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In this paper, adaptive control is proposed for hybrid position/force synchronization of master-slave teleoperation systems with time-varying delays in communication channels. Different from previous works on bilateral teleoperation systems, we investigate position/force control of bilateral teleoperation systems subject to time-varying delays and dynamical uncertainties. Using partial feedback linearization, the dynamics of both master and slave are transformed into two subsystems: local master/slave position/force control with unmodeled dynamics and delayed position/force synchronization. An adaptive control is proposed to deal with the dynamical uncertainties and robust against time delays, which guarantees the position/force synchronization trajectories converge to the desired manifolds with prescribed performance. The stability of the closed-loop system and the boundedness of synchronization tracking errors are proved using linear matrix inequalities based on Lyapunov stability synthesis. The position/force tracking error up to an ultimately bounded error is achieved. The proposed adaptive controls are robust against relative motion disturbances, parametric uncertainties, and time delays, and are validated by experimental studies.