<p>This paper investigates the problem of adaptive tracking control for a class of uncertain multi-input and multi-output nonlinear systems in the presence of asymmetric input constraints and external disturbance. In order to address the different action ranges of input signals in asymmetric dead-zone and saturation models, an adaptive backstepping control method related to asymmetric parameters is designed. A state-dependent upper bound of uncertainty is proposed instead of a constant upper bound. This avoids the problem of state constraints caused by the boundness of uncertainty before obtaining closed-loop characteristics. Certain positive results are emerged in this paper where an innovative adaptive control methodology is demonstrated to cope with system uncertainty. The proposed controller does not require a priori knowledge on the bound of them. By means of the Lyapunov stability theory, the close-loop system is proven to be uniformly ultimately bounded, the system states converge to a domain containing the origin, and the output tracks the reference signal commendably. Simulation examples are presented to show the effectiveness of the proposed control method.</p>