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The notion of bisimulation has been used in various fields including Modal Logic, Set theory, Formal Verification, and XML indexing. In this paper we present the first algorithm for incremental maintenance of maximum bisimulation relation of a graph with respect to changes in the graph. Given a graph, its maximum bisimulation relation, and the changes in the graph, we determine the maximum bisimulation relation with respect to the changed graph by computing the changes in the given bisimulation relation. When the change in the graph induces small changes in the maximum bisimulation relation, our incremental algorithm is able to update the bisimulation relation on average an order of magnitude faster than the fastest available non-incremental algorithm. Preliminary experiments demonstrate the effectiveness of our algorithm. Our algorithm finds extensive use in verification where the specification changes over time, and XML indexing in database where the index structure, obtained by bisimulation on XML graph structure, needs to be maintained with respect to changes in the XML documents.