The conventional Iterative Learning Control (ILC) algorithm for model-based ILC of nonlinear systems is presented with use of a nonlinear inverse model as ILC compensator. The nonlinear inverse model is solved with stable inversion. In addition an alternative ILC algorithm for model-based ILC of nonlinear systems is developed, also with using a nonlinear inverse model as ILC compensator. Some connections between the conventional and alternative ILC algorithms and Picard, Mann and Ishikawa iteration are explored. In a number of theoretical examples the conventional and alternative algorithms are compared.