The NASICON system LAGP (Li 1+x Al x Ge 2−x (PO 4 ) 3 was studied, which is a candidate material for solid state electrolytes. LAGP substrates with different compositions (x = 0.3-0.7) were prepared using a melt quenching route with subsequent heat treatment. In order to develop a better understanding of the relationships between the structure and the ionic as well as the thermal conductivity, respectively, the samples were characterized by X-ray diffraction. The ionic conductivity was measured using impedance spectroscopy while the thermal diffusivity and the specific heat were determined by Laser Flash technique and differential scanning calorimetry, respectively. Additionally, thermal analysis was performed in order to evaluate the thermal stability a higher temperatures and, also to identify the optimum temperature range of the thermal post-processing. The measured values of the ionic conductivities were in the range of 10 −4 Ω −1 ·cm −1 to 10 −3 Ω −1 ·cm −1 at room temperature, but exhibited an increasing behavior as a function of temperature reaching a level of the order 10 −2 Ω −1 · cm −1 above 200 °C. The thermal conductivity varies only slowly as a function of temperature but its level depends on the composition. The apparent specific heat depends also on the composition and exhibits enthalpy changes due to phase transitions at higher temperatures for LAGP samples with x > 0.5. The compositional dependencies of the ionic and thermal transport properties are not simply correlated. However, the compound with the highest Li-doping level shows the highest ionic conductivity but the lowest thermal conductivity, while the lowest doping level is associated with highest thermal conductivity but the lowest ionic conductivity.LAGP glasses were prepared using the melt-quench-route, which has been successfully proved in former studies [6,10]. Li 2 CO 3 (Fluka, 99.0 %), Al 2 O 3 (Sigma-Aldrich, 98.5 %), P 2 O 5 (Analar Normapur, 99.1 %) and GeO 2 (Alfa Aesar,