Summary. Dynamic models of geometrical nonlinear deformations of functionally graded carbon nanotubes reinforced composite thin-walled structures are obtained. Reddy higher- order shear deformation theory is used to derive this model. The nonlinear system of high dimension ordinary differential equations, which describes the structure nonlinear vibrations, is obtained using the assumed-mode method. The linear piston theory is used to describe the supersonic flow. The losses of the cylindrical shell dynamic stability owing to the Hopf bifurcations are analyzed. The self- sustained vibrations, which describe the circumferential traveling waves flutter, occur due to this bifurcation. The harmonic balance method is applied to analyze these self-sustained vibrations. The properties of the circumferential traveling waves are analyzed. The dynamic instability of conical- cylindrical thin-walled nanocomposite structure is treated.