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Teleoperation systems are subject to different types of disturbances. Such disturbances, when unaccounted for, may cause poor performance and even instability of the teleoperation system. This study presents a novel non-linear bilateral control scheme using the concept of `disturbance observer-based control` for non-linear teleoperation systems. Lumping the effects of dynamic uncertainties and external disturbances into a single disturbance term enables us to design a disturbance observer to suppress these disturbances and alleviate their adverse effects on the teleoperation system. A disturbance observer-based control law is proposed for non-linear teleoperation systems which will guarantee global asymptotic force tracking and global exponential position and disturbance tracking when the bilateral teleoperation system is experiencing slow-varying disturbances. In the case of fast-varying disturbances, the tracking errors are shown to be globally uniformly ultimately bounded, with an ultimate bound that can be made as small as desired using the design parameters. Simulations are presented to show the effectiveness of the proposed approach.