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 cooling stage and at least one compression stage, with the product gas stream b being brought into contact with at least one circulated organic solvent as coolant to give 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 absorption of the C 4 -hydrocarbons comprising butadiene and n-butenes in at least one circulated absorption medium, giving at least one absorption medium stream loaded with C 4 -hydrocarbons and the gas stream d2, and subsequent desorption of the C 4 -hydrocarbons from the loaded absorption medium stream to give a C 4 product gas stream d1; E) separation of the C 4 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 essentially of the selective solvent and a stream f2 comprising butadiene; where samples are taken from the circulated coolant in step C) and optionally the circulated absorption medium in step D) and the peroxide content of the samples taken is determined by means of iodometry, differential scanning calorimetry or microcalorimetry, where when the decomposition energy of the circulated coolant is greater than 400 J/g in the coolant, peroxides are destroyed by heating of the coolant, treatment of the coolant with bases or hydrogenation. 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 cooling stage and at least one compression stage, with the product gas stream b being brought into contact with at least one circulated organic solvent as coolant to give 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 absorption of the C 4 -hydrocarbons comprising butadiene and n-butenes in at least one circulated absorption medium, giving at least one absorption medium stream loaded with C 4 -hydrocarbons and the gas stream d2, and subsequent desorption of the C 4 -hydrocarbons from the loaded absorption medium stream to give a C 4 product gas stream d1; E) separation of the C 4 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 essentially of the selective solvent and a stream f2 comprising butadiene;