Abstract: The invention provides a method for resolving a data packet collision in a local network where a plurality of nodes which respectively comprise processors and terminal equipment utilize a single transmission line in accordance with a contention system.A contention phase is initiated unless a collision occurs. When a collision occurs, a resolution phase is initiated. The nodes which have been performing transmission immediately stop transmission. They discriminate their positions on the transmission line before a time interval (2.times.maximum transmission delay time interval) elapses from the start of transmission. If no signal is received by a given node from the left, the given node is regarded as the leftmost node among the conflicting nodes. The leftmost node immediately starts transmitting a packet. Other nodes except for the leftmost node stop retransmitting the packets. The nodes which have performed retransmission are stopped until the resolution phase is completed.