Method of managing priority during the transmission of a message, in an interconnections network comprising at least one transmission agent which comprises at least one input and at least one output, each input comprising a means of storage organized as a queue of messages. A message priority is assigned during the creation of the message, and a queue priority equal to the maximum of the priorities of the messages of the queue is assigned to at least one queue of messages of an input. A link priority is assigned to a link linking an output of a first transmission agent to an input of a second transmission agent, equal to the maximum of the priorities of the queues of messages of the inputs of said first agent comprising a first message destined for that output of said first agent which is coupled to said link, and the priority of the link is transmitted to that input of said second agent which is coupled to the link.