Process for treating subterranean oil-bearing formations comprising carbonate rocks wherein the process comprises at least the following steps • injecting an aqueous composition comprising at least one cationic surfactant into at least a portion of the oil-bearing formation, • allowing the composition to interact with oil-wet surfaces in the formation, wherein the cationic surfactant has general formula [R 1 -N(R 2)(R 3)(R 4)] + 1/mX m-, and R 1, R 2, R 3, R 4 and X m- have the following meaning: R 1: a group selected from the group of R 1a and R 1b wherein R 1a is an aliphatic linear or branched hydrocarbon radical having from 10 to 22 carbon atoms, and R 1b is an aliphatic linear or branched hydrocarbon radical having from 10 to 22 carbon atoms substituted by 1 to 3 OH-groups, and R 2, R 3, and R 4 may be the same or different and are selected from the group of R 2a, R 3a, R 4a: alkyl groups having from 1 to 4 carbon atoms, R 2b, R 3b, R 4b: OH-substituted alkyl groups having from 1 to 4 carbon atoms, and R 2c, R 3c, R 4c: alkylether groups of the formula -CH 2 CH 2 OCH 2 CH 2 OH and -CH 2 CH 2 OCH 2 CH 2 OCH 2 CH 2 OH, and X m- is an anion, wherein m is 1, 2, or 3, with the proviso, that at least one of the groups R 1, R 2, R 3, and R 4 comprises an OH-group and the total number of OH groups in the surfactant is from 1 to 4, and wherein the process is a process for enhanced oil recovery, wherein the aqueous composition is injected into the hydrocarbon containing subterranean formation through at least one injection well, the injected water flows through the subterranean formation towards a production well, thereby detaching oil from oil-wet surfaces of the formation, and producing a mixture comprising oil and water from the formation through at least one production well. • injecting an aqueous composition comprising at least one cationic surfactant into at least a portion of the oil-bearing formation, • allowing the composition to interact with oil-wet surfaces in the formation, wherein the cationic surfactant has general formula [R 1 -N(R 2)(R 3)(R 4)] + 1/mX m-, and R 1, R 2, R 3, R 4 and X m- have the following meaning: R 1: a group selected from the group of R 1a and R 1b wherein R 1a is an aliphatic linear or branched hydrocarbon radical having from 10 to 22 carbon atoms, and R 1b is an aliphatic linear or branched hydrocarbon radical having from 10 to 22 carbon atoms substituted by 1 to 3 OH-groups, and R 2, R 3, and R 4 may be the same or different and are selected from the group of R 2a, R 3a, R 4a: alkyl groups having from 1 to 4 carbon atoms, R 2b, R 3b, R 4b: OH-substituted alkyl groups having from 1 to 4 carbon atoms, and R 2c, R 3c, R 4c: alkylether groups of the formula -CH 2 CH 2 OCH 2 CH 2 OH and -CH 2 CH 2 OCH 2 CH 2 OCH 2 CH 2 OH, and X m- is an anion, wherein m is 1, 2, or 3, with the proviso, that at least one of the groups R 1, R 2, R 3, and R 4 comprises an OH-group and the total number of OH groups in the surfactant is from 1 to 4, and wherein the process is a process for enhanced oil recovery, wherein the aqueous composition is injected into the hydrocarbon containing subterranean formation through at least one injection well, the injected water flows through the subterranean formation towards a production well, thereby detaching oil from oil-wet surfaces of the formation, and producing a mixture comprising oil and water from the formation through at least one production well. R 1: a group selected from the group of R 1a and R 1b wherein R 1a is an aliphatic linear or branched hydrocarbon radical having from 10 to 22 carbon atoms, and R 1b is an aliphatic linear or branched hydrocarbon radical having from 10 to 22 carbon atoms substituted by 1 to 3 OH-groups, and R 1a is an aliphatic linear or branched hydrocarbon radical having from 10 to 22 carbon atoms, and R 1b is an aliphatic linear or branched hydrocarbon radical having from 10 to 22 carbon atoms substituted by 1 to 3 OH-groups, and R 2, R 3, and R 4 may be the same or different and are selected from the group of R 2a, R 3a, R 4a: alkyl groups having from 1 to 4 carbon atoms, R 2b, R 3b, R 4b: OH-substituted alkyl groups having from 1 to 4 carbon atoms, and R 2c, R 3c, R 4c: alkylether groups of the formula -CH 2 CH 2 OCH 2 CH 2 OH and -CH 2 CH 2 OCH 2 CH 2 OCH 2 CH 2 OH, and R 2a, R 3a, R 4a: alkyl groups having from 1 to 4 carbon atoms, R 2b, R 3b, R 4b: OH-substituted alkyl groups having from 1 to 4 carbon atoms, and R 2c, R 3c, R 4c: alkylether groups of the formula -CH 2 CH 2 OCH 2 CH 2 OH and -CH 2 CH 2 OCH 2 CH 2 OCH 2 CH 2 OH, and X m- is an anion, wherein m is 1, 2, or 3,