After the initiation of the offering of additional telephone paths or audible signals, the existing telephone connection is reswitched onto two subscriber inputs of a conference or offering device provided with the conference switching matrix array and arranged in a peripheral unit being reswitched by way of control devices and switching matrix arrays arranged in digital telephone switching systems. The two subscribers are connected via a preset conference switching matrix array. The additional telephone paths or audible signals are conducted to a further subscriber input of the conference or offering device with the assistance of the control devices and with the assistance of the switching matrix arrays and are designationally switched onto the existing connection in the conference or offering device via the conference switching matrix array. The method of the present invention serves for the realization of a subscriber's service features "offering" and "rapping" whose central functions are the offering of the third telephone path and the offering of audible offering signals onto an existing telephone connection or, respectively, the offering of audible rapping signals onto an existing telephone connection.
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