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This paper focuses on the tracking control problem for a class of nonlinear system with time delays and dead-zone input. The nonsymmetric dead-zone input case is considered without the knowledge of the dead zone parameters. The time delay uncertainties are bounded by a nonlinear function with unknown coefficients. By constructing a novel Lyapunov functional, we design a simple and smooth adaptive state feedback controller. It is shown that the solution of the resulting closed-loop error system converges to an adjustable region exponentially. Finally, numerical examples are included to show the effectiveness of the theoretical results.