An integrated communication system (e.g., BIGFON) includes the narrow-band telephone network and a superposed video-telephone network. The path search for setting up calls in the telephone network is carried out with the aid of the telephone call numbers. To permit a video-telephone network structure independent of the structure of the telephone network, each subscriber of the video-telephone network must be assigned a separate video-telephone call number for the path search in the broadband network. In order that a subscriber does not have to dial two different numbers to set up a video-telephone call, each exchange (V1, V2) of the communication system includes a mapping circuit (ZS) which establishes for each video-telephone subscriber (TEA, TEB) a correspondence between his or her telephone call number and a video-telephone call number serving to set up calls in the video-telephone network. This video-telephone call number can be called up from the mapping circuit (ZS) via the telephone network (FN).