While new actuation technologies promise to revolutionize modern control systems applications, effective compensation of new actuators is crucial for realizing such revolutions. One type of such actuators are the synthetic jet actuators which are being currently studied for a next generation of aircraft control systems. In this dissertation, an adaptive feedback control system is designed and analyzed for flight control of linear and nonlinear aircraft models using synthetic jet actuators. The novel features of this work are a new characterization of synthetic jet actuator nonlinearities over a wide range of angles of attack, a new adaptive compensation scheme for such nonlinearities, and a new systematic framework for feedback control of aircraft dynamics with synthetic jet actuators. Characteristics of synthetic jet actuators are nonlinear, and they change significantly with angle of attack when being applied to aircraft motion control. To effectively compensate such nonlinearities, an adaptive inversion-based compensation scheme needs to be designed with an augmented inverse function. Such an adaptive inverse is developed using adaptive approximation to handle the uncertainties of the actuator nonlinearities. A nonlinear state feedback control law is combined with the adaptive inverse compensator for a benchmark aircraft system with synthetic jet actuation signals. Related design issues are addressed for such an innovative actuation technology for aircraft, with stability analysis and simulation results for system demonstration.