Carbonate/oxide composites are very promising electrolyte materials in hybrid fuel cells which could operate at lower temperature than the usual Molten Carbonate Fuel Cells (MCFC) or Solid Oxide Fuel Cells (SOFC), presenting 0.1 S cm(-1) at 600 degrees C. This paper shows some significant and/or unexpected experimental data obtained by impedance spectroscopy, related to the impact of the carbonate/oxide ratios and the heating and cooling cycles in reducing atmospheres on the electrical behaviour of the composites. Based on this peculiar experimental behaviour, combined DFT calculations are selected for acquiring a deeper understanding of the transport mechanisms in such materials. A modelling strategy, in parallel with experimental results, is developed in the present paper. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.