Adaptive control algorithms have the potential to improve performance and reliability in flight control systems. Implementation of adaptive control on commercial and military aircraft requires validation and verification of the control system's robustness to modeling error and uncertainty. Currently, there is a lack of tools available to rigorously analyze the robustness of adaptive systems due to their inherently nonlinear dynamics. This thesis addresses the use of nonlinear robustness analysis for adaptive flight control systems. First, a model reference adaptive controller is derived for an aircraft short period model. It is noted that the controller is governed by polynomial dynamics. Polynomial optimization tools are then applied to the closed-loop model to assess its robustness to time delays. Time delay margins are computed for various tuning of design parameters in the adaptive law, as well as in the presence of model uncertainty.