Method for authenticating at least one mobile terminal (Ter01, Ter02) capable of communicating with radio frequency link stations of at least one mobile phone network (PLMN1) for communication by radio frequency waves, the terminal being capable of communicating furthermore with at least one wireless network access terminal (BOX1, PA1) managed by a device for management of the service access point type, the method comprising a step of connection to one of the stations of the mobile phone network, a password being determined by a calculating module of the mobile phone network, on the basis of data transmitted, by the mobile terminal or by a management node in the mobile phone network, characterised in that the mobile terminal stores a given type (APNAME1) of service available to a user of the mobile terminal, this type of service being provided by the mobile terminal, for connection to the station of the mobile phone network, the connection to the station of the mobile phone network is followed by a step of initialisation or updating of an authentication database storing identification data of the terminal user associated with the password, this transmitted data comprising at least one username (ID_Ter01) stored by the mobile terminal and a temporary code (PTMSI1) stored by the mobile terminal and determined by said management node as a function of the connection established between the mobile terminal and the mobile phone network, the step of initialisation or updating of the authentication database being followed by a step of access to the authentication database (BDRAD1) by the management device of the service access point type, in order to carry out authentication of the terminal user connecting to the wireless network access terminal (BOX1, PA1), the terminal being authenticated, upon connection thereof to the wireless network access terminal, by at least: - a step of determination, by a calculating module of the mobile terminal, of the identification data of the user and of the password determined by at least the username of the mobile terminal user and by the temporary code which depends on the previous connection established between the mobile terminal and the mobile phone network, - a step of provision of the password associated with the identification data of the user to the device for management of the wireless network access terminal, by the calculating module of the terminal, - a step of verification, by the device for management of the wireless network access terminal, of the password and of the identification data provided by the mobile terminal in the provision step, as a function of the data stored in the authentication database during the step of initialisation or updating of the authentication database following the previous access of the terminal to the mobile phone network, in order to authorise connection of the mobile terminal to the wireless network access terminal, in case of correspondence. - a step of determination, by a calculating module of the mobile terminal, of the identification data of the user and of the password determined by at least the username of the mobile terminal user and by the temporary code which depends on the previous connection established between the mobile terminal and the mobile phone network, - a step of provision of the password associated with the identification data of the user to the device for management of the wireless network access terminal, by the calculating module of the terminal, - a step of verification, by the device for management of the wireless network access terminal, of the password and of the identification data provided by the mobile terminal in the provision step, as a function of the data stored in the authentication database during the step of initialisation or updating of the authentication database following the previous access of the terminal to the mobile phone network, in order to authorise connection of the mobile terminal to the wireless network access terminal, in case of correspondence.