Four homogeneous solid solutions were found in the silver‐magnesium alloy system. The &agr;‐primary solid solution of magnesium in silver has a f.c.c. structure. The &bgr;‐solid solution has a b.c.c. structure. The &ggr;‐solid solution appears to have a complicated structure. While others have identified it as hexagonal, no definite structure could be assigned to it from our diffraction data. The &dgr;‐solid solution has a h.c.p. structure of magnesium.The lattic parametera0in the &agr;‐solid solution increases with increasing magnesium concentration but exhibits a marked negative deviation from Vegard's Law. Thea0in the &bgr;‐solid solution, however, increases linearly with increasing magnesium concentration.Silver and magnesium atoms are distributed at random in the &agr;‐phase but take up preferred positions in the &bgr;‐phase. The ordering process takes place throughout the &bgr;‐phase, but is most nearly complete in the region of 50 atomic percent Mg.