The reactivity of prospective capping-layer extreme-ultraviolet (EUV) mirror materials with hydrocarbons is studied in the gas phase by use of mass spectroscopy of metal-oxide clusters. We report the results of chemistry studies for ${\mathrm{Si}}_m$ , ${\mathrm{Ti}}_m$ , ${\mathrm{Hf}}_m$ , and ${\mathrm{Zr}}_m{\mathrm{O}}_n$ metal-oxide clusters in which the reaction products were ionized with little or no fragmentation by $26.5\mathrm{eV}$ photons from a desktop-size $46.9\mathrm{nm}$ Ne-like Ar laser. Hf and Zr oxides are found to be much less reactive than Si or Ti oxides in the presence of EUV light. The results are relevant to the design of EUV mirror capping layers that are resistant to carbon contamination.