In order to follow and understand time dependent contamination growth on multilayer mirrors for extreme ultraviolet (EUV) lithography applications, particular heterosystems were investigated with X-ray Photoemission Spectroscopy (XPS). Diverse capping layers can be used to terminate EUV multilayer mirrors to protect the underlying multilayer stack, e.g. Ru metal. In XPS problems were encountered when analyzing spectra as the core-level signals of Ru and C overlap. Further, Ru was not only present as pure metal, but also in its oxidized state. Disentangling the overlapping XPS spectra was achieved by application of factor analysis (FA) yielding not only the spectra of each component but also the according weights. Thus a model for the time dependent contamination growth was developed. This model was cross checked by advanced inelastic background analysis. Both methods displayed a way to unravel overlapping data sets and for deducing multilayer composition models.