Abstract: A process is disclosed whereby each of a plurality of stations, transmitting messages segmented into multiple sequential packets, is able to access a transmission channel of a local communications network. A residual packet number is associated with each message representing the number of packets remaining in the message after the instant packet has been transmitted. The number of packet collisions on the transmission channel is reduced by employing a resolution phase, which may be divided into several time intervals. Stations transmit messages with certain residual packet numbers during predetermined time intervals of the resolution phase. A station transmits its next packet after the end of the ongoing transmission if its residual packet number is smaller than the residual packet number of the ongoing message transmission.