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Preliminary investigations of nonlinear modeling of aircraft synchronous generators using neural networks are presented. Aircraft synchronous generators with high power density tend operate at current-levels proportional to the magnetic saturation region of the machine's material. The nonlinear model accounts for magnetic saturation of the generator, which causes the winding flux linkages and inductances to vary as a function of current. Finite element method software is used to perform a parametric sweep of direct, quadrature, and field currents to extract the respective flux linkages. This data is used to train a neural network which yields current as a function of flux linkage. The neural network is implemented in a Simulink synchronous generator model and simulation results are compared with a previously developed linear model. Results show that the nonlinear neural network model can more accurately describe the responsiveness and performance of the synchronous generator.