The problem of fault detection and isolation (FDI) is addressed for nonlinear dynamic systems modeled by polynomial differential-algebraic equations. Ritt＇s algorithm is used to obtain an input-output representation of the monitored system by eliminating unknown variables. A local approach to change detection is then applied to the input-output representation for FDI residual generation and evaluation. Simulation results on a microbial growth process are provided, which illustrate the relevance of the proposed FDI method.