The invention offers (a) a method of producing a magnesium-alloy material,
the method being capable of obtaining a magnesium-alloy material having
high strength, (b) a magnesium-alloy material having excellent strength,
and (c) a magnesium-alloy wire having high strength. A molten magnesium
alloy is supplied to a continuous casting apparatus provided with a
movable casting mold to produce a cast material. The cast material is
supplied to between at least one pair of rolls to perform an
area-reducing operation (a rolling operation). The rolling operation is
performed such that pressure is applied to the cast material using the
rolls from at least three directions in the cross section of the cast
material. A magnesium-alloy material obtained through the above-described
production method has a fine crystal structure and is excellent in
plastic processability.