A high-resolution photoemission (PES) study of the heavy-fermion compound YbAl3 has been undertaken to test the qualitative and quantitative predictions of the single-impurity model. Corroborating data on YbAgCu4 and YbCu2Si2 are also presented. For Yb-based heavy fermions the model predicts a fully occupied Kondo resonance so that its width, intensity, and temperature dependence should be directly accessible by PES. Due to the existence of temperature- and/or contamination-dependent surface features, which are not dealt with by the model, a rigorous normalization and curve-fitting procedure was required to extract the bulk 4f line shape. For the particular temperature cycling method employed by us, we do not observe any temperature dependence in the peak that had been previously identified as the Kondo resonance. We find that both the binding energy and width of this peak are significantly larger than theory predicts. It is also found that the trends in 4f line shape and surface shift between YbAl3 and LuAl3 are consistent with the trends seen between the 4f core levels of elemental Yb and Lu. Similar results are also found in YbCu2Si2 and YbAgCu4 for similar cycling methods. Recent observations of temperature dependence in these systems are most easily understood in terms of surface phenomena. © 1993 The American Physical Society.