Dielectric modulus spectra of the glasses in the system Na2O-Al2O3-B2O3 have been obtained from the impedance measurement and analyzed by a heterogeneous conductor (nanoscale level) model developed in the past years. Satisfactory agreement between the theory and the experiment has been observed. The beta exponent of the Kohlrausch-Williams-Watts (KWW) 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. (c) 2005 The Electrochemical Society. All rights reserved.