A theoretical investigation of the flutter and postflutter of infinitely long thin-walled circular cylindrical panels in a supersonic/hypersonic flowfield is presented. In this context, third-order piston theory and shockwave aerodynamics are used in conjunction with the geometrically nonlinear shell theory to obtain the pertinent aeroelastic governing equations. The effects of in-plane edge restraints and small initial geometric imperfections are also considered in the model. The objective is twofold: 1) to analyze the implications of nonlinear unsteady aerodynamics and structural nonlinearities on the character of the flutter instability boundary and 2) to outline the effects played, in the same respect, by a number of important geometrical, physical, and aerodynamic parameters characterizing the aeroelastic system. As a by-product of this analysis, the implications of these parameters on the linearized flutter instability behavior of the system are captured and emphasized. The behavior of the aeroelastic system in the vicinity of the flutter boundary is studied via the use of an encompassing methodology based on the Lyapunov first quantity. Numerical illustrations, supplying pertinent information on the implications of geometric and aerodynamic nonlinearities, as well as of other effects, such as curvature and thickness ratios, on the flutter instability and on the character of the flutter boundary are examined, and pertinent conclusions are outlined.