A process for preparing a compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group, comprising the stages: oxidation of a cyclic olefin with Z cycles and 7 to 16 carbon atoms and at least two C-C double bonds, selected from the group consisting of 1,5-cyclooctadiene, 1,5-cyclododecadiene, 1,9-cyclohexadecadiene, 1,8-cyclotetradecadiene, 1,6-cyclodecadiene, 1,6,11-cyclopentadecatriene, 1,5,9-cyclododecatriene, vinylcyclohexene, norbornadiene, ethylidenenorbornene by means of dinitrogen monoxide to give a composition, at least comprising - a cyclic compound with Z cycles and 7 to 16 carbon atoms with a keto group, - a cyclic olefin with Z cycles and 7 to 16 carbon atoms with at least two C-C double bonds and - a compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, separating off the cyclic olefin with Z cycles and 7 to 16 carbon atoms with at least two C-C double bonds from the composition from stage in order to obtain a composition, at least comprising - the cyclic compound with Z cycles and 7 to 16 carbon atoms with a keto group and - the compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, separating off the cyclic compound with Z cycles and 7 to 16 carbon atoms with a keto group from the composition from step, in order to obtain a composition, comprising at least 50% by weight of the compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, purification of the composition obtained in step in order to obtain a mixture which comprises at least 92% by weight of the compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, where Z may be 1, 2, 3 or 4, and stage is conducted in at least two distillation columns T1 and T2, where T1 has at least 15 theoretical plates and T2 at least 30 theoretical plates, or in a dividing wall column. oxidation of a cyclic olefin with Z cycles and 7 to 16 carbon atoms and at least two C-C double bonds, selected from the group consisting of 1,5-cyclooctadiene, 1,5-cyclododecadiene, 1,9-cyclohexadecadiene, 1,8-cyclotetradecadiene, 1,6-cyclodecadiene, 1,6,11-cyclopentadecatriene, 1,5,9-cyclododecatriene, vinylcyclohexene, norbornadiene, ethylidenenorbornene by means of dinitrogen monoxide to give a composition, at least comprising - a cyclic compound with Z cycles and 7 to 16 carbon atoms with a keto group, - a cyclic olefin with Z cycles and 7 to 16 carbon atoms with at least two C-C double bonds and - a compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, - a cyclic compound with Z cycles and 7 to 16 carbon atoms with a keto group, - a cyclic olefin with Z cycles and 7 to 16 carbon atoms with at least two C-C double bonds and - a compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, separating off the cyclic olefin with Z cycles and 7 to 16 carbon atoms with at least two C-C double bonds from the composition from stage in order to obtain a composition, at least comprising - the cyclic compound with Z cycles and 7 to 16 carbon atoms with a keto group and - the compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, - the cyclic compound with Z cycles and 7 to 16 carbon atoms with a keto group and - the compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, separating off the cyclic compound with Z cycles and 7 to 16 carbon atoms with a keto group from the composition from step, in order to obtain a composition, comprising at least 50% by weight of the compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds, purification of the composition obtained in step in order to obtain a mixture which comprises at least 92% by weight of the compound with Z-1 cycles and 7 to 16 carbon atoms with at least one aldehyde group and at least two C-C double bonds,