A process for selectively hydrogenating carbon-carbon double bonds in a diene-based polymer comprising subjecting the diene-based polymer which is present in an aqueous suspension to a hydrogenation by contacting the diene-based polymer with a catalytically active system characterized in that (i) the catalytically active system is based on a first main catalyst component having either the general formula (Ia) MQ x ·aH 2 O (Ia) wherein M is a group VIII transition noble metal, preferably rhodium, ruthenium, osmium or iridium, Q is identical or different, and a hydride or an anion other than a hydride, x is 1, 2, or 3, and a is in the range of from 0 to 3, or having the general formula (Ib) RhQ'Ly (Ib) wherein Q' is a hydride or an anion other than a hydride, y is 1, 2, 3 or 4, and L is identical or different and a water-soluble ligand and on a secondary water-insoluble catalyst component having either the general formula (IIa) or the general formula (IIb) R 1 m D (IIa) (R 2) 2 E-A-E(R 2) 2 (IIb) in which R 1 is identical or different and represents hydrogen, alkyl, preferably C 1 -C 8 -alkyl, aryl, preferably C 6 -C 15 -aryl, cycloalkyl, preferably C 4 -C 8 -cycloalkyl, or aralkyl, preferably C 7 -C 15 -aralkyl, D is phosphorus, nitrogen, arsenic, sulfur, or a sulphoxide group S=O, and m is 2 or 3, R 2 is identical or different and represents hydrogen, alkyl, preferably C 1 -C 8 -alkyl, aryl, preferably C 6 -C 15 -aryl, cycloalkyl, preferably C 4 -C 8 -cycloalkyl or aralkyl, preferably C 7 -C 15 -aralkyl, E is phosphorus, or arsenic, A represents either a single bond or a divalent spacer group, preferably phenylene or a -(CH 2) n - group with n being an integer from 1 to 20 and (ii) the catalytically active system is prepared in-situ in the presence of an aliphatic C 1 to C 5 alcohol. (i) the catalytically active system is based on a first main catalyst component having either the general formula (Ia) MQ x ·aH 2 O (Ia) wherein M is a group VIII transition noble metal, preferably rhodium, ruthenium, osmium or iridium, Q is identical or different, and a hydride or an anion other than a hydride, x is 1, 2, or 3, and a is in the range of from 0 to 3, or having the general formula (Ib) RhQ'Ly (Ib) wherein Q' is a hydride or an anion other than a hydride, y is 1, 2, 3 or 4, and L is identical or different and a water-soluble ligand and on a secondary water-insoluble catalyst component having either the general formula (IIa) or the general formula (IIb) R 1 m D (IIa) (R 2) 2 E-A-E(R 2) 2 (IIb) in which R 1 is identical or different and represents hydrogen, alkyl, preferably C 1 -C 8 -alkyl, aryl, preferably C 6 -C 15 -aryl, cycloalkyl, preferably C 4 -C 8 -cycloalkyl, or aralkyl, preferably C 7 -C 15 -aralkyl, D is phosphorus, nitrogen, arsenic, sulfur, or a sulphoxide group S=O, and m is 2 or 3, R 2 is identical or different and represents hydrogen, alkyl, preferably C 1 -C 8 -alkyl, aryl, preferably C 6 -C 15 -aryl, cycloalkyl, preferably C 4 -C 8 -cycloalkyl or aralkyl, preferably C 7 -C 15 -aralkyl, E is phosphorus, or arsenic, A represents either a single bond or a divalent spacer group, preferably phenylene or a -(CH 2) n - group with n being an integer from 1 to 20 and M is a group VIII transition noble metal, preferably rhodium, ruthenium, osmium or iridium, Q is identical or different, and a hydride or an anion other than a hydride, x is 1, 2, or 3, and a is in the range of from 0 to 3, Q' is a hydride or an anion other than a hydride, y is 1, 2, 3 or 4, and L is identical or different and a water-soluble ligand R 1 is identical or different and represents hydrogen, alkyl, preferably C 1 -C 8 -alkyl, aryl, preferably C 6 -C 15 -aryl, cycloalkyl, preferably C 4 -C 8 -cycloalkyl, or aralkyl, preferably C 7 -C 15 -aralkyl, D is phosphorus, nitrogen, arsenic, sulfur, or a sulphoxide group S=O, and m is 2 or 3, R 2 is identical or different and represents hydrogen, alkyl, preferably C 1 -C 8 -alkyl, aryl, preferably C 6 -C 15 -aryl, cycloalkyl, preferably C 4 -C 8 -cycloalkyl or aralkyl, preferably C 7 -C 15 -aralkyl, E is phosphorus, or arsenic, A represents either a single bond or a divalent spacer group, preferably phenylene or a -(CH 2) n - group with n being an integer from 1 to 20 (ii) the catalytically active system is prepared in-situ in the presence of an aliphatic C 1 to C 5 alcohol.