A process for preparing butadiene from n-butenes, which comprises the following steps: A) provision of a feed gas stream a comprising n-butenes; B) introduction of the feed gas stream a comprising n-butenes and an oxygen-comprising gas into at least one dehydrogenation zone and oxidative dehydrogenation of n-butenes to butadiene, giving a product gas stream b comprising butadiene, unreacted n-butenes, water vapor, oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases; C) cooling and compression of the product gas stream b in at least one compression stage, giving at least one condensate stream c1 comprising water and a gas stream c2 comprising butadiene, n-butenes, water vapor, oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases; D) separation of incondensable 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 Da) absorption of the C 4 -hydrocarbons comprising butadiene and n-butenes in a high-boiling absorption medium, giving an absorption medium stream loaded with C 4 -hydrocarbons and the gas stream d2, Db) removal of oxygen from the absorption medium stream loaded with C 4 -hydrocarbons by stripping with an inert gas and Dc) desorption of the C 4 -hydrocarbons from the loaded absorption medium stream to give a C 4 product gas stream d1 which comprises less than 100 ppm of oxygen; E) separation of the C 4 product stream d1 by extractive distillation with a solvent which is selective for butadiene into a stream e1 comprising butadiene and the selective solvent and a stream e2 comprising n-butenes; F) distillation of the stream e1 comprising butadiene and the selective solvent to give a stream f1 consisting essentially of the selective solvent and a butadiene-comprising stream f2. A) provision of a feed gas stream a comprising n-butenes; B) introduction of the feed gas stream a comprising n-butenes and an oxygen-comprising gas into at least one dehydrogenation zone and oxidative dehydrogenation of n-butenes to butadiene, giving a product gas stream b comprising butadiene, unreacted n-butenes, water vapor, oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases; C) cooling and compression of the product gas stream b in at least one compression stage, giving at least one condensate stream c1 comprising water and a gas stream c2 comprising butadiene, n-butenes, water vapor, oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases; D) separation of incondensable 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 Da) absorption of the C 4 -hydrocarbons comprising butadiene and n-butenes in a high-boiling absorption medium, giving an absorption medium stream loaded with C 4 -hydrocarbons and the gas stream d2, Db) removal of oxygen from the absorption medium stream loaded with C 4 -hydrocarbons by stripping with an inert gas and Dc) desorption of the C 4 -hydrocarbons from the loaded absorption medium stream to give a C 4 product gas stream d1 which comprises less than 100 ppm of oxygen; Da) absorption of the C 4 -hydrocarbons comprising butadiene and n-butenes in a high-boiling absorption medium, giving an absorption medium stream loaded with C 4 -hydrocarbons and the gas stream d2, Db) removal of oxygen from the absorption medium stream loaded with C 4 -hydrocarbons by stripping with an inert gas and Dc) desorption of the C 4 -hydrocarbons from the loaded absorption medium stream to give a C 4 product gas stream d1 which comprises less than 100 ppm of oxygen; E) separation of the C 4 product stream d1 by extractive distillation with a solvent which is selective for butadiene into a stream e1 comprising butadiene and the selective solvent and a stream e2 comprising n-butenes; F) distillation of the stream e1 comprising butadiene and the selective solvent to give a stream f1 consisting essentially of the selective solvent and a butadiene-comprising stream f2.