In this paper, iterative learning control (ILC) system is modeled and designed from a two-dimensional (213) system point of view. Based on a 2D cost function defined over a single-cycle or multi-cycle prediction horizon, two ILC schemes, referred respectively as single-cycle and multi-cycle generalized 2D predictive ILC (2D-GPILC) schemes, have been proposed and formulated in the GPC framework for the 2D system. Analysis shows that the resulted control schemes are the combination of a time-wise GPC and a cycle-wise ILC optimized in 2D sense. Guidelines for parameter tuning have been proposed based on the ultimate performance analysis for the control system. Simulation shows that the multi-cycle 2D-GPILC outperforms the single-cycle 2D-GPILC in term of cycle-wise convergence. (c) 2007 Elsevier Ltd. All rights reserved.