Pure tert.-olefins are prepared from mixtures of hydrocarbons, which contain at least one such tert.-olefin, by reaction with an alkanol to give the corresponding alkyl tert.-alkyl ethers, and subsequent cleavage of these ethers back to the corresponding pure tert.-olefins and the alkanol, and the separation of the pure tert.-olefin from the alkanol. For this, the alkanol present after the cleavage of the ether is separated from the tert.-olefin to the extent of 60 to 99% by weight by distillation, and the residual amount of alcohol in the olefin fraction is removed by adsorption from this fraction onto a synthetic ion exchanger as an absorber resin. The admixture of the alkanol to the mixture of hydrocarbons with at least one tert.-olefin is carried out partly by using the alkanol fraction arising from the separating off of the pure tert.-olefin, and partly by desorption of the alkanol from the absorber resin with the aid of the mixture of hydrocarbons containing at least 1 tert.-olefin.