In this dissertation, several adaptive control design schemes for a class of nonlinear systems are proposed. The first topic of the research is concerned with self-tuning PID controller design. The main problem of designing PID controller is how to determine the values of three control gains, i.e., proportional gain , integral gain , and derivative gain . We attempt to use the technique of adaptive control based on the Lyapunov approach to design the PID controller for some class of partially known nonlinear systems. Three PID control gains are adjusted on-line such that better output performance can be achieved. The stability of the closed-loop PID control systems is analyzed and guaranteed by introducing a supervisory control and a modified adaptation law with projection. Second, two kinds of adaptive neural control systems including the direct and indirect neural controls are considered by using simple single auto-tuning neuron. We will first propose a novel neuron called auto-tuning neuron and use it to take place of the roles of the traditional neural networks used in the direct and indirect adaptive neural control systems. This can greatly reduce the computational time and network complexities due to the simple configuration of the auto-tuning neuron. It is also easy for hardware implementation. Third, based on the idea borrowed from natural evolution, genetic algorithm can search for optimal or near-optimal solutions for an optimization problem over the search domain. An optimization technique of real-coded genetic algorithm is used to design the PID controller by minimizing the performance index of integrated absolute error. The improvements of our results over that using other methods are also illustrated. In the last part of each section, some computer simulation results will also be provided to illustrate our proposed methods.