Thermally crystallized glasses of compositions (Li2,O2, MgO).Al2O3.nSiO2 were studied by X‐ray powder diffraction methods. High‐quartz solid solution phases developed at relatively low temperatures and, for n 3.5, transformed at higher temperatures to keatite solid solution phases. Associated phases, if present, were Mg spinel and/or cordierite, or a few other trace phases. The a crystallographic axis (a0) of high‐quartz solid solutions decreased with increase of MgO and/or SiO2. The c crystallographic axis (c0) decreased with increasing MgO; it also decreased with increasing SiO2, but only when MgO content was low. X‐ray diffraction photographs of single crystals of high‐quartz solid solutions of compositions LiaO.Al2O3.nSiO3 demonstrated that the maintenance of a basic high‐quartz structure is the basis of the solid solution relation. Three modifications of the high‐quartz structure were recognized in the Li2O‐Al2O3−SiO3 system. These modifications were based on the occurrence and positions of superlattice reflections. The high‐quartz solid solution from Li2O Al2O3−2SiO2, showing streaky reflections in its precession photographs, suggested a defective structure. The term “high‐quartz solid solution,” with or without additional prefixes specifying the compositional series and modification, was considered the preferred nomenclature for these solid solution phases. Copyright © 1968, Wiley Blackwell. All rights reserved