The power-law frequency dependence of both the conductivity, (), and permittivity, (), of ion-conducting materials suggests that self-similar or scale-invariant behavior influences the transport of ions at high frequencies. Using an anomalous-diffusion model, we derive relevant power-law expressions for () and () and compare these with measurements performed on LiPO3 glass. Superior fits to the measured data are obtained compared to the commonly used Kohlrausch-Williams-Watts (KWW) description of the electrical modulus, most particularly in the notorious high-frequency regime. Evaluation of our results in terms of an anomalous-diffusion model suggests the dominance of interaction-based constraints to diffusion. © 1995 The American Physical Society.