This paper describes the adaptive nonlinear control structure composed of approximate linearization and backstepping design procedures which guarantee high quality output regulation in the presence of unknown parameters and unstable internal dynamics. Through the theoretical analysis by the constructive Lyapunov functions on the specified conditions, the closed-loop stability of linearizable systems as well as output tracking without offset can be guaranteed. The effectiveness of the present design procedures is demonstrated on an isothermal Van de Vusse reaction in two instances. The first can be denoted as the Lyapunov-based controller for the nominal system. The second is an adaptive control scheme with the aid of the dead-zone technique to avoid parameter drift and obtain satisfactory performance for uncertain systems.