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A unified presentation of recursive algorithms for plant model identification in closed loop is given. From the basic formulation of the problem of finding the plant model that gives the best predictor for the closed-loop system, two families of algorithms using either a reparameterized predictor for the closed loop or a plant predictor operating on filtered data are presented, and their asymptotic properties are examined. Validation tests for the models identified in closed loop are proposed. A comparative evaluation of the various algorithms in simulation and on real-time experiments concludes the paper.