A process for the hydrogenation of polymers comprising at least one C—C multiple bond in the presence of a catalyst comprising, as active metal, ruthenium alone or together with at least one Group Ib, VIIb or VIIIb metal in an amount of from 0.01 to 30 wt %, based on the total weight of the catalyst, applied to a support, or in the presence of a catalyst comprising, as active metal, palladium alone or together with at least one Group Ib, VIIb or VIIIb metal in an amount of from 0.01 to 30 wt %, based on the total weight of the catalyst, applied to a support, wherein the catalyst is characterized in that from 10 to 50% of the pore volume of the support comprises macropores having a pore diameter in the range of from 50 nm to 10,000 nm and from 50 to 90% of the pore volume of the support comprises mesopores having a pore diameter in the range of from 2 to 50 nm, the sum of said pore volumes being 100%.