During the last decade significant progress has been made in the control of nonlinear systems, and a number of nonlinear process-model-based control techniques have appeared in the literature. In this Note two of the most attractive nonlinear controller design techniques are considerd : the Generic Model Control technique and the Globally Linearizing Control technique. The problem of how to tune the two controllers in order to obtain identical closed-loop responses is addressed. It is shown that, by properly choosing the tuning parameters of the external PI controller, a GLC controller yields a closed-loop response perfectly equivalent to the one induced by a GMC controller.