This paper introduces the Global-Local Mapping Approximation algorithm as a candidate for identifying nonlinear, six degree-of-freedom rigid body aircraft dynamics. The technique models the nonlinear dynamical model as a sum of linear model and nonlinear model. The linear model dynamics are assumed to be perturbed by a nonlinear term which represents the system nonlinearities that are not captured by the linear model. Lyapunov stability analysis is used to derive the learning laws. To demonstrate the suitability of the algorithm for nonlinear system identification of aircraft dynamics, a longitudinal and a lateral/directional example using nonlinear simulation data, and flight test data are conducted. The true nonlinear model is generated using both the six degree-of-freedom nonlinear equations of motion of an aircraft, and by flight test data. Results presented in the paper demonstrate the utility of the Global-Local Mapping Approximation for the realistic cases of an unknown control distribution matrix B and unknown influence coefficient matrix C.