The invention discloses removal of ATM cells from an ATM communications device. A first algorithm is provided by means of which, with the exception of a first and a last ATM cell in a frame, all newly arriving cells in the frame are removed. A second algorithm is provided by means of which all the ATM cells in a frame, from a first cell to a last cell, are removed on arrival in a queue from the ATM communications device. At a start of a transmission process, a user indicates a maximum number of ATM cells per frame, and the ATM cells using the number are transmitted when the maximum number is exceeded, the associated frame is discarded or the first algorithm is used. The invention solves this problem by defining rules whose application results in this method now being used only to a very limited extent.