Fault detection is critical in many applications, and analytical redundancy (AR) has been the key underlying tool for many approaches to fault detection. However, the conventional AR approach is formally limited to linear systems. In this brief, we exploit the structure of nonlinear geometric control theory to derive a new nonlinear analytical redundancy (NLAR) framework. The NLAR technique is applicable to affine systems and is seen to be a natural extension of linear AR. The NLAR structure introduced in this brief is tailored toward practical applications. Via an example of robot fault detection, we show the considerable improvement in performance generated by the approach compared with the traditional linear AR approach.