A process for hydrogenating a nitrile rubber comprising a) preparing a catalyst composition by contacting a complex catalyst based on ruthenium or osmium as central metal and bearing at least one ligand which is bound to the ruthenium or osmium central metal in a carbene-like fashion with at least one co-catalyst in a molar ratio of the complex catalyst to the co-catalyst in the range of 1: (20 to below 100) wherein the co-catalyst must contain at least one vinyl group, wherein the co-catalyst has the general formula CH 2 = CRR' in which R is hydrogen and R' represents OR 1 wherein R 1 shall mean C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, -C(=O)(R 2), -C(=O)N(R 2) 2, -[(CH 2) n O] m R 2, -[(CH 2) n O] m -CH=CH 2, or -(CH 2) P -C(R 3) 2 R 4, wherein R 2 are identical or different and represent H, C 1 -C 6 -alkyl, C 5 -C 8 -cycloalkyl, C 2 -C 8 -alkenyl, C 2 -C 8 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, R 3 are identical or different and represent methyl, ethyl or-(CH 2) n -O-CH=CH 2, R 4 represents (CH 2) p -O-CH=CH 2, n is 1, or 2, m is 1, 2, or 3, and p is 0, 1, or 3. and thereafter b) hydrogenating the nitrile rubber in the presence of the catalyst composition formed in step a). a) preparing a catalyst composition by contacting a complex catalyst based on ruthenium or osmium as central metal and bearing at least one ligand which is bound to the ruthenium or osmium central metal in a carbene-like fashion with at least one co-catalyst in a molar ratio of the complex catalyst to the co-catalyst in the range of 1: (20 to below 100) wherein the co-catalyst must contain at least one vinyl group, wherein the co-catalyst has the general formula CH 2 = CRR' in which R is hydrogen and R' represents OR 1 wherein R 1 shall mean C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, -C(=O)(R 2), -C(=O)N(R 2) 2, -[(CH 2) n O] m R 2, -[(CH 2) n O] m -CH=CH 2, or -(CH 2) P -C(R 3) 2 R 4, wherein R 2 are identical or different and represent H, C 1 -C 6 -alkyl, C 5 -C 8 -cycloalkyl, C 2 -C 8 -alkenyl, C 2 -C 8 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, R 3 are identical or different and represent methyl, ethyl or-(CH 2) n -O-CH=CH 2, R 4 represents (CH 2) p -O-CH=CH 2, n is 1, or 2, m is 1, 2, or 3, and p is 0, 1, or 3. and thereafter R is hydrogen and R' represents OR 1 wherein R 1 shall mean C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, -C(=O)(R 2), -C(=O)N(R 2) 2, -[(CH 2) n O] m R 2, -[(CH 2) n O] m -CH=CH 2, or -(CH 2) P -C(R 3) 2 R 4, wherein R 2 are identical or different and represent H, C 1 -C 6 -alkyl, C 5 -C 8 -cycloalkyl, C 2 -C 8 -alkenyl, C 2 -C 8 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, R 3 are identical or different and represent methyl, ethyl or-(CH 2) n -O-CH=CH 2, R 4 represents (CH 2) p -O-CH=CH 2, n is 1, or 2, m is 1, 2, or 3, and p is 0, 1, or 3. OR 1 wherein R 1 shall mean C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 2 -C 6 -alkenyl, C 2 -C 6 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, -C(=O)(R 2), -C(=O)N(R 2) 2, -[(CH 2) n O] m R 2, -[(CH 2) n O] m -CH=CH 2, or -(CH 2) P -C(R 3) 2 R 4, wherein R 2 are identical or different and represent H, C 1 -C 6 -alkyl, C 5 -C 8 -cycloalkyl, C 2 -C 8 -alkenyl, C 2 -C 8 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, R 3 are identical or different and represent methyl, ethyl or-(CH 2) n -O-CH=CH 2, R 4 represents (CH 2) p -O-CH=CH 2, n is 1, or 2, m is 1, 2, or 3, and p is 0, 1, or 3. R 2 are identical or different and represent H, C 1 -C 6 -alkyl, C 5 -C 8 -cycloalkyl, C 2 -C 8 -alkenyl, C 2 -C 8 -alkynyl, phenyl, imidazolyl, triazolyl, or pyridinyl, R 3 are identical or different and represent methyl, ethyl or-(CH 2) n -O-CH=CH 2, R 4 represents (CH 2) p -O-CH=CH 2, n is 1, or 2, m is 1, 2, or 3, and p is 0, 1, or 3. b) hydrogenating the nitrile rubber in the presence of the catalyst composition formed in step a).