1. A method for monitoring virtual connections within a digital telecommunication network that is formed of exchanges, connected by transmission lines, operating in asynchronous transfer mode via which information transmitted in synchronous transfer mode is also switchable, wherein transmission monitoring cells, that contain a regular error-detecting code word and that may contain a sequence identifier as well as a particular about a length of an information cell block, are respectively allocated to information cell blocks to be transmitted, each of the monitoring cells having a header part and an information part and being allocated to a respective information cell block at an originating location of transmission links carrying the virtual connections, the error-detecting code word being formed using a totality of the information cell blocks, wherein an evaluation, on the basis whereof an information falsification is recognizable, respectively occurs at an end point of an appertaining transmission link by renewed formation of a further error-detecting code word and by comparison thereof to the regular error-detecting code word transmitted from the originating location, and wherein a message at least to the originating location of the appertaining transmission link is undertaken in case of a recognized information falsification, comprising the steps of: forming error-detecting code words at an access boundary of a respective exchange upon exclusive acquisition of information parts of information cells of information cell blocks; forming transition monitoring cells from said error-detecting code words and said information cells; transmitting said error-detecting code words through the respective exchange as a component part of said transition monitoring cells; evaluating said error-detecting code words at an exit boundary of the respective exchange and outputting an appertaining error message to a maintenance position responsible therefor given an information falsification that is thereby identified; before the information cell blocks pass the exit boundary, replacing the transition monitoring cells by newly formed transmission monitoring cells whose regular error-detecting code word respectively covers the entire, appertaining information cell block; and wherein the information cell block is thereby faultlessly transmitted over the respective virtual connection.