Our goal is to provide insights into surface processes that affect the reflectivity and lifetimes of TiO2 and Rucapped multilayer mirrors used in extreme ultraviolet (EUV) lithography. Several surface-sensitive ultrahigh-vacuum techniques are used to characterize thermally-induced and electron-induced surface reactions of methyl methacrylate (MMA), a model for hydrocarbons found in EUV lithography vacuum chambers; low-energy electron beams are used to mimic excitations initiated by EUV radiation. Carbon film growth is measured on TiO2 surfaces during electron bombardment (at 20 eV and 100 eV) in MMA vapor; C growth rates are compared on Ru surfaces. The initial rates on the clean surfaces are very different: a C film grows more rapidly on TiO2 than on Ru. However, the limiting growth rates are the same for C thicknesses greater than ~1 to 1.5 nm, when MMA interacts with a C film. Irradiation of the C films in O2 gas, or in MMA + O2, has a mitigating effect on TiO2 surfaces.