The present invention relates to a process for the hydrogenation, in particular the selective hydrogenation of unsaturated hydrocarbon compounds, such as the selective hydrogenation of acetylene to ethylene, using a hydrogenation catalyst comprising an ordered intermetallic compound, namely an ordered cobalt-aluminum or iron-aluminum intermetallic compound. According to another aspect, the present invention relates to a catalyst comprising a support and at least one specific ordered cobalt-aluminum and/or iron-aluminum intermetallic compound supported thereon, as well as to the use of specific ordered intermetallic cobalt-aluminum and iron-aluminum intermetallic compounds as catalysts. The ordered cobalt-aluminum and iron-aluminum intermetallic compounds proved to be highly selective and long-term stable catalysts, e.g. in the selective hydrogenation of acetylene to ethylene in a large excess of ethylene.