Ditertiary aliphatic peroxides are prepared by reacting a tertiary alkyl hydroperoxide or halogen - substituted tertiary alkyl hydroperoxide with an aliphatic or halogen-substituted aliphatic tertiary alcohol in the presence of an acid, or an acid acting catalyst such as sulphuric acid, phosphoric acid, hydrochloric acid, hydrobromic acid or benzene sulphonic acids and their homologues, especially aqueous solutions of mineral acids and preferably aqueous sulphuric acid of strength 50 to 75 per cent w/w. The reaction is carried out generally at between about 15 DEG C. to about 50 DEG C., preferably employing substantially equimolar amounts of all three substances. The products have the formula R-O-O-R1, where n R and R1 represent the same or different tertiary groups; the compounds represented when R and R1 are each a different tertiary alkyl or halo-substituted tertiary alkyl group are stated to be novel; the preferred compounds are those in which R and R1 represent different tertiary alkyl groups, in particular when one is the tertiary butyl radical and the other a saturated alkyl radical having at least 5 carbon atoms such as tertiary amyl, hexyl, heptyl radicals or higher homologues thereof. The tertiary hydroperoxides used as starting materials may be prepared by several methods; preferably a hydrocarbon containing at least one tertiary carbon atom of aliphatic character is subjected to controlled non-explosive catalytic oxidation, for example, in the presence of hydrogen bromide; alternatively, a tertiary alkyl alcohol may be reacted with aqueous hydrogen peroxide in the presence of a dehydrating agent such as anhydrous sodium sulphate, and another method comprises the formation of an acid monoalkyl hydrogen sulphate, for example, that obtained by reacting isobutylene with aqueous sulphuric acid, treating it with hydrogen peroxide, neutralizing the reaction product and recovering the hydroperoxide, in this case tertiary butyl hydroperoxide. Other examples of suitable hydroperoxides are tertiary amyl hydroperoxide, and homologues as obtained by substitution of the hydroperoxyl radical for the hydrogen atom on one or more of the tertiary carbon atoms of such saturated aliphatic hydrocarbons as 2-ethyl butane, 2-methyl pentane, 3-methyl pentane, 2,3-dimethyl butane, 2,4-dimethyl pentane and their homologues. Suitable halo-substituted tertiary hydroperoxides may be obtained by the controlled oxidation with oxygen in the presence of hydrogen bromide of, for example, 1-halo-2-methyl propane, 1-halo-2-ethyl propane, 1-halo-3-methyl butane and 2-halo-3-methyl butane. Specified tertiary aliphatic alcohols are tertiary butyl and amyl alcohols, 2-methyl-pentanol-2, 3-methyl-pentanol - 3, 2 : 3 - dimethyl - butanol - 2, 2,3,3-trimethyl butanol-2 and their homologues; halogenated tertiary aliphatic alcohols include 1 - bromo - 2 - methyl - propanol - 2, 1 - chloro - 2 - methyl-propanol-2, 1,1-dichlor-2-methyl-propanol - 2, 1,3 - dichlor - 2 - methyl propanol - 2, 1 - chloro - 2 - methyl - butanol - 2, 1 - chlor - 2 - methyl-butanol-2, 4-chloro-2-methyl-butanol-2 3-bromo-2-methyl-butanol-2, 1,2-dichlor-2-methyl-butanol-2, 1-chloro-2-methyl-pentanol-2, 2-chloro-3-methyl-pentanol-3, 3-chlormethyl-pentanol-3, 3-chloro-2,3-dimethyl-butanol-2 and their homologues. There may also be used tertiary alcohols containing at least two hydroxyl groups, at least one being attached to a tertiary carbon atom. Instead of employing tertiary alcohols per se, the corresponding products obtained by absorbing tertiary olefines in aqueous acid solutions, particularly aqueous sulphuric acid, may be employed. The novel unsymmetrical peroxides of the invention may be used as additives to improve the cetane value of Diesel engine fuels. They may also be employed as polymerization catalysts, either singly, in combination, or with other catalysts such as benzoyl peroxide, lauroyl peroxide, acetyl peroxide, benzoyl acetyl peroxide and hydrogen peroxide. There may be polymerized unsaturated organic compounds having a single olefinic linkage such as styrene, alpha-methyl styrene, vinyl and allyl derivatives, and nitriles and esters of acrylic and alpha-substituted acrylic acids; unconjugated unsaturated compounds, for example, the unsaturated aliphatic polyethers of saturated polyhydric alcohols, and unsaturated aliphatic esters of unsaturated aliphatic acids; unsaturated compounds containing polymerizable organic radicals and one or more inorganic radicals, for example, the allyl and methallyl esters of phosphoric acid and the ortho-acids of silicon and boron; conjugated unsaturated compounds including butadiene-1 : 3, 2-chlorbutadiene-1 : 3, isoprene and higher homologues thereof. The peroxides may be employed in copolymerization of, for example, one or more conjugated diene hydrocarbons with styrene, acrylonitrile, isobutylene, vinyl chloride, and methyl methacrylate. Plasticisers, stabilisers, lubricants, dyes, pigments and fillers may be added if they do not react with the ingredients of the reaction mixture. These polymerizations may be applied to monomeric compounds in the massive state or to dispersions or solutions of the monomers. In examples: (1) tertiary amyl alcohol is reacted with tertiary butyl hydroperoxide in aqueous sulphuric acid to yield tertiary-butyl tertiary-amyl peroxide; and similarly (2) tertiary butyl hydroperoxide and tertiary butyl alcohol are reacted to yield di-tertiary butyl peroxide; (3) tertiary amyl hydroperoxide and tertiary amyl alcohol are reacted to yield di-tertiary amyl peroxide; and (4) chloro-t-butyl hydroperoxide and tertiary butyl alcohol are reacted to yield chloro-t-butyl tertiary butyl peroxide. The Specification as open to inspection under Sect. 91 relates to the preparation of peroxides from hydroperoxides of the type