In this paper, an adaptive motion/force controller is developed for unilateral or bilateral teleoperation systems. The method can be applied in both position and rate control modes, with arbitrary motion or force scaling. No acceleration measurements are required. Nonlinear rigid-body dynamics of the master and the slave robots are considered. A model of the flexible or rigid environment is incorporated into the dynamics of the slave, while a model of the human operator is incorporated into the dynamics of the master. The master and the slave are subject to independent adaptive motion/force controllers that assume parameter uncertainty bounds. Each parameter is independently updated within its known lower and upper bounds. The states of the master (slave) are sent to the slave (master) as motion/force tracking commands instead of control actions (efforts and/or flows). Under the modeling assumptions for the human operator and the environment, the proposed teleoperation control scheme is L-2 and L-infinity stable in both free motion and flexible or rigid contact motion and is robust against time delays. The controlled master-slave system behaves essentially as a linearly damped free-floating mass. If the parameter estimates converge, the environment impedance and the impedance transmitted to the master differ only by a control-parameter dependent mass/damper term. Asymptotic motion (velocity/position) tracking and force tracking with zero steady-state error are achieved. Experimental results are presented in support of the analysis.