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We present a coevolutionary algorithm for inferring the topology and parameters of a wide range of hidden nonlinear systems with a minimum of experimentation on the target system. The algorithm synthesizes an explicit model directly from the observed data produced by intelligently generated tests. The algorithm is composed of two coevolving populations. One population evolves candidate models that estimate the structure of the hidden system. The second population evolves informative tests that either extract new information from the hidden system or elicit desirable behavior from it. The fitness of candidate models is their ability to explain behavior of the target system observed in response to all tests carried out so far; the fitness of candidate tests is their ability to make the models disagree in their predictions. We demonstrate the generality of this estimation-exploration algorithm by applying it to four different problems—grammar induction, gene network inference, evolutionary robotics, and robot damage recovery—and discuss how it overcomes several of the pathologies commonly found in other coevolutionary algorithms. We show that the algorithm is able to successfully infer and/or manipulate highly nonlinear hidden systems using very few tests, and that the benefit of this approach increases as the hidden systems possess more degrees of freedom, or become more biased or unobservable. The algorithm provides a systematic method for posing synthesis or analysis tasks to a coevolutionary system.