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In this paper, a positioning control of a nonlinear elastically coupled two-mass system is presented. Structures of two-mass systems can often be found, e.g., in robotics or machine tools. The contained mechanical parts, like gears and shafts, can lead to limit cycles and stick-slip effects. In order to avoid the unwanted effects an H∞ control design is used for the system. Parameter uncertainties and elastic torsion are also taken into account in the control synthesis. If the measurability is limited, so that only the system output can be measured, a nonlinear observer is used. The standard output-feedback H∞ control structure needs some basic changes for this nonlinear observer. The result is an H∞ control, which can handle the nonlinear system, even if only the system output can be measured. The control shows good dynamics, robustness, and can handle disturbances. Measured results are shown in this paper.