In this paper, adaptive controller is proposed for bilateral teleoperation systems with parametric uncertainties, asymmetric time-varying delays in their communication channel and sandwich linearity in their actuators. The proposed bounded adaptive approach is a nonlinear-Proportional plus nonlinear Damping (nP+nD) controller which nonlinear adaptive terms are also employed locally to cope with the parametric uncertainties. The designed controller has  the  ability  to deal with  parameter variations  in  the  dynamics  of  the  master and  slave robots . The proposed controller also guarantees asymptotic stability and position tracking and avoiding the inputs to reach their usual actuator bounds. The asymptotic stability and tracking performance of the teleoperation system are proved using a Lyapunov-Krasovskii functional. The effectiveness of the proposed method is corroborated through simulation results.