A book on spacecraft momentum control systems would not be complete without a discussion of kinematic singularities inherent in CMGs. Therefore, this chapter starts with a discussion of common singularities associated with DGCMGs (e.g., gimbal lock) and then moves on to the more troublesome singularities associated SGCMGs. The mathematical structure of these singularities and how it relates to difficulties in avoiding them is also discussed in a way made more accessible to the reader not familiar with the subject matter. Also discussed is the location of singularities associated with an array of CMGs by way of a three-dimensional surface in the momentum space. This chapter concludes with some brief discussion on techniques to perform zero-momentum spin up of an array of CMGs in the presence of singularities at zero momentum.