The catalytic characteristics of Pd–Ag/Al2O3 bimetallic catalysts with an Ag/Pd atomic ratio of 0.03–3.0 have been studied in the selective liquid-phase hydrogenation of diphenylacetylene and 1-phenyl-1-propyne. It has been found that an increase in the Ag/Pd ratio leads to a significant increase in selectivity, which, however, is accompanied by a decrease in the catalyst activity. Comparison with data of an earlier structural study suggests that an increase in selectivity observed with an increase in the Ag/Pd ratio to 0.5–1.0 is attributed to the following two factors: (1) the suppression of the formation of palladium hydride and (2) an increase in the fraction of “single-atom” Pd1 sites isolated from each other by Ag atoms on the surface of the Pd–Ag nanoparticles. An increase in the Ag/Pd value to 2.0–3.0 leads to a further increase in the selectivity, which exceeds the selectivity of a commercial Lindlar catalyst (Pd–Pb/CaCO3). In this case, the most probable cause of the high selectivity is the formation of the single-atom Pd1 sites on the surface of the Pd–Ag alloy and an increase in the stability of the structure.