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In this paper stochastic approximation theory is used to produce Iterative Learning Control algorithms which are less sensitive to stochastic disturbances, a typical problem for the learning process of standard ILC algorithms. Two algorithms are developed, one to obtain zero mean controlled error and one to minimise the mean 2-norm of the controlled error. The former requires a certain knowledge of the system but in the presence of noise can give reasonably rapid convergence. The latter can either use a model or be model free by employing a second experiment. Simulations have been carried out to demonstrate the effectiveness of the methods.