This thesis is divided into two parts, i.e., adaptive extremum control and modelling and control of a wind turbine. The rst part of the thesis deals with the design of adaptive extremum controllers for some processes which have the behaviour that process should have as high e ciency as possible. Firstly, it is assumed that the nonlinear processes can be divided into a dynamic linear part and static nonlinear part. Consequently the processes with input nonlinearity and output nonlinearity are treated separately. With the nonlinearity at the input it is easy to set up a model which is linear in parameters, and thus directly lends itself to parameter estimation and adaptive control. The extremum control law is derived based on static optimization of a performance function. For a process with nonlinearity at output the intermediate signal between the linear part and nonlinear part plays an important role. If it can be emphasis on control design. The models have beenvalidated by experimental data obtained from an existing wind turbine. The e ective wind speed experienced by the rotor of a wind turbine, which is often required by some control methods, is estimated by using a wind turbine as a wind measuring device. The investigation of control design is divided into below rated operation and above rated operation. Below ratedpower, the aim of control is to extract maximumenergy from the wind. The pitch angle of the rotor blades is xed at its optimal value and turbine speed is adjusted to follow thechanges in wind speed. Above rated power, the control design problem is to limit and smooth the output electrical power. The pitch control is investigated for both constant speed and variable speed wind turbines. The minimization of the turbine transient loads is focussed in both cases.