A cellular communication network comprises a core network interconnecting a set of cells, an item of equipment in the core network being responsible for managing the mobility of the user equipment between the cells. An item of user equipment transmits (401) to said equipment in the core network an attachment request message for registering itself and also transmitting a message requesting updating of localization areas at the expiry of a period with a duration set by said equipment in the core network in an attachment acceptance message and/or in a message accepting updating of localization areas. The user equipment includes, in each message requesting attachment to the core network and/or in each message requesting updating of localization areas, a proposed duration to be applied to said time delay.