Magnesium alloys having long-period stacking order phases

Magnesium alloys comprising a long period stacking order (LPSO) phase having an 14H-i or an 18R-i structure are provided. The alloys comprise magnesium as a majority element, a first alloying element that is larger than magnesium and a second alloying element that is smaller than magnesium. The first alloying elements include non-rare earth elements.