In order to migrate a first stateful network function running on a first instance of a processing device to a second stateful network function running on a second instance of the same or another processing device, a salient idea is, after starting the migration, to keep applying the first stateful network function by the first instance only on received data items for which the first stateful network function has an active state corresponding to a source address of the received data item, and to forward the received data item without processing by the first instance to the second instance otherwise, the second instance being in charge of applying the second stateful network function on the data item received from the first instance. Active states are then deactivated in the first stateful network function by detecting when the first instance no longer receives any data item for these active states. When the first stateful network function only has inactive states, the data traffic is steered to the second instance so that the migration can successfully terminate