Abstract: A process for preparing diols or triols made up of a1) reacting at least one monoolefin having 4 to 20 carbon atoms with hydrogen peroxide and formic acid in the presence of water to form a mixture or a2) reacting at least one monoolefin alcohol having 4 to 20 carbon atoms first with formic acid, and then reacting the product formed thereby with hydrogen peroxide in the presence of water to form a mixture, b) removing, by distillation, the water and formic acid from the mixture obtained in a1) or a2), c) reacting the mixture obtained from b) with an aliphatic alcohol in the presence of a sulfonic acid to form the diol or triol and at least one formic ester by-product, and d) optionally removing, by distillation, the at least one formic ester by-product formed together with any residual at least one aliphatic C1-C4-alcohol to isolate the diol or triol.