The present invention relates to a process and also to a service computer, a switching center, terminals, program modules and memory means with program modules for handling incoming telephone calls for a subscriber line (VA1) of a telecommunications network (PSTN) during an online data-network session blocking the subscriber line (VA1). In this process a terminal (TERA) sets up a connection (VA11, VA1, VPOP1) to an online data-network access device (POP) via the subscriber line (VA1). Thereupon the online data-network access device (POP) sends current access data to the terminal (TERA), which the terminal (TERA) signals to a service computer (SCP) of the telecommunications network. If a switching center (SW1) of the telecommunications network then detects an incoming call destined for the subscriber line (VA1), the switching center (SW1) then signals the fact that this call is waiting to the service computer (SCP) which supplies at least one predetermined service for the purpose of processing the incoming call. The service may, for example, consist in a message being sent to the terminal (TERA), in which attention is drawn to the incoming call, or in the incoming call being forwarded to an alternative destination (TELA2).