A method for the transmission of digital messages by the output terminals of a monitoring circuit which is integrated into a microprocessor, the digital messages being representative of first specific events which are dependent on the execution of a series of instructions by the microprocessor. The method includes transmitting the following signals to the monitoring circuit by dedicated access points, namely (i) a request signal for the sending of a message that is associated with a specific event from second specific events which are independent of the execution of the series of instructions by the microprocessor and (ii) a signal comprising characteristic data which are associated with the aforementioned specific event; forcing the monitoring circuit to read the request message and, if the resource management conditions are fulfilled, sending an acknowledgement message and storing said characteristic data signal and transmitting a digital message which is representative of the stored characteristic data signal.