This paper considers an output feedback learning control for a class of uncertain nonlinear systems with flexible components. The distinct time delay caused by system flexibility leads to the phase lag phenomenon and low system bandwidth. Therefore, the tracking problem of such systems is very difficult and challenging. To improve the tracking performance of such systems, an iterative learning control scheme using the Fourier neural network (FNN) is presented in this paper. This scheme uses only local output information for feedback. FNN employs orthogonal complex Fourier exponentials as its activation functions and the physical meaning of its hidden-layer neurons is clear. The FNN-based learning controller introduced here relies on the frequency-domain method, which converts the tracking problem in the time domain into a number of regulation problems in the frequency domain. A novel phase compensation method is introduced to deal with the phase lag phenomenon, so that the bandwidth of the closed-loop system is increased. Experiments on a belt-driven positioning table are conducted to show the effectiveness of the proposed controller.