A process for isomerizing a saturated, branched and cyclic hydrocarbon, in which a tertiary carbon atom of the hydrocarbon is converted to a secondary carbon atom in the course of isomerization, by performing the isomerization in the presence of a superacidic ionic liquid comprising an organic cation and an inorganic anion, where the anion is a superacidic aluminum trichloride-Lewis base adduct, and of a copper(II) compound.