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This paper proposes a class of additive dynamic connectionist (ADC) models for identification of unknown dynamic systems. These models work in continuous time and are linear in their parameters. Also, for this kind of model two on-line learning or parameter adaptation algorithms are developed: one based on gradient techniques and sensitivity analysis of the model output trajectories versus the model parameters and the other based on variational calculus, that lead to an off-line solution and an invariant imbedding technique that converts the off-line solution to an on-line one. These learning methods are developed using matrix calculus techniques in order to implement them in an automatic manner with the help of a symbolic manipulation package. The good behavior of the class of identification models and the two learning methods is tested on two simulated plants and a data set from a real plant and compared …