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We report on theoretical and experimental investigations of a novel hysteresis effect that has been observed on the magnetoresistance of quantum-Hall bilayer systems. Extending to these system a recent approach, based on the Thomas-Fermi-Poisson nonlinear screening theory and a local conductivity model, we are able to explain the hysteresis as being due to screening effects such as the formation of ``incompressible strips’', which hinder the electron density in a layer within the quantum Hall regime to reach its equilibrium distribution.

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