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This paper presents an adaptive approximation-based design methodology and analytical results for distributed detection and isolation of multiple sensor faults in a class of nonlinear uncertain systems. During the initial stage of the nonlinear system operation, adaptive approximation is used for online learning of the modeling uncertainty. Then, local sensor fault detection and isolation (SFDI) modules are designed using a dedicated nonlinear observer scheme. The multiple sensor fault isolation process is enhanced by deriving a combinatorial decision logic that integrates information from local SFDI modules. The performance of the proposed diagnostic scheme is analyzed in terms of conditions for ensuring fault detectability and isolability. A simulation example of a single-link robotic arm is used to illustrate the application of the adaptive approximation-based SFDI methodology and its effectiveness in detecting and isolating multiple sensor faults.