I will discuss a convergence analysis of adaptive finite element methods for certain class of nonlinear elliptic problems. The problem class includes semi-linear elliptic equations such as stationary Navier-Stokes, reaction-diffusion equations with subcritical reaction term, as well as some quasi-linear problems. The class of finite element methods that can be dealt with with this technique is very general, including practically all types of error estimates and refinement strategies. This is an extension of a recent work of Pedro Morin, Kunibert Siebert and Andreas Veeser, and is an ongoing work joint with Michael Holst and Yunrong Zhu.