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We describe an accommodation hysteresis model based on a combination of history-dependent and history-independent models. The amount of accommodation is changed by varying the weights of the models employed in the resulting model. We illustrate the operation of the proposed model with accommodating cycles attached to the major loop. The model can be useful in further investigations of the accommodation phenomenon, as we show by using complex trajectories constructed by it. It can be incorporated in magnetodynamic calculations and circuit analysis.