The Li-6 and Li-7 MAS-NMR signals of fast ionic conducting Li2-2xMg1+xCl4 have been assigned to the two lithium ion positions of their inverse spinel-type structure. The chemical shift of the two Li-6 signals of Li2MgCl4 is 1.2 and 0.3 ppm compared to (LiCl)-Li-6, that of normal spinel-type (Li2ZnCl4)-Li-6 is 0.2 ppm. Whereas the relative intensities of the Li-6 signals fairly well reflect the occupation factors of the tetrahedral and octahedral sites, the intensities of the Li-7 signals strongly deviate from the occupation factors. This is probably caused by distortion of the Li-7 signals through quadrupolar interaction. The different chemical shift and halfwidth of the signals are discussed with respect to shielding and dipolar interaction. Their change with increasing magnesium content can be explained by formation of vacancies at the tetrahedral sites on substitution of Li+ by Mg2+ and clustering of the randomly distributed Li+ and Mg2+ ions at the octahedral sites.