In a simulated mobile bed separation process, perturbations are corrected in the compositions of an extract (EA) or raffinate (RB) due to the dead volume introduced by at least one recycling pump (P) or compressor for a liquid, supercritical or gaseous mixture in a closed circuit of columns. The process is characterized in that each time an extract extraction stream (EA) or that of the raffinate (RB) passes from a position immediately anterior to a position immediately posterior to each of the dead volumes in the circuit, the flow rate of the flow rate regulated recycling pump or compressor is increased for the time which the extract or raffinate remains in the position immediately posterior to the dead volume When the extract or raffinate extraction stream passes from the immediately posterior position to the dead volume to the following position, the flow rate of the recycling pump or compressor is reduced so that the flow rate regains the value which would have been applied if the dead volume had been ignored.The invention is applicable to the separation of aromatic hydrocarbons containing 8 carbon atoms.