A process for producing butadiene from n-butenes, comprising the steps of: A) providing a vaporous n-butenes-comprising input gas stream a1 by evaporating a liquid n-butenes-comprising stream a0; B) introducing the vaporous n-butenes-comprising input gas stream a1 and an oxygenous gas into at least one oxidative dehydrogenation zone and oxidatively dehydrogenating n-butenes to butadiene to obtain a product gas stream b comprising butadiene, unconverted n-butenes, steam, oxygen, low-boiling hydrocarbons, high-boiling secondary components, possibly carbon oxides and possibly inert gases; Ca) chilling the product gas stream b by contacting with a cooling medium comprising an organic solvent, the cooling medium comprising an aqueous phase and an organic phase, in at least one chilling zone, the cooling medium being at least partially recycled into the chilling zone, Cb) compressing the chilled product gas stream b which is possibly depleted of high-boiling secondary components in at least one compression stage to obtain at least one aqueous condensate stream c1 and a gas stream c2 comprising butadiene, n-butenes, steam, oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases, D) removing noncondensable and low-boiling gas constituents comprising oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases as gas stream d2 from the gas stream c2 by absorbing the C 4 hydrocarbons comprising butadiene and n-butenes into an absorption medium to obtain a C 4 -hydrocarbons-laden absorption medium stream and the gas stream d2 and subsequently desorbing the C 4 hydrocarbons from the laden absorption medium stream to obtain a C 4 product gas stream d1, wherein at least some of the recycled cooling medium from step Ca) is brought into thermal contact with the liquid n-butenes-comprising stream a0 in one or more indirect heat exchangers and at least some of the liquid n-butenes-comprising stream a0 is evaporated by indirect heat transfer with the recycled cooling medium, and wherein stage Ca) is performed in three stages Ca1), Ca2) and Ca3) in three chilling zones, and an organic solvent from the second stage Ca2) which solvent is laden with high-boiling secondary components is passed into the first stage Ca1) and an organic solvent from the third stage Ca3) which solvent is less heavily laden with high-boiling secondary components is passed into the second stage Ca2). A) providing a vaporous n-butenes-comprising input gas stream a1 by evaporating a liquid n-butenes-comprising stream a0; B) introducing the vaporous n-butenes-comprising input gas stream a1 and an oxygenous gas into at least one oxidative dehydrogenation zone and oxidatively dehydrogenating n-butenes to butadiene to obtain a product gas stream b comprising butadiene, unconverted n-butenes, steam, oxygen, low-boiling hydrocarbons, high-boiling secondary components, possibly carbon oxides and possibly inert gases; Ca) chilling the product gas stream b by contacting with a cooling medium comprising an organic solvent, the cooling medium comprising an aqueous phase and an organic phase, in at least one chilling zone, the cooling medium being at least partially recycled into the chilling zone, Cb) compressing the chilled product gas stream b which is possibly depleted of high-boiling secondary components in at least one compression stage to obtain at least one aqueous condensate stream c1 and a gas stream c2 comprising butadiene, n-butenes, steam, oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases, D) removing noncondensable and low-boiling gas constituents comprising oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases as gas stream d2 from the gas stream c2 by absorbing the C 4 hydrocarbons comprising butadiene and n-butenes into an absorption medium to obtain a C 4 -hydrocarbons-laden absorption medium stream and the gas stream d2 and subsequently desorbing the C 4 hydrocarbons from the laden absorption medium stream to obtain a C 4 product gas stream d1,