In this article, the tracking control problems of the nonlinear nonstrict-feedback systems are considered. By combining the backstepping technique and bound estimation method, a novel nonlinear adaptive asymptotical control law is proposed, which offsets the effect of the unknown virtual control parameters and the uncertain nonlinearities. Correspondingly, an improved Lyapunov function by introducing the lower bounds of control parameters has been devised in this article. Compared with the existing adaptive tracking control schemes, the controller designed in this article can guarantee that the tracking control error converges to zero asymptotically and all the signals which contain the state variables and the adaptive laws are bounded. Moreover, the asymptotic stability of the system is realized for the first time. Finally, simulation examples are applied to test and prove the availability of the presented methods and the performance of the controlled system.