the present invention relates to a method of setting up a connection between a first terminal , which may be a calling telephone , telefax machine , computer or other equipment that can make a call , and a second terminal which may be a called telephone on the one hand or , on the other hand , a called telefax machine , a computer or other equipment that can receive a call . according to the invention , the first terminal calls a subscriber number , a fictitious response is sent to the first terminal and monitoring of the first terminal 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 is ordered to commence ringing . when signals or a message are / is detected , the called telephone is ordered to stop ringing and the possible message is received and sent to a second terminal , or else the called telephone is connected to the first terminal .