In this work, we present results of a periodic density-functional theory study of the adsorption of carbon monoxide (CO) and hydroxyl (OH) on platinum, ruthenium, and a series on platinum-ruthenium alloys. The surfaces are modeled as four-layer slabs. The binding energies and geometries of CO and OH are computed, as well as the vibrational properties of chemisorbed CO. We find that the mixing of Pt by Ru. leads to a weaker bond of both CO and OH to the Pt sites, whereas mixing of Ru by Pt causes a stronger, bond of CO and OH to the Ru sites. The binding energy trends for CO do not show a clear-cut relationship with its vibrational characteristics. The binding energy changes are electronic alloying effects that can be explained by the d band shift model of Hammer and Norskov. From our calculations, we can conclude that for a good CO oxidation fuel cell catalyst, it is important to have both Pt sites (which bind CO weakly) and Ru sites (which bind OH strongly) on the surface. However, if a low surface coverage of CO is required, which may be case for the oxidation of 112 in the presence of a small amount of CO, Ru with a monolayer of Pt might be more advantageous, as this is the Pt-Ru surface that shows the weakest CO binding.