Process for hydrogenation of ketones having at least a carbon-carbon double bond in the γ, δ -position to the keto group by hydrogen in the presence of at least one chiral iridium complex of formula wherein n is 1 or 2; X 1 and X 2 are independently from each other hydrogen atoms, C 1-4 -alkyl, C 5-7 -cycloalkyl, adamantyl, phenyl (optionally substituted with one to three C 1-5 -alkyl, C 1-4 -alkoxy, C 1-4 -perfluoroalkyl groups and/or one to five halogen atoms)), benzyl, 1-naphthyl, 2-naphthyl, 2-furyl or ferrocenyl; Z 1 and Z 2 are independently from each other hydrogen atoms, C 1-5 -alkyl or C 1-5 -alkoxy groups; Y is an anion, particularly selected from the group consisting of halide, PF 6 -, SbF 6 -, tetra(3,5-bis(trifluoromethyl)phenyl)borate(BAr F -), BF 4 -, perfluorinated sulfonates, preferably F 3 C-SO 3 - or F 9 C 4 -SO 3 -; ClO 4 -, Al(OC 6 F 5) 4 -, Al(OC(CF 3) 3) 4 -, N(SO 2 CF 3) 2 - N(SO 2 C 4 F 9) 2 - and B(C 6 F 5) 4 -; R 1 represents a group of formula or or wherein R 2 and R 3 represent either both H or an C 1 -C 4 -alkyl group or represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups R 4 and R 5 represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups; R 6 and R 7 and R 8 represent each a C 1 -C 4 -alkyl group; R 9 and R 10 represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups; and wherein * represents the chiral centre of the catalyst of formula; and the dotted line represents the bond by which formula or or is bound to the rest of formula; wherein the ketones having at least a carbon-carbon double bond in the γ, δ -position to the keto group have two aliphatic carbon atoms between the keto group and the carbon-carbon double bond; and wherein the ketones having at least a carbon-carbon double bond in the γ, δ-position to the keto group have an additional alkyl substituent in the δ-position so that a chiral centre is produced in the δ-position of the hydrogenated product. wherein n is 1 or 2; X 1 and X 2 are independently from each other hydrogen atoms, C 1-4 -alkyl, C 5-7 -cycloalkyl, adamantyl, phenyl (optionally substituted with one to three C 1-5 -alkyl, C 1-4 -alkoxy, C 1-4 -perfluoroalkyl groups and/or one to five halogen atoms)), benzyl, 1-naphthyl, 2-naphthyl, 2-furyl or ferrocenyl; Z 1 and Z 2 are independently from each other hydrogen atoms, C 1-5 -alkyl or C 1-5 -alkoxy groups; Y is an anion, particularly selected from the group consisting of halide, PF 6 -, SbF 6 -, tetra(3,5-bis(trifluoromethyl)phenyl)borate(BAr F -), BF 4 -, perfluorinated sulfonates, preferably F 3 C-SO 3 - or F 9 C 4 -SO 3 -; ClO 4 -, Al(OC 6 F 5) 4 -, Al(OC(CF 3) 3) 4 -, N(SO 2 CF 3) 2 - N(SO 2 C 4 F 9) 2 - and B(C 6 F 5) 4 -; R 1 represents a group of formula or or wherein R 2 and R 3 represent either both H or an C 1 -C 4 -alkyl group or represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups R 4 and R 5 represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups; R 6 and R 7 and R 8 represent each a C 1 -C 4 -alkyl group; R 9 and R 10 represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups; wherein R 2 and R 3 represent either both H or an C 1 -C 4 -alkyl group or represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups R 4 and R 5 represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups; R 6 and R 7 and R 8 represent each a C 1 -C 4 -alkyl group; R 9 and R 10 represent a divalent group forming together a 6-membered cycloaliphatic or an aromatic ring which optionally is substituted by halogens atoms or by C 1 -C 4 -alkyl groups or by C 1 -C 4 -alkoxy groups;