Iterative learning control laws can be applied to systems that execute the same finite duration task over and over again. Previous research for linear dynamics has used the stability theory of linear repetitive processes to design control laws that have been experimentally verified. This paper applies recently developed stability theory for nonlinear repetitive processes to differential dynamics that can be feedback linearized. The design in then completed by applying the stability theory for linear dynamics. An example using the model of a single-link flexible joint is used to illustrate the new design.