Adaptive control algorithms have the potential to improve performance and reliability of flight control systems. The application of adaptive control on commercial or military aircraft will require validation and verification of the robustness of these algorithms to modeling errors and uncertainties. Currently, there is a lack of tools to rigorously analyze the performance and robustness of adaptive systems. This paper addresses the development of nonlinear robustness analysis tools for such systems. First a model-reference adaptive controller is derived for an aircraft short-period model. It is noted that the adaptive control law is a polynomial system. Polynomial optimization tools are applied to the closed loop model to assess the performance and robustness of the adaptive control law. Two sets of results are presented in this paper. First, input-output gains are calculated in the presence of model uncertainty to evaluate the performance of the adaptive law. Second, time delay margins are computed for varying parameters in the adaptive law, as well as in the presence of model uncertainty.