In this article, the authors present aluminium-27 MAS and triple quantum MAS NMR data, collected at 14.1 and 18.8 T magnetic fields, for two samples of Libyan Desert Glass. The spectra are unusually broad and unresolved, and can be best simulated by NMR parameters consistent with a predominance of tetrahedral aluminium in highly distorted sites (chemical shifts about 50-60ppm, quadrupolar coupling constants Co of 12-15 MHz). A triple quantum spectrum reveals as well the presence of a small percentage of sites with much smaller Co values, consistent with previous NMR studies at a lower field, which probably could not reveal the high Co sites. Annealing of several samples did not produce major changes in the spectra of the glasses.