Palladium nanoparticles catalyze the reduction of Ag+ ions with hydrogen on their surface, thereby leading to the formation of bimetallic particles with the “core–shell” structure. The catalytic reaction of methylviologen reduction with hydrogen at ratio [Ag] : [Pd] > 1 is suppressed by silver atoms located on the surface of palladium nanoparticles. At [Ag] : [Pd] ≤ 1, the reduction takes place; however, it is preceded by an induction period, and, the higher the silver content on the nanoparticle surface, the longer the induction period. The rate constant of the catalytic reduction, which begins after the end of the induction period, decreases with increasing silver content on the surface of palladium nanoparticles.