A process and a device for separating ethane and ethylene from a hydrocarbon steam-cracking effluent is described. Effluent (1) is absorbed in an absorption column (7) by a cooled solvent (9). At the bottom of the column, liquid phase (12) that contains the solvent and the C2+ hydrocarbons is recovered and hydrogenated (15). The hydrogenation effluent that contains the solvent is introduced into a first distillation column (70) where the solvent is regenerated. The solvent is cooled and recycled at the top of absorption column (7). The C2+ hydrocarbons are collected at the top, and a condensed liquid phase is distilled in a second distillation column (77) to recover a C2 fraction that consists of ethane and ethylene.