It is suggested that a charge carrier transport in superionic conductors may follow an anomalous (e.g., superdiffusive) mechanism owing to effects of the fractality and the clustering. An anomalous penetration of "hot" deuterium ions (D of about 100 keV) in doped SrCeO3-type oxides can be modeled by using a diffusion-like equation with fractional derivatives in place of commonly used Fick's law. A tail exponent gamma for concentration distribution in proton conductors is introduced, A comparison with experimental data is made.