Provided are a magnesium alloy which is inexpensive, can be produced at a high yield, and has both high strength and high ductility; and a production process of the magnesium alloy. The magnesium alloy contains from 1 to 4 atomic % of Zn and from 1 to 4.5 atomic % of Y at a Zn/Y composition ratio ranging from 0.6 to 1.3, and contains both an intermetallic compound Mg 3 Y 2 Zn 3 , and Mg 12 YZn having a long period structure. It may contain from 2 to 3.5 atomic % of Zn and from 2 to 4.5 atomic % of Y at a Zn/Y composition ratio falling within a range of from 0.8 to 1.2. It may contain from 1 to 4 atomic % of Zn, from 1 to 4.5 atomic % of Y and from 0.1 to 0.5 atomic % of Zr and contains, as a remaining portion, Mg and inevitable impurities. An alloy structure having both an intermetallic compound Mg 3 Y 2 Zn 3 and Mg 12 YZn having a long period structure is available by casting an Mg alloy containing from 1 to 4 atomic % of Zn and from 1 to 4.5 atomic % of Y at a Zn/Y composition ratio ranging from 0.6 to 1.3, followed by plastic processing.