Abstract: The invention relates to a process for preparing butadiene from n-butenes, comprising the steps of: A) providing an input gas stream a comprising n-butenes, B) feeding the input gas stream a comprising n-butenes and a gas containing at least oxygen into at least one oxidative dehydrogenation zone and oxidatively dehydrogenating n-butenes to butadiene, giving a product gas stream b comprising butadiene, unconverted n-butenes, water vapor, oxygen, low-boiling hydrocarbons and high-boiling secondary components, with or without carbon oxides and with or without inert gases; Ca) cooling the product gas stream b by contacting with a cooling medium in at least one cooling zone, the cooling medium being at least partly recycled and having an aqueous phase and an organic phase of an organic solvent, wherein the organic solvent is selected from the group consisting of toluene, o-, m- and p-xylene, mesitylene, mono-, di- and triethylbenzene, mono-, di- and triisopropylbenzene and mixtures thereof, and the mass ratio of