We report on impedance measurements of nano- and microcrystalline composites of the Li ion conductor Li2O and the ionic insulator B2O3 as well as their interpretation in the frame of percolation models. In the experimental part, besides the dc conductivity and its dependence on composition and temperature (i.e. its activation energy) also the ac conductivity and its dependence on composition, temperature and frequency (i.e. the conductivity exponent) are presented. Striking differences between the nanocrystalline and the corresponding microcrystalline composites were found. Deviations of the ac from the dc results can be explained by the fact that the experiments probe ion dynamics on different time and thus length scales. In the theoretical part, a continuum percolation model, a brick-layer type bond percolation approach and a Voronoi construction are alternatively used to model the dc behaviour. Based merely on the largely different volume fractions of the interfaces between ionic conductor and insulator grains in the nano- and microcrystalline composites, good overall agreement with the experimental dc results is obtained. The high critical insulator content above which the experimental conductivity vanishes in the nanocrystalline composites suggests the presence of an additional Li diffusion passageway of nanometer length in the interface between nanocrystalline insulator grains. © 2005, Oldenbourg Wissenschaftsverlag GmbH