The invention relates to a method for selective hydrogenation of a hydrocarbon feedstock that contains at least 2 carbon atoms per molecule and that has a final boiling point that is less than or equal to 250° C. and that comprises at least one polyunsaturated compound, in which in the presence of hydrogen, said feedstock is brought into contact with at least one catalyst that comprises a substrate and an active metal phase deposited on said substrate; said active metal phase comprises copper and at least one metal that is selected from between nickel and cobalt in a molar ratio of Cu:(Ni and/or Co) of greater than 1.