New notion -Maxwell displacement current on potential barrier -is introduced in the structuredynamic approach of nanoionics for description of collective phenomenon: coupled ion-transport and dielectric-polarization processes occurring during ionic space charge formation and relaxation in non-uniform potential relief. We simulate the processes: (i) in an electronic conductor/advanced superionic conductor (AdSIC) ideally polarizable coherent heterojunction, (ii) in a few strained monolayers of solid electrolyte (SE) located between two AdSICs forming coherent interfaces with SE. We prove the sum of ionic current over any barrier and Maxwell displacement current through the same barrier is equal to the current of current generator.-Universal‖ dynamic response, Re*() n (n < 1), was found for frequency-dependent conductivity *() for case (ii) with an exponential distribution of potential barrier heights in SE. The nature of phenomenon is revealed. The amplitudes of non-equilibrium ion concentrations (and induced voltages) in space charge region of SE change approximately as -1 . Amplitudes yield a main linear contribution to Re*(). The deviation from linearity is provided by the cosine of phase shift between current and voltage in SE-space charge but cos depends relatively slightly on (near constant loss effect) for coupled ion-transport and dielectric-polarization processes.The canonical physical-mathematical formalism for the description of ion transport in solids [1] is based on the concept of a regular crystalline potential relief, i.e. the heights of potential barriers are const. As a consequence, ion-transport characteristics (mean-square displacement, diffusion coefficient, mobility, activation energy) have a clear physical meaning only at averaging in the scale much exceeding the length of an elementary ion jump. However, the variation of with a space coordinate x can be considerable in objects of solid state ionics. For example, local regions with variation about 1 eV/nm exist in disordered solid electrolytes (SE) [2][3][4] and in crystals of superionic conductors (SIC) [5]. Various degrees of ordering occur near surfaces and in the region of interphase and intercrystalline boundaries [6] where specific ion dynamics can arise on the nanoscale [7] due to a non-uniform potential relief. The interface structure exhibits itself in, e.g., frequency-capacitance characteristics of EC/SIC heterojunctions [8][9][10]. The classification of solid ionic conductors [8-10] distinguishes a class of advanced superionic conductors (AdSIC) among SE and SIC because AdSIC-crystal structure is close to optimal for fast ion transport (FIT). This crystal structure determines the record high level of iontransport characteristics. The FIT structure represents a rigid sub-lattice of immobile ions in which there are the crystallographic positions interconnected with each other by low potential barriers (conduction tunnels) for hopping mobile ions. The number of such positions is several times larger ...