The slave robot in this research is a 1-DOF piezo actuatorwhich includes hysteresis nonlinearity. Nonlinear hysteresis behavior makes robot control a complex task. In this research, the nonlinear and uncertain dynamics of the slave robot has been considered through the teleoperation control loop. LuGre friction model is used as the estimator of the hysteresis loop. An impedance controller for the master side and a sliding-mode-based impedance controller for the slave side have been proposed. The latter is a sliding mode controller, because the plant is nonlinear and uncertain. Also, it is an impedance controller providing both high performances during contact and excellent tracking in free space motion. These controllers make teleoperator robustly stable against uncertainties and bounded constant time delay. Meanwhile, scaling factors, known as sources of instability, have no disturbing effect. After canceling the nonlinear term out of the teleoperator by the controllers, stability of the entire system will be guaranteed by Llewellyn's absolute stability criterion. Performance of the proposed controllers is investigated through simulation.