A method (and corresponding equipment) for use in reauthentication—after a first, full authentication by a first authentication server (23a)—of a communication session involving the exchange of information between a terminal (21) and a server (24), the method including: a step (11) in which the first authentication server (23a) and other authentication servers (23b) are each assigned a respective unique realm name; and a step (13) in which during authentication between the terminal and the first authentication server (23a), the first authentication server (23a) transmits to the terminal (21) a reauthentication identity including the unique realm name assigned to the first authentication server. Then, later, during reauthentication, to make possible that the reauthentication is performed by the same authentication server (23a) as performed the full authentication—i.e. by the first authentication server (23a)—the reauthentication identity is included in a request for reauthentication.