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Algorithms for parameter estimation and model selection that identify both the structure and the parameters of an ordinary differential equation model from experimental data are presented. The work presented here focuses on the case of an unknown structure and some time course information available for every variable to be analysed, and this is exploited to make the algorithms as efficient as possible. The algorithms are designed to handle problems of realistic size, where reactions can be nonlinear in the parameters and where data can be sparse and noisy. To achieve computational efficiency, parameters are mostly estimated for one equation at a time, giving a fast and accurate parameter estimation algorithm compared with other algorithms in the literature. The model selection is done with an efficient heuristic search algorithm, where the structure is built incrementally. Two test systems are used that have previously been used to evaluate identification algorithms, a metabolic pathway and a genetic network. Both test systems were successfully identified by using a reasonable amount of simulated data. Besides, measurement noise of realistic levels can be handled. In comparison to other methods that were used for these test systems, the main strengths of the presented algorithms are that a fully specified model, and not only a structure, is identified, and that they are considerably faster compared with other identification algorithms.