Abstract: Apparatus for monitoring a flow of ATM cells in which a measured value is calculated in all cases. A `leaky bucket` mechanism known for this purpose has too few degrees of freedom to be able to monitor the flow of cells accurately enough for it to be possible to deduce from cell flow variations whether a (temporary) cell rate increase is the consequence of an unavoidable variation induced by the transmission system or of an unduly high cell rate (which is in fact avoidable) on the part of the system users. The operation of the apparatus can be adjusted better to the cell flow characteristics if the measured value (CV.sub.n) is a function of a previously calculated reference arrival time (RAT.sub.n) and the actual arrival time (AT.sub.n) of the arriving cell. The reference arrival time is, in turn, a function of the reference arrival times (RAT.sub.n-p, RAT.sub.n-q, . . . ) of one or more preceding cells (n-p, n-q, . . . ) and of the actual arrival times (AT.sub.n-p, AT.sub.n-q, . . .