The application of ultrahigh vacuum surface analytical techniques to the study of the oxidation of Al-Pd-Mn and Al-Cu-Fe quasicrystals is presented. Comparisons of the effects of various oxidation environments are made for each material as well as for a cubic phase of Al-Pd-Mn. We find that the oxidation of the two icosahedral alloys is similar. Exposure to oxygen in vacuum, normal air, humid air and immersion in water represent progressively better oxidizing environments, resulting in increasingly deeper oxides. Oxidation of Al occurs most readily, but oxidation of other metals also becomes apparent upon going from oxygen in vacuum to immersion in water; which also attests to the effectiveness of water as an oxidant. Oxide thicknesses for both quasicrystalline alloys are comparable for each oxidation environments. Comparison of quasicrystalline to cubic Al-Pd-Mn shows that the cubic phase is more readily oxidized. In addition, while the surfaces of both quasicrystalline alloys become significantly enriched in Al upon oxidation, such enrichment is not observed for the cubic alloy. This suggests that the structure of quasicrystals plays an important role in their oxidation chemistry.