Abstract: 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 a dehydrogenation reactor and oxidative dehydrogenation of n-butenes to butadiene; C) cooling and compression of the product gas stream b in at least one cooling stage comprising a quenching column and in a compression stage comprising a compressor, with the product gas stream b being brought into contact with at least one circulated coolant; D) separation of incondensable and low-boiling gas constituents as gas stream d2 from the gas stream c2 by absorption of the C4-hydrocarbons in at least one circulated absorption medium; E) separation of the C4 product stream d1 by extractive distillation using 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 essenti