Method, system, converter and switch for communication in asynchronous transmission mode (ATM) between a source end station (13) and a destination end station (14) by means of information cells and data cells following the information cells, the information cells representing a signalling message containing an information element (IE) which contains an indication of a requested kind of traffic contract (ATC) for, in accordance therewith, processing the data cells. When a kind of traffic contract requested from a switch of the system or from the destination end station is not supported, but a kind of traffic contract which is not more unfavorable than a kind of traffic contract requested by the source end station (13) is supported, the signalling message is converted, the requested kind of traffic contract being replaced by the other kind of traffic contract as the new requested kind of traffic contract, in such a way that eventually there is converted back to the kind of traffic contract supported by the destination end station (14), which is equal to the kind of traffic contract requested by the source station. After each conversion, the data cells of a traffic flow received are processed in accordance with the kind of traffic contract to which there is converted.