In this book, a method is presented for detecting faults in a reaction wheel of the attitude control system of a spacecraft. A nonlinear observer is proposed as a residual generator to detect the anomalies and faults. To justify the need for the proposed complex nonlinear observer, a linear residual generation scheme is also considered as a benchmark and also for comparison. The linear observer is designed through linearization of the highly nonlinear dynamics of the reaction wheel. The performance and limitations of the linear observer subject to the three fault scenarios, commonly present in the reaction wheel, are investigated. The advantages and capabilities of applying the proposed nonlinear observer are demonstrated and emphasized through numerical simulations.