The present invention relates to a process for the selective hydrogenation of a feed of hydrocarbons containing polyunsaturated molecules comprising at least 3 carbon atoms, using a single principal fixed bed reactor R1 containing at least two catalytic beds A1 and A2 and a fixed bed guard reactor which is reduced in size, said hydrogenation reactors being disposed in series for use in a cyclic manner in accordance with a sequence of steps which can be used to short-circuit the catalytic bed or beds of the principal reactor which have been at least partially deactivated with the aid of the guard reactor, while ensuring the continuous operation of the process.