A non-linear robust adaptive bilateral impedance controller is proposed to provide the absolute stability of multi-DOF teleoperation systems with communication delays, in addition to the force and position tracking performance. The proposed controller realises two desired (or reference) impedance models for the master and slave robots using a new non-linear robust version of the model reference adaptive control scheme. Using the absolute stability criterion, the robustness condition of the teleoperation system against communication delays is obtained, resulting in suitable adjustments of parameter values in the desired impedance models. In addition, using the Lyapunov stability theorem, the tracking performance of the master and slave robots and the robustness of the proposed controller against parametric and bounded unstructured modelling (non-parametric) uncertainties were proven. The performance of the proposed non-linear bilateral controller is investigated by performing some experiments on non-linear multi-degree-of-freedom (DOF) telerobots with and without communication delays. © The Institution of Engineering and Technology 2018.