The problem of stabilizing a non-linear recursive system ∑ using a closed-loop configuration with compensation and feedback is considered. Most attention is devoted to the design of the dynamical behaviour of the stabilized closed-loop configuration. It is shown that, except for some obvious restrictions, any stable dynamics can be assigned to the closed-loop system. Compensators that yield the desired dynamics are explicitly constructed in implementable recursive form, and their formulae are expressed in terms of quantities derived directly from the given descriptions of the system ∑ and the desired dynamics. It is assumed that the state of the system ∑ is accessible. The resulting closed-loop configurations are internally stable.