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Vector hysteresis models are regarded as helpful tools that can be utilized in the simulation of multidimensional field-media interactions. Recently, substantial efforts have been focused on the refinement of vector Preisach-type models of hysteresis. The purpose of this paper is to present a computationally efficient vector Preisach-type hysteresis model constructed from only two scalar models having orthogonally inter-related elementary operators. Such a model is implemented via a linear neural network (LNN) fed from the outputs of discrete Hopfield neural network (DHNN) blocks having step activation functions. With this DHNN-LNN configuration, it is possible to carry out the identification process using well-established widely available algorithms. Details of the model, its identification, and experimental testing are presented.