In this paper, we extend the family of algorithms presented in Algorithms for identification of continuous time nonlinear systems. A passivity approach. In A. Isidori, F. Ramnabhi-Lagarrigue, & W. Respondek (Eds.), Nonlinear control in the year 2000, vol. 2 (pp. 13-44) Berlin: Springer; (Automatica 37 (2000) 469) for the identification of continuous time nonlinear plants operating in closed loop. The new algorithms presuppose that one can construct a stable kernel representation for the "to be identified model" structure. The new theory results in a less restrictive passivity condition. The main novelty is that the identification of unstable plants can be tackled by an appropriate choice of the kernel representation, i.e. there is an additional degree of freedom when constructing the kernel representation. The implicit stability of the controller is still required by the new passivity condition.