We report a systematic study of the face-centered-cubic compounds Yb XCu4 (X=Ag, Au, Cd, Mg, Tl, and Zn), as well as their corresponding nonmagnetic analogues LuXCu4. X-ray diffraction, heat capacity, magnetic susceptibility, high-field magnetization, electrical resistivity, Hall effect, and LIII-edge absorption measurements have been performed. The compounds have Kondo temperatures that range from about 10 K to nearly 1000 K. Although the single-impurity Kondo model qualitatively describes the physical properties of these materials, the quantitative details are not well described and the quality of the fits varies strongly from compound to compound. Compound-to-compound variations in crystal-electric fields, effective valence, and the strength of f-ligand hybridization effects, as well as the influence of intrinsic disorder, may help to explain these discrepancies. © 1999 American Physical Society.