Communication system for electronic messages with a plurality of data processing devices and a data network for a data transmission of electronic messages between two data processing devices. Data of an electronic message includes an assignment data block, besides, image data, text data, audio data and the like, which includes specific assignments between particular data segments of said image, text or audio data, such that with the assignement data block interrelations between particular segments of the message can be transmitted in a simple manner and can be used for a subsequent display or reproduction of the message.