A process for the recovery of a pure aromatics-containing product is disclosed. This product is obtained by extractive distillation of a gasoline rich in aromatics, in which olefins, diolefins and polyolefins are separated, and this extractive distillation is followed by a hydrogenation of the recovered aromatics-rich, olefin-lean product stream, in which the alkylated aromatics, especially toluene and xylene, are dealkylated and the paraffinic dealkylation products further converted into methane so that a significant portion of hydrogen can be saved by carrying out the hydrogenation subsequent to the extractive distillation, as the aromatics mixture is then free of olefins and no hydrogen is required for an olefin hydrogenation, with extractive distillation and recovery of the extracting solvent taking place in one column. An apparatus for carrying out the process described is also disclosed. A column is preferably used for the extractive distillation which allows performing the extractive distillation with a solvent recycling system so that it is not required to provide an additional stripping column for removing the extracting solvent.