This talk considers the effect of Anderson acceleration (AA) on the convergence order of nonlinear solvers in fixed point form x_{k+1}=g(x_{k}), that are looking for a fixed point of g. While recent work has addressed the fundamental question of how AA affects the convergence rate of linearly converging fixed point iterations (at a single step), we give the first analytical results for how AA affects the convergence order of solvers that do not converge linearly.