner layer TOECs of CCT will obviously affect the driving source of DFCGW mode and its modal expansion coefficient,which is intrinsically able to influence the efficiency of cumulative second-harmonic generation (SHG) by primary CGW propagation.Theoretical analyses and numerical simulations demonstrate that the second harmonic of primary CGW is monotonic and very sensitive to the changes in the inner layer TOECs of CCT,while the linear properties of primary CGW propagation almost remain unchanged.Our results provide a potential application for accurately characterizing the level of early damage in the inner layer of CCT through the efficiency of cumulative SHG by primary CGW propagation.