Method for authenticating a terminal connecting to an internet access server via an access point of the Wi-Fi type of a fixed communication network, with a SIM card associated with a unit for communication with a mobile telephone network, this SIM card and these means being integrated into or connected to this terminal, wherein the access server collects from the terminal authentication data that is established at this terminal on the basis in particular of an identifier memorised in the SIM card and a reference associated with this SIM card and previously received via a connection to the mobile telephony network established with the SIM card and the associated communication unit, and wherein the access server verifies the validity of the authentication data collected to authenticate the terminal; characterised in that the identifier memorised in the SIM card as well as the reference associated with this SIM card are memorised together in a database accessible by a telephone server to which the access server is connected, wherein the authentication data comprises the reference associated with the SIM card as well as a code, and wherein the access server: - collects from the terminal the reference associated with the SIM card as well as the code, this code being calculated in the terminal by applying a predetermined processing function to at least the identifier memorised in the SIM card; - collects from the telephone server the identifier that is memorised in the database while being associated therein with the reference that was collected from the terminal, determines a value by applying the predetermined processing function to at least the identifier that was collected from the telephone server; - authenticates the terminal when the value calculated is identical to the code transmitted by the terminal; the predetermined processing function is also applied to at least one of the following elements: - a time variable such as the date or the time, the identification by the internet access server being preceded by a synchronisation of the terminal with the internet access server, - an alphanumeric key incorporated into a programme of the terminal and/or of the SIM card, - a piece of geolocation data determined by the terminal, the access server having a piece of information on location of the terminal by the location of the access point or via the telephone network, - an identification of the access point, - an identification of the cell of the mobile cellular network used; the processing function is divided into a plurality of parts that are recorded on distinct physical media out of the terminal, a communication unit associated with the terminal, the SIM card and/or one or more servers (4, 6) accessible from the terminal. - collects from the terminal the reference associated with the SIM card as well as the code, this code being calculated in the terminal by applying a predetermined processing function to at least the identifier memorised in the SIM card; - collects from the telephone server the identifier that is memorised in the database while being associated therein with the reference that was collected from the terminal, determines a value by applying the predetermined processing function to at least the identifier that was collected from the telephone server; - authenticates the terminal when the value calculated is identical to the code transmitted by the terminal; - a time variable such as the date or the time, the identification by the internet access server being preceded by a synchronisation of the terminal with the internet access server, - an alphanumeric key incorporated into a programme of the terminal and/or of the SIM card, - a piece of geolocation data determined by the terminal, the access server having a piece of information on location of the terminal by the location of the access point or via the telephone network, - an identification of the access point, - an identification of the cell of the mobile cellular network used;