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A neural network-based adaptive attitude tracking controller is developed in this paper, which achieves attitude tracking in the presence of parametric uncertainty, nonlinear actuator disturbances, and unmodeled external disturbance torques, which do not satisfy the linear-in-the-parameters assumption (i.e., non-LP). The satellite control torques are produced by means of a cluster of control moment gyroscopes (CMGs), which have uncertain dynamic and static friction in the gimbals in addition to unknown electromechanical disturbances. Some challenges encountered in the control design are that the control input is premultiplied by a non-square, time-varying, nonlinear, uncertain matrix and is embedded in a discontinuous nonlinearity. Controller performance is proven via Lyapunov stability analysis.