Abstract: The present invention relates to a method of setting up a connection between a first terminal (A), which may be a calling telephone, telefax machine, computer or other equipment that can make a call, and a second terminal (Ct, Cf) which may be a called telephone (Ct) on the one hand or, on the other hand, a called telefax machine (Cf), a computer (Cf) or other equipment (Cf) that can receive a call. According to the invention, the first terminal (A) calls a subscriber number, a fictitious response is sent to the first terminal (A) and monitoring of the first terminal (A) is commenced so as to identify the type of terminal concerned with the aid of possible signals and/or a possible message, while a called telephone (Ct) is ordered to commence ringing. When signals or a message are/is detected, the called telephone (Ct) is ordered to stop ringing and the possible message is received and sent to a second terminal (Cf), or else the called telephone (Ct) is connected to the first terminal (A).