In a process for producing olefins, a hydrocarbon-containing feed is fed into a cracking furnace where relatively long-chain hydrocarbons of the hydrocarbon-containing feed are cracked at least partly to form shorter-chain olefins, encompassing ethylene and propylene. Cracking gas (1) formed during cracking is conveyed in succession through an upper section (11) and a lower section (12) of a scrubbing column (10) in countercurrent to a liquid scrubbing medium (43, 31), is proposed. A fraction (43) rich in petroleum spirit is used in the lower section (11) of the scrubbing column (10) and a water-rich fraction (31) is used in the upper section (11) of the scrubbing column (10) as scrubbing medium (43, 31). A plant configured for carrying out the process is likewise provided by the present invention.