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In this paper we introduce an adaptive control scheme for robots with elastic joints (in particular for the DLR medical robot) in order to increase the positioning accuracy and the performance of control with respect to uncertainties of the parameters of the robot dynamics. In order to design control and analyze system stability a static friction model is applied which describes Coulomb, viscose and load dependent friction. A stability analysis is done for this adaptive control scheme, allowing a Lyapunov based convergence analysis in the context of the nonlinear robot dynamics. Experimental results validate the practical efficiency of the approach.