Limit cycle oscillations (LCOs) as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of an airfoil with control surface in an incompressible potential flow are presented in the time domain. The harmonic balance (HB) method is utilized to calculate the LCO frequency and amplitude for the airfoil. Also the semi-analytical method has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. The system response is determined by numerically integrating the governing equations using a standard Runge-Kutta algorithm and the obtained results are compared with the HB method. Also the results by the third order HB (HB3) method for control surface are consistent with the other numerical solution. Finally, by combining the numerical and the HB methods, types of bifurcation, be it supercritical, subcritical, or divergent flutter area are identified.