Li-7-NMR measurements of the mixed ionic-electronic conductor beta-LixAl1-x are presented for compositions covering the entire range of the beta-phase. From NMR spectra the Knight shift K at room temperature was obtained as K < 5 ppm in accordance with theoretical predictions. The measurements of the SLR rate T1(-1) revealed two regions of different dependences of the SLR rate on temperature T. Below 100 K a linear dependence T1T = const is observed which is assigned to coupling of conduction electrons. Above 100 K a sharp rise of the SLR rate and a maximum in T1(-1)(T) is found. The dependence of T1(-1) on the Larmor frequency is weaker than predicted by the standard theory for diffusion induced SLR. Here the SLR which is predominantly dipolar is described with spectral density functions typical for SLR in disordered ionic conductors. The deviation from the standard SLR behaviour is found to increase with the total concentration of defects.