An organic compound having at least one C—C double bond is epoxidized by means of hydrogen peroxide in the presence of at least one catalytically active compound and at least one solvent, wherein a product mixture comprising -hydroperoxyalcohols is reduced using at least one reducing agent. The process advantageously comprises at least the following steps:

(i) reacting an organic compound having at least one C—C double bond with hydrogen peroxide in the presence of at least one catalytically active compound and at least one solvent to give a product mixture P1 comprising -hydroperoxyalcohols;

(ii) separating an epoxide formed in the reaction in step (i) and the unreacted organic compound having at least one C—C double bond from P1 or P1 to give a product mixture P2 or P2, where P2 comprises the -hydroperoxyalcohols formed as by-product in the reaction in step (i) and P2 is largely free of -hydroperoxyalcohols;

(iii) treating P1 and/or P2 with at least one reducing agent so that the -hydroperoxyalcohols are converted into corresponding glycols to give a product mixture P1 or P3.