A process for the hydrogenation of double or triple bonds between carbon atoms in unsaturated hydrocarbon compounds in the presence of a catalytic composition comprising a polar non-aqueous solvent which is ionic in nature and liquid at a temperature below 150.degree. C. mainly containing at least one molten quaternary ammonium and/or phosphonium salt with general formula Q.sup.+ A.sup.-, where Q.sup.+ represents a quaternary ammonium and/or phosphonium cation, and A.sup.- represents an anion, said composition also comprising at least one compound of at least one transition metal from groups 8, 9 or 10 dissolved in said non-aqueous solvent, said non-aqeuous solvent optionally further comprising an organic solvent in an amount less than said molten salt.