Laws of spatial averaging on nanoscale for local electrostatic potential differences in ionic conductors are of key importance for the understanding of ion-transport phenomena and effects in space-charge layers. Currently, these laws are not investigated. As a consequence, the leading software packages for nanoscience do not have any competence for modeling of space-charge formation/relaxation in nanostructures with ionic hopping conductivity. So the article addresses the theme. For a layered nanostructure {X-k}, formed by parallel crystallographic X-k planes, an average electrostatic potential difference (< V-k,V-k+1 >) in a non-uniform field is defined in terms of normalized sums Sigma of the local works W-k,W-k+1 for X-k -> Xk+1 transitions of mobile ions in a field of a single point charge. At a weak external electrical influence on {X-k}, the < V-k,V-k+1 > can be easily generalized for a non-uniform field created by a set of point charges. The sums Sigma W(k,k+1 )are calculated for small average distances (similar to 0.6 nm) between mobile ions (as in advanced superionic conductors). Computer experiments show: (i) Sigma W-k,W-k+1 sums are independent of k-indices with the accuracy similar to 10%, (ii) probability density functions for local potential differences V-k,V-k+1 are close to normal distributions and (iii) < V-k,V-k+1 > approximate to V-k,k+1(U) where V-k,k+1(U) is a potential difference in a uniform electrostatic field. These nanoscale laws allow manipulating by an average potential difference (< V-k,V-k+N >) between X-k and Xk+N planes (N > 1), so the modeling of non-stationary ion-transport processes and energy flows in parallel combinations of nanostructures become possible.