The admittance spectra of NASICON samples, Na1+xZr2SixP3-xO12 (0 < x < 3), were investigated for compositions 1.2 < x < 2.2 in the frequency range from 1 Hz to 150 kHz. It was found that the spectra consist of three regions of dispersion independent of the composition of the sample. The low frequency semicircle of the admittance spectra is attributed to the dispersion on electrode double layers connected in series to the total de electric resistance of the sample. The high frequency semicircle-like part of the spectra is composed of two dispersions. One is attributed to the partial blocking of ion carriers on grain-boundary phases and the other to dispersion on a glassy phase present in inter-grain regions of NASICON samples. The plausibility of such an assumption is confirmed by the results of an additional investigation of admittance spectra of Co-doped NASICON samples in which the glassy phase was found to be extremely strong and endurable. Although the investigated samples differ greatly in their composition (from x = 1.2 to x = 2.2) the electric conductivity of their glassy phase obeys the Meyer-Neldel rule. This seems to indicate that the composition of the glassy phase is quite homogeneous over a range of NASICON-like compounds.