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A powder of Li(1.3)Al(0.15)Y(0.15)Ti(1.7)(PO(4))(3) has been synthesized by solid state reaction. The powder was a single phase material and had rhombohedral symmetry (space group [Formula: see text]) with six formula units in the unit cell. Impedance spectra of Li(1.3)Al(0.15)Y(0.15)Ti(1.7)(PO(4))(3) ceramics were recorded in the frequency range from 10(6) to 1.2 × 10(9) Hz and temperature range from 300 to 600 K. Two relaxation type dispersions of electrical quantities in the frequency range were found. The dispersion regions are presumably related to the ionic transport processes in bulk and grain boundaries of the ceramics. The activation energy of the conductivity of the bulk and the activation energy of the characteristic relaxation frequency, at which the dispersion sets in, has the same value of 0.25 eV. The only contribution of the mobility of Li(+) ions defines the temperature dependence of the bulk conductivity in the investigated temperature range. The values of ε(') may be related to the contributions of the polarization of the fast ionic migration, vibrations of the lattice and electronic polarization. Nuclear magnetic resonance (NMR) investigation shows that the T(1) of (7)Li and (6)Li at room temperature are 6 ms and 2 s respectively. This result confirms that the relaxation of the (7)Li nucleus occurs through quadrupolar fluctuations although the relaxation of the (6)Li nucleus occurs via dipolar fluctuations. Furthermore, the T(1) minimum allows us to evidence a motion with a characteristic frequency in the range of the Larmor frequency.