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The properties of a strong double layer in a current circuit with a capacitance and an inductance are investigated in a triple-plasma device. The double layer gives rise to a region of negative differential resistance in the current-voltage characteristic of the device, and this gives nonlinear oscillations in the current and the potential drop over the double layer (Â¿DL). For a sufficiently large circuit inductance Â¿DL reaches an amplitude given by the induced voltage (-Ldl/dt) which is much larger than the circuit EMF due to the rapid current decrease when Â¿DL increases. A variable potential minimum exists in the plasma on the low-potential side of the double layer, and the depth of the minimum increases when Â¿DLFDL increases. An increasing fraction of the electrons incident at the double layer are then reflected, and this is found to be the main process giving rise to the negative differential resistance. A qualitative model for the variation of the minimum potential with Â¿DL is also proposed. It is based on the condition that the minimum potential must adjust itself self-consistently so that quasi-neutrality is maintained in the plasma region where the minimum is assumed.