A bilateral nonlinear adaptive impedance controller is proposed for the control of multi-degrees-of-freedom (DOF) teleoperation systems. In this controller, instead of conventional position and/or force tracking, the impedance of the nonlinear teleoperation system is controlled. The controller provides asymptotic tracking of two impedance models in Cartesian coordinates for the master and slave robots. The proposed bilateral controller can be used in different medical applications, such as telesurgery and telerehabilitation, where the impedance of the robot in interaction with human subject is of great importance. The parameters of the two impedance models can be adjusted according to the application and corresponding objectives and requirements. The dynamic uncertainties are considered in the model of the master and slave robots. The stability and the tracking performance of the system are proved via a Lyapunov analysis. Moreover, the adaptation laws are proposed in the joint space for reducing the computational complexity, however, the controller and the stability proof are all presented in Cartesian coordinates. Using simulations on a 2DOF robot, the effectiveness of the proposed controller is investigated in telesurgery and telerehabilitation operations.