We report a similar feature in the response of resistor-memristor and capacitor-memcapacitor circuits with threshold-Type memory devices driven by triangular waveform voltage. In both cases, the voltage across the memory device is stabilized during the switching of the memory device state. While in the memristive circuit this feature is observed when the applied voltage changes in one direction, the memcapacitive circuit with a ferroelectric memcapacitor demonstrates the voltage stabilization effect at both sweep directions. The discovered behavior of capacitor-memcapacitor circuit is also demonstrated experimentally. We anticipate that our observation can be used in the design of electronic circuits with emergent memory devices as well as in the identification and characterization of memory effects in threshold-Type memory devices.