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A novel adaptive tracking control law for nonlinear Hamiltonian multi-input-multi-output (MIMO) systems with uncertain parameters in the actuator modeling as well as the inertia and/or the Coriolis and centrifugal terms is developed. The physical properties of the Hamiltonian systems are effectively used in the control design and the stability analysis. The number of the parameter estimates is significantly lowered as compared to the conventional adaptive control methods which are based on the state-space form. The developed control scheme is applied for attitude control of a spacecraft with both the inertia and the actuator uncertainties, and numerical examples show that the controller successfully deals with the unknown inertia/actuator parameters.