The purpose of this work is to compare some linear and nonlinear control strategies, with the aim of benefiting as well as possible of wind energy conversion systems. Below rated wind speed, the main control objective is to perform an optimal wind power capture while avoiding strong loads on the drive train shafts. To explicitly take into consideration the low speed shaft flexibility, a two-mass nonlinear model of the wind turbine is used for controllers synthesis. After adapting a LQG controller based on the linearized model, nonlinear controllers based on a wind speed estimator are developed. They take into account the nonlinear dynamic aspect of the wind turbine and the turbulent nature of the wind. The controllers are validated upon an aeroelastic wind turbine simulator for a realistic wind speed profile. The study shows that nonlinear control strategies bring more performance in the exploitation of wind energy conversion systems.