A process for the selective hydrogenation of a feed of hydrocarbons containing polyunsaturated molecules comprising at least 3 carbon atoms and selected from the group constituted by a C3 cut from steam cracking, a C4 cut from steam cracking, a C5 cut from steam cracking and a pyrolysis gasoline, and a mixture thereof, in which said feed and a gaseous phase comprising hydrogen are passed, under hydrogenation conditions, over a hydrogenation catalyst in a single principal fixed bed reactor containing at least two catalytic beds and a fixed bed guard reactor which is smaller in size containing at least one catalytic bed, said reactors being disposed in series for use in a cyclic manner by repeating the steps a), b), c), c'), d) and d') defined below in succession: - a step a), during which the feed passes in succession through all of the catalytic beds of the principal reactor, - when the first catalytic bed of the principal reactor starts to become deactivated, a step b), during which the feed is introduced into the guard reactor then, by short-circuiting the first partially deactivated catalytic bed of the principal reactor, into the next non-deactivated catalytic bed of said principal reactor located immediately downstream with respect to the direction of movement of the feed, - a step c), during which the feed passes uniquely and successively through all of the catalytic beds of the principal reactor, - a step c'), simultaneously with step c), during which the deactivated catalyst of the catalytic bed or beds of the guard reactor is regenerated and/or replaced with fresh catalyst, - a step d), during which the feed only passes through the guard reactor, - a step d'), simultaneously with step d), during which the deactivated catalyst of the at least two catalytic beds of the principal reactor is regenerated and/or replaced with fresh catalyst; process in which the period of operation for each of steps a), b), c) and d), defined with respect to a maximum operating period tmax for each step, which is the time to reach a maximum tolerable value for a temperature or a selectivity for a given feed, is respectively: • for step a): between 10% and 70% of t Amax • for step b): between 40% and 100% of t Bmax • for step c): between 90% and 100% of t Cmax • for step d): between 70%and 100% of t Dmax; and in which • the maximum tolerable value for a C3 feed is the selectivity in accordance with the specifications in force; • the maximum tolerable value for a C4 feed is a maximum temperature of 160°C; • the maximum tolerable value for a C5 feed is a maximum temperature of 160 °C; • the maximum tolerable value for a feed of pyrolysis gasoline is a maximum temperature of 200°C. - a step a), during which the feed passes in succession through all of the catalytic beds of the principal reactor, - when the first catalytic bed of the principal reactor starts to become deactivated, a step b), during which the feed is introduced into the guard reactor then, by short-circuiting the first partially deactivated catalytic bed of the principal reactor, into the next non-deactivated catalytic bed of said principal reactor located immediately downstream with respect to the direction of movement of the feed, - a step c), during which the feed passes uniquely and successively through all of the catalytic beds of the principal reactor, - a step c'), simultaneously with step c), during which the deactivated catalyst of the catalytic bed or beds of the guard reactor is regenerated and/or replaced with fresh catalyst, - a step d), during which the feed only passes through the guard reactor, - a step d'), simultaneously with step d), during which the deactivated catalyst of the at least two catalytic beds of the principal reactor is regenerated and/or replaced with fresh catalyst; • for step a): between 10% and 70% of t Amax • for step b): between 40% and 100% of t Bmax • for step c): between 90% and 100% of t Cmax • for step d): between 70%and 100% of t Dmax; • the maximum tolerable value for a C3 feed is the selectivity in accordance with the specifications in force; • the maximum tolerable value for a C4 feed is a maximum temperature of 160°C; • the maximum tolerable value for a C5 feed is a maximum temperature of 160 °C; • the maximum tolerable value for a feed of pyrolysis gasoline is a maximum temperature of 200°C.