In order to control the authorisation of a user during an attempt to access an IP transport network (5) by means of an access network (1, 2), a user terminal (11, 12, 13) emits an access request to an access supplier (6, 7, 8), containing data for authenticating the user to the access supplier, and said request is then transmitted to an access server (9) of the access network (1, 2) in view of being addressed to a remote authentication server (15) of the access supplier. On reception of the access request, the access server (9) emits a RADIUS request to a proxy server (10) of the access network (1, 2) which determines whether the user must be locally authenticated, and if this is the case, the proxy server transmits, to the access server (9), a request for authentication data to be addressed to the terminal of the user, and carries out a local procedure to authenticate the user, on the basis of the authentication data supplied by the user.