Adaptive control has long focused on establishing stable adaptive control methods for various nonlinear systems. Existing methods are mostly based on the certainty equivalence principle which states that the controller structure developed in the deterministic case (without uncertain system parameters) can be used for controlling the uncertain system along by adopting a carefully determined parameter estimator. Thus, the overall performance of the regulating/tracking control depends on the performance of the parameter estimator, which often results in the poor closed-loop performance compared with the deterministic control because the parameter estimate can exhibit wide variations compared to their true values in general. In this dissertation, we introduce a new adaptive control method for nonlinear systems where unknown parameters are estimated to within an attracting manifold and the proposed control method always asymptotically recovers the closed-loop error dynamics of the deterministic case control system. Thus, the overall performance of this new adaptive control method is comparable to that of the deterministic control method, something that is usually impossible to obtain with the certainty equivalent control method. We apply the noncertainty equivalent adaptive control to study application arising in the n degree of freedom (DOF) robot control problem and spacecraft attitude control. Especially, in the context of the spacecraft attitude control problem, we developed a new attitude observer that also utilizes an attracting manifold, while ensuring that the estimated attitude matrix confirms at all instants to the special group of rotation matrices SO(3). As a result, we demonstrate for the first time a separation property of the nonlinear attitude control problem in terms of the observer/controller based closed-loop system. For both the robotic and spacecraft attitude control problems, detailed derivations for the controller design and accompanying stability proofs are shown. The attitude estimator construction and its stability proof are presented separately. Numerical simulations are extensively performed to highlight closed-loop performance improvement vis-a-vis adaptive control designs obtained through the classical certainty equivalence based approaches.