This paper investigates the effects of nonlinearities on the dynamics of flat panels in supersonic flow and presents new bifurcation results for a fairly general nonlinear aeroelastic system. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools. The first part of this paper deals with modeling unsteady aerodynamic forces and moments acting on flat panels undergoing arbitrary motion in supersonic flow. This modeling also considers the structural nonlinearities inherent in panels. While deriving the equations of motion, many in the past have neglected some nonlinear aerodynamic terms as insignificant from the modeling point of view. However, inclusion of these terms in the analysis may completely change the bifurcation behavior. In aeroelastic systems it is the nonlinear dissipative terms that can change the behavior, and it is essential to carefully model these terms in the physical problems. In the absence of dissipative terms the nonlinear system is reversible, which provides the governing equations with near integrable structure. Thus certain analytical methods are used to study the bifurcation behavior of the system near critical points. For general nonlinear fiat panels in supersonic flow, we present these effects as various bifurcation results due to symmetry-breaking imperfections. For aeroelastic systems, the reversible symmetry is broken by the addition of unsteady aerodynamic terms.