Oxidation of Al-Cu-Fe and Al-Pd-Mn quasicrystals as compared to related crystalline phases was studied in air at high temperatures. Parabolic rate constants at 840 o C were about 6x10 - 1 2 g 2 cm - 4 s - 1 for icosahedral Al-Cu-Fe, but only 3x10 - 1 3 g 2 cm - 4 s - 1 for cubic AlFe. The oxide layer formed on the icosahedral alloy was inhomogeneous with respect to the oxide growth morphology. Oxide compositions were studied by Auger electron spectroscopy (AES) and X-ray induced photo electron spectroscopy (XPS). The θ-Al 2 O 3 layer on Al-Cu-Fe did not contain any quantities of Cu or Fe that were significant according to the analyses by AES and XPS. In an advanced oxidation stage the θ-Al 2 O 3 layer was penetrated by α-Al 2 O 3 nodules, which contained about 5% Cu.Oxidation of Al-Pd-Mn quasicrystals was found to be strongly influenced by evaporation of Mn. Whereas the formation of δ-Al 2 O 3 was observed at 800 o C on Al-Pd-Mn quasicrystals followed by growth of needle-like θ-Al 2 O 3 , oxidation of hot isostatically pressed (HIPed) specimens at 850 o C led to the formation of a θ-Al 2 O 3 layer containing also extremely thin areas. The metallic Al(LMM) Auger peak observed in these areas was four times the oxidic Al(LMM) peak. Neither in the thick nor the thin oxide areas were Pd or Mn observed.