The paper presents a nonlinear approach, using a two-mass model and a wind speed estimator, for variable-speed wind turbine (WT) control. The use of a two-mass model is motivated by the need to deal with flexible modes induced by the low-speed shaft stiffness. The main objective of the proposed controllers is the wind power capture optimization while limiting transient loads on the drive-train components. This paper starts by an adaptation of some existing control strategies. However, their performance are weak, as the dynamics aspects of the wind and aeroturbine are not taken into consideration. In order to bring some improvements, nonlinear static and dynamic state feedback controllers, with a wind speed estimator, are then proposed. Concerning the wind speed estimator, the idea behind this is to exploit the WT dynamics by itself as a measurement device. All these methods have been first tested and validated using an aeroelastic WT simulator. A comparative study between the proposed controllers is performed. The results show better performance for the non-linear dynamic controller with estimator in comparison with the adapted existing methods.