The natural oxidation of amorphous CuxZr1-x (x = 0.33, 0.5, 0.67 and 0.75) alloys has been studied by X-ray diffraction, scanning electron microscopy, X-ray photoelectron spectroscopy and cross-sectional transmission electron microscopy. It is revealed that passivation behavior occurs for amorphous CuxZr1-x alloys where x <= 0.67, which provides an effective composition range of amorphous CuZr alloys for long time service. A thin (2-5 nm) ZrO2 film is formed on top of amorphous alloys, with a Cu-enriched amorphous alloy layer at below. Surprisingly, tetragonal ZrO2 nucleates between the oxide film and the alloy at room temperature in the naturally oxidized am-Cu0.33Zr0.67 alloy. Amorphous Cu2O layer forms on top of the oxide film and surface segregation forming metallic Cu occurs for amorphous CuxZr1-x when x >= 0.75.