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The networked teleoperation design problem is considered. The communication delays are assumed to be both time varying and asymmetrical, which is the case for network-based teleoperation systems. Two cases are considered, i.e., that gravity functions are available and not available. To avoid the heavy collision between the slave robot and the environment, a new torque design scheme is proposed. A designed force is added to the master robot to make the human operator feel the environment before touching the object. The master velocity signal and the distance signal between the slave robot and the object are all embedded in the designed force function. By constructing Lyapunov functional, the stability of the closed-loop system is proved. For the case that the gravity function is not available, an adaptive compensator design method is proposed on both sides. The stability of the closed-loop system is also proven with the new master-slave adaptive controllers. Finally, the simulations are performed, and the results show the effectiveness of the proposed method.