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A plasma-sheath resonance has been observed at low pressures in argon plasmas. This phenomenon was known in a different context, that of the plasma resonance probe, but was hitherto unknown in parallel-plate plasma reactors. Two different models have been used to resolve the plasma-sheath resonances. A simple linear model is used to represent the plasma system as a series circuit of two capacitors (sheaths) and an inductor (plasma region). The plasma-sheath resonance occurs at a frequency where the cold plasma behaves inductively and resonates together with the two sheaths. The second model treats the plasma bulk as a series combination of an infinite number of elementary cells each one constituted by an inductor and a capacitor in parallel. By assuming an electron density profile the total impedance of the plasma can be obtained. Furthermore, the calculations show that the resonant energy is absorbed at an infinitely thin resonance plane. This causes the impedance of the system, filled with a lossless inhomogeneous plasma, to have a real part. This resonance can be used as a diagnostic, to measure the electron density. It could perhaps be exploited as the basis of a new plasma reactor. © 1998 American Institute of Physics.