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This paper proposes a new fuzzy identification approach for the special class of nonlinear hybrid dynamic systems having switching characteristics. An online fuzzy identification methodology is formulated to recursively estimate an evolving Takagi-Sugeno (ETS) rule-base model for each dynamic mode of the nonlinear hybrid systems using a modified potential clustering scheme. A simple Recursive Least-Squares (RLS) algorithm is used to estimate the free parameters in the consequence part of the created fuzzy rules. Each system mode represents an independent dynamic model structure with relevant free parameters which is characterized via a set of corresponding fuzzy rules being generated under the potential influence of the recursive incoming input-output data. The generated ETS rule-base model of each observed dynamic mode is adaptively evolved by either adding new rules or updating existing rules and rule consequent parameters. The developed algorithm has been utilized to identify an ETS dynamic model for a practical pharmaceutical batch reactor to demonstrate its efficiency. The results illustrate the efficiency of the approach for identification of nonlinear hybrid dynamic systems.