The purpose of this invention is to describe a method for extracting a more than 80% pure mixture of one or more long-chain, branched α,β unsaturated aldehydes having chain lengths of between 44 and 78 carbon atoms, the main compound thereof being the aldehyde C 56 .<sb /> <sb /> The extract is obtained from sugarcane and from byproducts from the sugar production process, such as: honeys or syrups, non-centrifugal sugar (NCS), jaggery, panela, kokuto, raspadura, whole cane sugar, unrefined sugar, brown sugar or black sugar, molasses or blackstrap, mud or press filter mud ("cachaza" in Spanish) and the byproducts thereof such as bagasse. The method comprises: selecting the raw material, although preferably this can be obtained from the wax extracted from the press filter mud, which can be treated by means of chemical methods such as solvents; for example, hexane, heptane, isooctane, ethyl ether, petroleum ether, ethyl alcohol, methyl alcohol, isopropyl alcohol, butyl alcohol, water, ethyl acetate, acetone, etc., or a mixture of these. Although preferably an alcohol solution having a solid–liquid ratio between 1:5 and 1:40 is used to adjust the pH of the solution, a base can be used, such as sodium hydroxide, potassium hydroxide, calcium hydroxide, aluminium hydroxide, sodium carbohydrate, etc., or acids such as hydrochloric acid, sulfuric acid, nitric acid, acetic acid, etc., in recommended concentrations of 5-40%. The solution is then heated to dissolving temperature, which may reach the boiling temperature of the solvent or mixture of solvents used, causing the solution to split into two phases that are separated by means of decanting, filtration, centrifuging or another suitable operation or device. The previous process is repeated four times as a purification method, although it can also be carried out by means of dissolution and subsequent precipitation in one or more mixtures of the previously mentioned solvents. The solid is cooled to room temperature or less and is dried to remove the residues of the solvent used in the previous steps. The use of other methods to obtain this product is not excluded; for example: supercritical extraction, chromatography columns, vacuum distillation, etc. The invention also relates to the demonstration of the antioxidant and anticarcinogenic properties of the mixture of one or more of the branched, very-long-chain α,β unsaturated aldehydes isolated from sugarcane or from the production process and the association of the mixture with antioxidant and anticarcinogenic activity, by means of in vitro and in vivo tests, a result that allows these compounds to be used to prepare pharmaceutical compositions, nutritional supplements and/or food additives in order to increase the antioxidant status of the organism and to prevent and/or treat cancer, as well as other acute or chronic diseases associated with oxidative stress, such as cancer, atherosclerosis, hypercholesterolaemia, hyperlipidaemia, diabetes, high blood pressure, cardiovascular and cerebrovascular diseases, Alzheimer's disease dementias, multiple sclerosis, arthritis, etc. The invention can also have effects such as anti-inflammatory and immunomodulatory effects, with a beneficial impact in diseases such as migraines, HIV and others. The extract can be used in humans and in animals.