The gaseous feed flowing in through line 1 is contacted in contacting zone ZA with a liquid solvent flowing in through line 2. The solvent comprises between 0.001% and 100% by weight of a liquid olefin. Contacting in zone ZA is carried out in the presence of an acid catalyst. The purified gaseous feed is discharged from zone ZA through line 3. The sulfide-laden solvent is discharged through line 4, then regenerated in unit RE. The regenerated solvent is recycled through lines 7 and 2 to zone ZA.