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A new oscillation behavior in a phase-change memory device is presented and analyzed. The device consists in a chalcogenide resistor with a parallel capacitance and no inductance. Biasing the device immediately after a proper trigger pulse leads to damped relaxation oscillations, which can be controlled in frequency by the bias voltage. The oscillation mechanism is explained by repetitive cycles of threshold switching and recovery of the high-resistance (off) state of the amorphous chalcogenide region in the device. Damping is explained by oscillation-induced phase change in the chalcogenide layer.