The quasicrystal structure of primary intermetallic particles found in the as-cast microstructure of a permanent mould-cast Mg-8 wt% Zn-4 wt% Al alloy has been characterized using transmission electron microscopy. Most primary intermetallic particles have an average composition of Mg9±2Zn4±1Al3±1 and a primitive icosahedral structure, with a quasilattice parameter of 0.515 nm and a point group of m3̄5̄. The metastable quasicrystalline phase persists for extended periods at elevated temperatures; while the volume fraction decreases with thermal exposure at 325 °C, the decrease is small up to 120 h and a fraction persists after 720 h. There is no evidence of transformation of or within the quasicrystalline phase during this period. Instead, the metastable quasicrystalline phase is gradually replaced by the equilibrium Φ phase (Mg21(Al, Zn)17; space group, Pbcm). The relationship between the quasicrystalline phase, its cubic approximant T phase (Mg32(Al, Zn)49; space group, Im3̄) and the Φ phase is discussed.