In ATM networks, digital data in ATM cells are sent to a destination node over more than one transmission link in round robin fashion. This is called inverse multiplexing. At connection start-up, the source node informs the destination node of the specific round robin fashion of the transmission links so that the ATM cells are reassembled in a proper sequential order. Inverse multiplexing control cells are used to communicate between the source node and destination node for connectivity testing of transmission links. Cell stuffing is also provided in one embodiment to accommodate non-synchronized links among transmission links. In a particular embodiment, two consecutive control cells indicate a stuffing cell. A start-up procedure is described when not all the transmission links are usable.