Process for the work-up of naphtha, wherein a) naphtha or a stream produced from naphtha in a pretreatment step is separated in a membrane unit into a stream A which is depleted in aromatics and a stream B which is enriched in aromatics, with the aromatics concentration in stream A being from 2 to 12% by weight (step a), b) at least part of the substream A is fed to a steam cracker (step b), c) at least part of the substream B is fed to a unit in which it is separated by means of a thermal process into a stream C which has a lower aromatics content than stream B or a plurality of streams C', C'', C''' . . . which each have lower aromatics contents than stream B and a stream D which has a higher aromatics content than stream B or a plurality of streams D', D'', D''' . . . which each have higher aromatics contents than stream B (step c), and d) the stream C or at least one of the streams C', C'', C''', in each case in part or in its entirety, is added to the feed to the steam cracker or fed into the steam cracker itself (step d).