A nonextensive scenario for ionic transport is discussed in the framework of Tsallis thermostatistics. It is shown that the power-like concentration distributions could be obtained within a generalized stochastic approach based on a random component in the potential relief for ion migration. In a sharp contrast to the ordinary diffusion approach, this gives an explanation for anomalous penetration of energetic deuterium ions in doped SrCeO3-type oxides. (C) 2004 Elsevier B.V. All rights reserved.