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This study is concerned with an adaptive state estimation problem for a class of stochastic delay systems with state-dependent Markovian switching. Since the upper bound of parameters related to a transition rate of stochastic Markovian jump system is assumed to be unknown, an adaption law is developed to estimate such an unknown parameter. A class of adaptive state estimator is proposed such that not only the estimated parameter is bounded almost surely but also the estimated state error is mean-square exponentially stable. Finally, a numerical example is given to show the validity of the results.