The anomalous low-frequency dispersion process observed in perovskite ceram
ics (X2BaCuO5,X = La-Y) is described by a fractal model. The interpretation
is given in terms of the Dissado-Hill-Jonscher theory and is based on a cl
uster description of the structural ordering and fluctuation in carrier-dom
inated dielectrics. The relationship of the mechanism to that of power-law
noise in electrical systems is identified and its dynamical and structural
interpretation explored. Particular features of several ceramics related to
superconductor compounds are described. [S0163-1829(99)09931-2].