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This paper extends the algorithms used to fit standard support vector machines (SVMs) to the identification of auto-regressive exogenous (ARX) input Hammerstein models consisting of a SVM, which models the static nonlinearity, followed by an ARX representation of the linear element. The model parameters can be estimated by minimizing an ɛ-insensitive loss function, which can be either linear or quadratic. In addition, the value of the uncertainty level, ɛ, can be specified by the user, which gives control over the sparseness of the solution. The effects of these choices are demonstrated using both simulated and experimental data.