We generate a bright atomic beam containing laser-cooled rubidium and cesium, and we use this beam to load a mixed-species ultrahigh-vacuum (UHV) magneto-optical trap. We have characterized our two-species atomic beam over a range of operating conditions, and we obtain similar atom fluxes for each species. Within the UHV trap, interspecies inelastic collisions are observed in the form of enhanced decay rates of a given species in the presence of a second trapped species. We analyze the trap decays to obtain a loss rate due to heteronuclear cold collisions, and we compare our result to similar measurements in vapor-cell traps [Phys. Rev. A 63, 033406 (2001)].