The invention concerns authentication to be performed in a telecommunications network, especially in an IP network. To allow a simple and smooth authentication of users of IP networks in a geographically large area, the IP network's terminal (TE1) uses a subscriber identity module (SIM) as used in a separate mobile communications system (MN), whereby a response may be determined from the challenge given to the identity module as input. The IP network also includes a special security server (SS), to which a message about a new user is transmitted when a subscriber attaches to the IP network. The subscriber's authentication information containing at least a challenge and a response is fetched from the said mobile communications system to the IP network and authentication is carried out based on the authentication information obtained from the mobile communications system by transmitting the said challenge through the IP network to the terminal, by generating a response from the challenge in the terminal's identity module and by comparing the response with the response received from the mobile communications system. Such a database (DB) may also be used in the system, wherein subscriber-specific authentication information is stored in advance, whereby the information in question need not be fetched from the mobile communications system when a subscriber attaches to the network.