The current practice to validate flight control laws relies on applying linear analysis tools to assess the closed loop stability and performance characteristics about many trim conditions. Nonlinear simulations are used to provide further confidence in the linear analyses and also to uncover dynamic characteristics, e.g. limit cycles, which are not revealed by the linear analysis. This chapter reviews nonlinear analysis techniques which can be applied to systems described by polynomial dynamic equations. The proposed approach is to approximate the aircraft dynamics using polynomial models. Nonlinear analyses can then be solved using sum-of-squares optimization techniques. The applicability of these methods is demonstrated with nonlinear analyses of an F/A-18 aircraft and NASA's Generic Transport Model aircraft. These nonlinear analysis techniques can fill the gap between linear analysis and nonlinear simulations and hence used to provide additional confidence in the flight control law performance.