The stability of PdRu/Ru(0001) and PtRu/Ru(0001) surface alloys and the tendency for surface segregation of Pd and Pt subsurface guest metals in these surface alloys is studied by scanning tunneling microscopy (STM) and Auger electron spectroscopy (AES). Atomic resolution STM imaging and AES measurements reveal that upon overgrowing the surface alloys with a 1-2 monolayer Ru film and subsequent annealing to the temperatures required for initial surface alloy formation, the Ru-covered Pd (Pt) atoms float back to the outermost layer. The lateral distribution of these species is also essentially identical to that of the initial surface alloys, before overgrowth by Ru. In combination, this clearly demonstrates that the surface alloys represent stable surface configurations, metastable only towards entropically favored bulk dissolution, and that there is a distinct driving force for surface segregation of these species. Consequences of these data on the mechanism for surface alloy formation are discussed.