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The dynamics of a strong barrier discharge is investigated analytically in the simplest model that still keeps the essential discharge features. It is shown that at high overvoltage, the discharge develops into the ionizing wave moving from the anode toward the cathode. The velocity of this wave is found to be controlled mainly by the charge production rate in the cathode fall region and can considerably exceed the characteristic ion velocity. The influence of the capacitor formed by the dielectric layers on the discharge dynamics is analyzed. It is shown that, depending on the magnitude of the capacitance, two qualitatively different charging regimes exist. © 2003 American Institute of Physics.