A family of algorithms for the identification of continuous-time nonlinear plants operating in closed loop is presented. An adjustable closed-loop output error-type predictor parameterized in terms of the existing controller and the estimated plant model is used. The algorithms are derived from stability considerations in the absence of noise and assuming that the plant model is in the model set. Some convergence results based on passivity concepts are presented. Subsequently, the algorithms are analyzed in the presence of noise and when the plant model is not in the model set.