In practice, fault prognostics has often touched with incomplete and noisy data collected at irregular time steps, e.g. in correspondence of the occurrence of triggering events in the system. Under these conditions, we investigate the possibility of predicting the Remaining Useful Life (RUL) of industrial systems using a properly tailored Echo State Network. A synthetic case study is used to show the effectiveness of the developed ESN-based methods and its superior performance with respect to traditional feedforward neural networks.