A process for preparing hydroperoxy alcohols with the following formula (Ia) and/or (Ib): R 1 -CR 4 -CR 3 -R 2 (Ia) R 2 -CR 3 -CR 4 -R 1 ( Ib) wherein R 1 and R 2 are each independently an optionally substituted alkyl group with 1 to 20 carbon atoms or a -L-A group wherein L is a bond or a linear or branched alkylene chain with 1 to 12 carbon atoms, which is optionally substituted, and A is a hydrogen atom or a -COXR group wherein X is an oxygen atom or a -NR' group with R and R' being independently a group selected from a hydrogen atom, a C1-C8 alkyl group, or a-(CH 2)-CH(OCOR 5)-CHOCOR 6 group, with R 5 and R 6 being independently a C8-C22 linear or branched alkyl group which is optionally substituted by at least one hydroperoxy or hydroxyl substituent, or R 1 and R 2 form together a carbocycle consisting of a 6 to 12 membered ring which is optionally substituted. R 3 and R 4 are each independently a hydrogen atom, an optionally substituted alkyl group with 1 to 20 carbon atoms or a group -L-A wherein L is a bond or a linear or branched alkylene chain with 1 to 12 carbon atoms, which is optionally substituted, and A is a hydrogen atom or a -COXR group wherein X is an oxygen atom or a -NR' group with R and R' being independently a group selected from a hydrogen atom, a C1-C8 alkyl group, or a -(CH 2)-CH(OCOR 5)-CHOCOR 6 group, with R 5 and R 6 being independently a C8-C22 linear or branched alkyl group which is optionally substituted by at least one hydroperoxy or hydroxyl substituent, comprising reacting at least one functionalized or unfunctionalized, linear or cyclic, olefin which comprises at least one carbon - carbon double bond with aqueous hydrogen peroxide in a solvent selected from water-soluble carboxylic acids, in the presence of a heterogenous catalyst which is a metallic mixed oxide having formula: M x M' y O z wherein: M is a metal; M' is W or Mo, x is a number from 1 to 10, preferably from 1 to 5, more preferably from 1 to 2; y is a number from 1 to 10, preferably from 1 to 5, more preferably from 1 to 3; z is a number from 1 to 40, preferably from 2 to 20, more preferably from 3 to 15. wherein R 1 and R 2 are each independently an optionally substituted alkyl group with 1 to 20 carbon atoms or a -L-A group wherein L is a bond or a linear or branched alkylene chain with 1 to 12 carbon atoms, which is optionally substituted, and A is a hydrogen atom or a -COXR group wherein X is an oxygen atom or a -NR' group with R and R' being independently a group selected from a hydrogen atom, a C1-C8 alkyl group, or a-(CH 2)-CH(OCOR 5)-CHOCOR 6 group, with R 5 and R 6 being independently a C8-C22 linear or branched alkyl group which is optionally substituted by at least one hydroperoxy or hydroxyl substituent, or R 1 and R 2 form together a carbocycle consisting of a 6 to 12 membered ring which is optionally substituted. R 3 and R 4 are each independently a hydrogen atom, an optionally substituted alkyl group with 1 to 20 carbon atoms or a group -L-A wherein L is a bond or a linear or branched alkylene chain with 1 to 12 carbon atoms, which is optionally substituted, and A is a hydrogen atom or a -COXR group wherein X is an oxygen atom or a -NR' group with R and R' being independently a group selected from a hydrogen atom, a C1-C8 alkyl group, or a -(CH 2)-CH(OCOR 5)-CHOCOR 6 group, with R 5 and R 6 being independently a C8-C22 linear or branched alkyl group which is optionally substituted by at least one hydroperoxy or hydroxyl substituent, comprising reacting at least one functionalized or unfunctionalized, linear or cyclic, olefin which comprises at least one carbon - carbon double bond with aqueous hydrogen peroxide in a solvent selected from water-soluble carboxylic acids, in the presence of a heterogenous catalyst which is a metallic mixed oxide having formula: M x M' y O z wherein: M is a metal; M' is W or Mo, x is a number from 1 to 10, preferably from 1 to 5, more preferably from 1 to 2; y is a number from 1 to 10, preferably from 1 to 5, more preferably from 1 to 3; z is a number from 1 to 40, preferably from 2 to 20, more preferably from 3 to 15. M is a metal; M' is W or Mo, x is a number from 1 to 10, preferably from 1 to 5, more preferably from 1 to 2; y is a number from 1 to 10, preferably from 1 to 5, more preferably from 1 to 3; z is a number from 1 to 40, preferably from 2 to 20, more preferably from 3 to 15.