A method for producing one or more hydrocarbons, includes subjecting a first feed stream to a steam cracking to obtain a first product stream and subjecting a second feed stream containing ethane to an oxidative dehydrogenation to obtain a second product stream At least a portion of the first product stream is subjected to a treatment to obtain hydrocarbon fractions. The treatment includes a selective hydrogenation of hydrocarbons having two carbon atoms and a demethanization. At least a portion of the second product stream is subjected to a trace removal, which comprises the removal of oxygen and/or acetylene, to obtain an subsequent stream. At least a portion of the subsequent stream is fed to the treatment at a position downstream of the selective hydrogenation and upstream of the demethanization. A portion of the subsequent stream is subjected to a carbon dioxide removal upstream of the feed point into the treatment.