The purpose of this study is a search for compositional ranges available to replace expensive heavy rare-earth elements (Gd, Dy) by a cheaper element such as Nd on keeping the heat resistance. The equilibrium phase diagrams of magnesium-rich portion of ternary alloys are made. Investigated compositional ranges are less than 9 masss%Gd or Dy, and less than 7 mass%Nd, and aging characteristics in such compositional ranges were investigated. Alloys with 3 mass%Nd have a single phase of magnesium solid solution(α-phase)at 535°C, but their solubility limits of Gd or Dy shift largely to lower concentration than those of M-Gd or-Dy binary alloys with decreasing temperature. Even alloys containing the smallest content of heavy rare earth elements such as Mg-3 mass%Gd(Dy)-3 mass%Nd alloys show marked age hardenlng even at 250°C. Aging characterlstlcs, mechanlcal property, and corroslon reslstance of Mg-5, 6, 7 mass%Gd(Dy)-3 mass%Nd alloys with zirconium as a grain refinement agent are evaluated. The remarkable age hardening is found to be caused by the precipitation of matastableβ"-phase with a D0₁₉ crystal structure from the results of observation of precipitates using a transmission electron microscope. Heat resistance of quaternary alloys containing more than 6 mass%Gd or Dy, and 3 mass%Nd is better than that of WE54A magnesium alloy. Furthermore, the specific strength of these alloys is as high as about twice of the conventional heat resistant aluminum alloys.