To obtain an equilibrium between titanium and magnesium at high temperatures, an air-tight titanium container, in whlch a magnesium rod or a mixture of titanium and magnesium in equal parts was placed, was heated to various temperatures up to 1200 C. The results of microscopic, x-ray, and electron diffraction studies confirmed that no intermetallic compound (such as Mg/ sub 2/Ti) occurs in the titanium--magnesium system. It was also found that the solubility of titanium in magnesium is 0.85 wt.% at 1200 C, 0.30 wt.% at 900 C, and 0.17 wt.% at 700 C. In all cases these results are higher than those found previously. With respect to the solubility of magnesium in titanium, it is doubtful whether the results obtained correspond to the equilibrium state. However, it was found that magnesium dissolves in solid titanium to at least 0.68 wt.% at 1100 C. A phase diagram of the magnesium--titanium system was proposed and is given. (tr-auth)