The system for managing messages transmitted in an interconnect network connecting blocks on a chip comprises agents linked by point-to-point links able to transmit, by static routing, messages comprising a priority information item quantified on N levels. The system comprises at least one agent initiating request messages to at least one recipient agent. A request message comprises a header and, where appropriate, content data. The system comprises means of generating a priority message, to a recipient agent, to which at least on request message has previously been transmitted with no response message received in return.