An increase of the ac conductivity with increasing frequency, observed in ionic conductors, is accompanied by a finite decrease of the dielectric constant. In a range of materials, the dielectric function can be well described by the empirical functions of Cole-Cole or Havriliak-Negami, which in the limit of high frequencies give the power law frequency dependence of conductivity. The relaxation strength Delta epsilon, the dc conductivity sigma(0) and the relaxation frequency omega(C) obey the Barton-Nakajima-Namikawa relation: sigma(0)=P epsilon(0)Delta epsilon omega(C), where P is a coefficient, whose value is characteristic for a given ionic conductor. Impedance spectra of an oxide ion conductor-Bi2Cu0.1V0.9O5.35 single crystal and of lithium ion conductors: glass from the Li2O-SnO2-TiO2-P2O5 system and polymer electrolyte-LiN(CF3SO2)(2) salt dissolved in poly(ethylene oxide), were analyzed by the least squares fitting. Good quality of fit and accurate estimates of parameters were obtained when the equivalent circuit comprised contributions of all processes affecting the ac response. In all cases a sub-circuit was included that modeled the ion-blocking electrodes. At low temperature a contribution of nearly constant dielectric loss was allowed at high frequencies. A broad relaxation associated with the C-O bond dipoles within PEO chain was seen in polymer electrolyte. Values of the coefficient P were between 2.3 and 2.7 for lithium ion conducting oxide glass, between 3 and 5 for lithium polymer electrolyte and between 6.5 and 15 for single crystal of BICUVOX. It is proposed that value of coefficient P provides information about the length scale and the time scale of local, non-random motion of hopping ions. (c) 2005 Elsevier B.V. All rights reserved.