It has been shown that the set of all nonlinear plants stabilised by a known linear controller, which also stabilises a linear nominal model of the plant, can be parametrised by a stable operator known as the Youla-Kucera parameter. By utilising this description it is possible to convert the closed-loop plant identification problem to one of open-loop identification. This paper extends previous work by allowing the model of the nominal plant and the controller in the above scenario to be nonlinear. The ideas rely on a concept of differential coprimeness for nonlinear fractional system descriptions.