Abstract: Method of transferring, via a transmission medium comprising asynchronously time-division-multiplexed transmission channels, a data stream comprised of data cells. A monitoring apparatus at the beginning of the transmission medium stores, for each transmission channel, a counter position (variable) which, when a data cell arrives at the monitoring apparatus, is amended as a function of time which has elapsed from a reference time instant. Depending on the amended counter position and a threshold value, the data cell is granted or refused access to the downstream transmission medium. The reference time instant is determined by the monitoring apparatus completely or at least partly, independent of the time instant of the appearance of the data cells. A first option provides for the monitoring apparatus to shift the reference time instant in time in accordance with a fixed sequence schedule. According to a second option, the reference time instant is shifted in time in accordance with a fixed time schedule.