NMR studies of (7)Li and (31)P nuclei are reported in the 150-900 K temperature range for the [Formula: see text] NASICON compounds with x = 0.8, 0.7, 0.6 and 0.3. Magic angle spinning (MAS mode) experiments were performed at room temperature on the (7)Li and (31)P nuclei. The linewidth and the spin lattice relaxation times of these nuclei are studied versus temperature in the static mode. The spectra recorded in the MAS mode show that the (7)Li ions occupy three chemical sites, the occupation of which being very sensitive to the x values but not sensitive to the coexistence of the two varieties [Formula: see text] and [Formula: see text] observed at room temperature in compounds with x≤0.5. On the other hand, the (31)P nucleus MAS spectra are very sensitive to lithium content but also to the variety coexistence. T(1) measurements were performed in a static mode on the (7)Li and (31)P nuclei. In all the compounds, the (7)Li spin lattice relaxation time exhibits two branches with several minima, indicating the complex dynamics for this ion. One of these minima appears in the same temperature range as the minimum of the (31)P nucleus T(1), strongly suggesting a cross-relaxation process between these nuclei. T(1ρ) measurements on (7)Li (static mode) allow us to show a slow motion different from the one probed by the T(1). The analysis of the T(1ρ) behaviour with temperature and composition allows us to ascribe the motion probed by this time to the oxygen ion motion which monitors the opening and closing of the lithium pathways. A qualitative interpretation of the (7)Li T(1) results is done; it takes into account the cross-relaxation phenomena between (31)P and (7)Li and quadrupolar fluctuations.