The Hilbert-Huang Transform is used to analyze the nonlinear aeroelastic response of a 2D 3DOF aeroelastic airfoil system with control surface freeplay under transonic flow conditions. Both static aerodynamic condition and dynamic aerodynamic condition, that is for accelerating freestream speed, are considered using a linearized aerodynamic model. The main aim of this paper is to provide physical insights as to the observed transition between periodic and aperiodic behavior, and the presence of a stable periodic region well below the region characterized by stable limit cycles. Physical insights towards this transition are presented by showing that multiple internal resonances exist. It is shown that the abrupt transition from aperiodic / chaotic to periodic behavior is a result of multiple internal resonances between linear and nonlinear modes. Initially a 2:1 IR between linear modes leads to a shift in the frequency composition and dynamic behavior of the system, then immediately a secondary 2:1 IR occurs between of linear and nonlinear modes which drives a stable periodic region.