NOVELTY - Selective hydrogenation of an unsaturated less than or equal to 4C olefinic feedstock, comprises passing the unsaturated olefinic feedstock and a gaseous phase comprising hydrogen over a hydrogenation catalyst in fixed-bed hydrogenation reactors (R1) for a period that is equal to a deactivation time of one of the reactors, introducing the feedstock into a non-deactivated reactor for a period that is equal to the deactivation time of the downstream reactor, and regenerating the catalyst of the deactivated reactor and/or replacing the catalyst by fresh catalyst.    USE - The process is useful for selective hydrogenation of an unsaturated less than or equal to 4C olefinic feedstock for refining petroleum and for production of intermediate products for petrochemistry,    ADVANTAGE - The process improves the selectivity of the hydrogenation reaction, and increases the duration of the cycle times by delaying the formation of oligomers (or gums), proportionately postponing the deactivation of the catalyst.    DETAILED DESCRIPTION - Selective hydrogenation of an unsaturated less than or equal to 4C olefinic feedstock, comprises passing the unsaturated olefinic feedstock and a gaseous phase comprising hydrogen over a hydrogenation catalyst, under hydrogenation conditions, in fixed-bed hydrogenation reactors (R1) for a period that is equal to a deactivation time of one of the reactors, introducing the feedstock into a non-deactivated reactor located immediately downstream, relative to the direction of circulation of the feedstock, from the deactivated reactor, by short-circuiting the deactivated reactor, for a period that is equal to the deactivation time of the downstream reactor, and regenerating the catalyst of the deactivated reactor and/or replacing the catalyst by fresh catalyst, where the reactors contain catalytic beds and are arranged in series.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a process for selective hydrogenation of an unsaturated olefinic feedstock (Drawing includes non-English language text).    Heat exchanger (E1)    Hydrogen (H2)    Static mixer (M1)    Hydrogenation reactor (R1)    Valve. (V1)