Dielectric modulus spectra of the glasses in the system Na 2 O-Al 2 O 3 -B 2 O 3 have been obtained from the impedance measurement and analyzed by a heterogeneous conductor ͑nanoscale level͒ model developed in the past years. Satisfactory agreement between the theory and the experiment has been observed. The  exponent of the Kohlrausch-Williams-Watts ͑KWW͒ stretched exponential function appears to be correlated with the amount of the alkali ion fluctuation in the conducting phase of the glasses. The Na 1s X-ray photoelectron spectra provide evidence of the presence of the alkali ion fluctuation in these glasses.It has been established that the non-Debye processes ͑distribution of relaxation times͒ dominate in the real system. It has become customary to fit the ac impedance data of amorphous materials to a relaxation function incorporating the Kohlrausch-Williams-Watts ͑KWW͒ stretched exponential 1-3where R is the effective relaxation time and the exponent  has a value in the range between 0 and 1. It gives a measure of the distribution of relaxation times within the system. The physical mechanism responsible for such a fractional value of  has been a source of some controversy. The origin of the relaxation in ionically conducting glasses has been modeled 4 using diffusion-controlled relaxation process without assuming a distribution of relaxation times. The model can be regarded as a combined series and parallel relaxation process: in the series aspect the interionic interaction is associated with the diffusion triggering of relaxation at an interstitial site, and in the parallel aspect all such diffusion-controlled relaxation events occur independently. Non-Debye relaxation in amorphous conductors 5 was also explained by introducing the mutual interactions among mobile ion species of considerable concentration. The correlation between the decoupling index, which is the ratio of mechanical to dielectric relaxation times, and KWW stretching parameter was discussed by Hunt. 6 A general coupling theory 7,8 which is based on the cooperative effects between the species primarily responsible for the conductivity relaxation and the other surrounding equivalent ions has been proposed. Many of the predictions arising out of this model have been tested on several oxide glasses. 9,10 The model has also been found to be similar to a jump relaxation model. 11 The structure of the glasses and the distribution of the mobile ions within these glasses were either considered homogeneous or essentially disregarded in these models. At the end of the twentieth century, a different approach was developed to understand the non-Debye relaxation behavior of the oxide glasses. Based on a diagonal layer model 12 a spatial variation of the alkali ion concentration has been assumed in calculating the dielectric modulus spectra of several alkali silicate glasses. 13,14 Obviously this model will be applicable only to those glasses which do not possess a homogeneous distribution of the mobile ions. Satisfactory agreement between the experime...