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In this paper a generalized structure for IIR adaptive filtering is presented. The structure uses both the training and desired signals for its inputs, to generate the synthetic signal which minimizes the mean square of a given error measure. The structure is shown to be linear in all its adaptive coefficients, and hence a unique minimum is available for the error surface under consideration. Also, it is shown that other IIR and IIR-like structures are special cases of the one introduced here. The limitations of this filter structure are discussed, and computer simulations of adaptive algorithms which use this structure are also presented.