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In this paper, adaptive fuzzy control is investigated for nonlinear teleoperators with time delays, which ensures synchronization of positions and velocities of the master and slave manipulators and does not rely on the use of the scattering transformation. Compared with the previous passivity framework, the communication delays are assumed to be stochastic time varying. By feedback linearization, the nonlinear dynamics of the teleoperation system is transformed into two subsystems: local master/slave position control with unmodeled dynamics and delayed motion synchronization. Then, based on linear matrix inequalities (LMI) and Markov jump linear systems, adaptive fuzzy-control strategies are developed for the nonlinear teleoperators with modeling uncertainties and external disturbances by using the approximation property of the fuzzy logic systems. It is proven that the master-slave teleoperation system is stochastically stable in mean square under specific LMI conditions, and all the signals of the resulting closed-loop system are uniformly bounded. Finally, the extensive simulations are performed to show the effectiveness of the proposed method.