Samples of Pd/C and Pd–Ag/C, where C represents carbon nanofibers (CNFs), are synthesized by methane decomposition on a Ni–Cu–Fe/Al2O3 catalyst. The properties of Pd/CNF are studied in the reaction of selective hydrogenation of acetylene into ethylene. It is found that the activity of the catalyst in hydrogenation reaction increases, while selectivity decreases considerably when the palladium content rises. The obtained dependences are caused by the features of palladium’s interaction with the carbon support. At a low Pd content (up to 0.04 wt %) in the catalyst, the metal is inserted into the interlayer space of graphite and the catalytic activity is zero. It is established by EXAFS that the main share of palladium in catalysts of 0.05–0.1 wt % Pd/CNF constitutes the metal in the atomically dispersed state. The coordination environment of palladium atoms consists of carbon atoms. An increase in the palladium content in a Pd/CNF catalyst up to 0.3 wt % leads to the formation of highly dispersed (0.8–1 nm) Pd particles. The Pd/CNF samples where palladium is mainly in the atomically dispersed state exhibit the highest selectivity in the acetylene hydrogenation reaction. The addition of silver to a 0.1 wt % Pd/CNF catalyst initially probably leads to the formation of Pd–Ag clusters and then to alloyed Pd–Ag particles. An increase in the silver content in the catalyst above 0.3% causes the enlargement of the alloyed particles and the palladium atoms are blocked by a silver layer, which considerably decreases the catalytic activity in the selective hydrogenation of acetylene.