Formation of icosahedral quasicrystalline phase (i-phase) was investigated for Mg-Al-X (X=Co, Ni, Cu, Rh, Ag, Pt and Au) ternary systems. A Mackay-icosahedron (MI) type i-phase was found to form in the Mg-Al-Rh system at the composition Mg8Al68Rh24. The i-phase has the F-type ordered structure and the quasilattice constant is 0.447nm. Differential thermal analysis (DTA) studies showed that the i-phase has a high stability. On the other hand, the formation of a Frank-Kasper (FK) type i-phase was found in the Mg-Al-Pt system at the composition Mg45Al42Pt13. The conditions necessary for the formation of the i-phases are discussed in terms of the atomic radius ratio and the electronegativity as well as the electron-per-atom ratio.